2010

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December
2010
Annual Report
National Center for Theoretical Sciences
I.
Words from the Director -----
1
II. Mathematics Division ---------
3
Report of the Division Head -------------------
4
Executive Committee Members ---------------
6
Academic Committee Members ---------------
7
Highlights of the Focus Programs -------------
8
Highlights of the Regional Programs --------- 58
Activities of Onsite Scientists ------------------ 68
Preprints ------------------------------------------- 83
Appendix ------------------------------------------ 92
I. Visiting Mathematicians -------------------- 92
II. Conference, Workshop, School &
Special Lecture -------------------------------111
III. Physics Division
--------------------119
Report of the Division Head -------------------120
Highlights of Programs ------------------------- 124
Focus Group & Working Group
Complex Systems ------------------------------ 124
Condensed Matter Physics --------------------131
Particles and Fields -----------------------------144
Interdisciplinary Fields ------------------------162
Initiative -------------------------------------------176
Research Activities of Individuals ------------183
Introducing New Members --------------------220
Annual Report
National Center for Theoretical Sciences
December 2010
Publisher:
Editors:
Wen-Ching Winnie Li
Mandy Chen ( Mathematics Division)
Sherry Pang(Physics Division)
Words from the Director
his is the s econd
year of phase three,
a six year project funded by
the National Science Council
(NSC). In late December
2009 NSC conducted a thorough
review of both mathematics
and physics divisions of our
center. The review committee
members were internationally
renowned scientists, mostly
from abroad. I am very
pleased to report that the
committee spoke highly of
the important role NCTS has
played, and contributions
NCTS has made in promoting theoretical research
as well as training young theorists in Taiwan.
They were very impressed by the achievements of
theoretical scientists in Taiwan. They also
offered some advices, which have led to certain
re-organizations in both divisions.
There have been important leadership changes
this year. In early January 2010, Professor ChungYu Mou of National Tsing Hua University
(NTHU) completed his term as the physics
division head. We are very grateful to him for his
selfless service, devotion, and leadership in the
past three years. His insightful advices were very
helpful and valuable to me. The new division
head of theoretical physics is Professor LingFong Li from Carnegie Mellon University.
Currently a Distinguished Chair Professor of the
Physics Department of NTHU, L-F. Li is an
expert in high energy physics. He has visited
NCTS frequently in the past, hence is very
familiar with the operations of our center. We are
very pleased to have someone of
Professor Li's calibre and statue to
lead the physics division.
The PI and Co-PI of Subproject
I in Taipei are Professor Wei-Shu
Hou from the Physics Department
of National Taiwan University
(NTU) and Professor ChuinChuan Chen from the Mathematics
Department of NTU, respectively.
The PI of Subproject II in Tainan is
Professor Yan-Tien Lu from the
Physics Department of National
Cheng Kung University; the
mathematics Co-PI of Subproject
II is Professor Ching-Hung Lam from the
Mathematics Institute of Academia Sinica.
International cooperation is a very important
mission of the center. This year we signed a new
MOU with Pohang Mathematics Institute (PMI),
Postech, Korea. NCTS and PMI started
cooperation in 2009 when I led 5 delegates from
Taiwan to attend a workshop at Postech. This year
11 Korean mathematicians visited NCTS and
attended two conferences. In Jan. and July 2011
some Taiwanese mathematicians will visit
Postech to attend activities there. The interaction
between physicists of the two countries began
much earlier when NCTS joined APCTP,
headquartered at Postech. This year, many
APCTP members attended a big conference in
theoretical physics held at NCTS. In addition,
NCTS is actively seeking more cooperation
opportunities with Russia and Germany.
The highlight at the center this year was the
visit by Professor Don Zagier, the Director of the
1 ‹‹- Words from the Director
Max Planck Institute of Mathematics in Germany.
During his visit Aug 1-11, Professor Zagier gave 4
lectures on "Modular Forms, Mock Theta
Functions and Black Holes", which attracted many
mathematicians and physicists. Promoting
interactions between mathematicians and
physicists is one of the missions of the center. Last
year there was the joint workshop in theoretical
sciences; this year it was Zagier's lectures; next
Words from the Director -›› 2
year there will be a bilateral Taiwan-France
conference on symplectic geometry and quantum
symmetries in mathematical physics.
Through collective efforts, the level of
theoretical research has been elevated
progressively. We are proud of our achievements
this year and look forward to a prosperous next
year.
Mathematics Division
Report of the Division Head
his is the second year of phase III of
NCTS, a six year project, funded by the
National Science Council (NSC). Thanks to the
collective efforts, the mathematics division
received high praises in last year's review
conducted by NSC. The review committee spoke
highly of the role NCTS has played in promoting
research and training future leaders in
mathematics in Taiwan. The members were very
impressed by the high quality research activities
conducted at NCTS and results obtained by people
involved with the NCTS programs.
I am happy to report that Professor ChingHung Lam of the Mathematics Institute, Academia
Sinica, has agreed to serve as the Mathematics
Co-PI at the Subproject II in Tainan since April
2010. Professor Lam was also appointed as an
adjunct professor at the National Cheng Kung
University. This will assure more smooth working
relationship with NCKU. The Mathematics Co-PI
at the Subproject I in Taipei has been Professor
Chiun-Chuan Chen of the National Taiwan
University since 2009.
2010 NCTS Distinguished Lecture Series were
delivered by Professor Don Zagier, the Director of
the Max Planck Institute in Mathematics in Bonn,
Germany and Professor of College de France in
Paris, France. During his visit Aug 1-11, 2010, he
gave 4 lectures on "Modular Forms, Mock Theta
Functions and Black Holes". His beautiful lectures
have attracted many mathematicians and
physicists.
In July 2010, the mathematics division of
NCTS signed an MOU with Pohang Mathematics
Institute (PMI) of Postech, Korea, to promote
international cooperation with Korean
mathematicians. Interactions between NCTS and
Report of the Division Head -›› 4
PMI began in 2009. This year 11 Korean number
theorists visited Taiwan. More interactions with
them are planned for next year. It is hoped that
contacts will extend to fields other than number
theory in the future. Special efforts are also being
made to establish cooperation programs with other
countries.
To carry out the NCTS tradition of nurturing
young mathematicians, Professor Jing Yu of
National Taiwan University led a group of number
theorists to visit Waseda University in Japan,
while I invited Taiwanese mathematicians to
speak in a conference I co-organized at CRM,
Montreal, Canada in March 2010. Next year I'll
lead a group of young number theorists to attend a
workshop at Postech, Korea. For conferences held
in Taiwan, we pay special attention to balance
domestic and international speakers. We have
continued the policy initiated last year to seek
foreign counterparts to actively support our
international conferences. This year the organizers
of the conference on PDE Models of Biological
Process, to be held December 13-17, successfully
secured funding from the National Science
Foundation in U.S.A.. This kind of co-sponsored
activities will enhance our international visibility
and statue, and we intend to continue this policy
whenever appropriate.
There are four new recipients of the Young
Theorists Award of NCTS in 2010. They are
Professor Jeng-Daw Yu of National Taiwan
University, specializing in arithmetic geometry
and number theory, Professor Jiun-Cheng Chen of
National Tsing Hua University in algebraic
geometry, Professor Ching-Lung Lin of National
Cheng Kung University in differential equations,
and Professor Jung-Chao Ban of National Dong
Hua University in dynamical systems. The
continuing recipient is Professor Nan-Kuo Ho of
National Tsing Hua University in symplectic
geometry. These recipients were selected from all
applicants by the Executive Committee based on
the rigorous evaluations by international experts.
It is a great pleasure to see so many outstanding
promising young researchers, which bodes well
for the future of mathematics in Taiwan.
Professor Kuo-Chang Chen of National Tsing
Hua University is named the second S. S. Chern
Fellow for his outstanding achievements in
celestial research in N body problem. This highest
honor endowed by NCTS is awarded to young
people with demonstrated exceptional talent and
ability in mathematical research. The selection
process is the same as the Young Theorists Award,
but the standard is much higher. Professor ChinLung Wang of National Taiwan University was
the first Chern Fellow.
We designed the "NCTS thematic year" by
allocating more resources to one subject area on
rotating basis. This year the theme is number
theory. The academic and executive committees
have agreed that the theme of 2010 will be
geometry, followed by applied mathematics in
2011. We look forward to lively and productive
years ahead!
5 ‹‹- Report of the Division Head
Executive Committee Members
Committees
Affiliation
Chiun-Chuan Chen
National Taiwan University
Liang-Chung Hsia
National Central University
Sze-Bi Hsu
National Tsing-Hua University
Ching-Hung Lam
Academia Sinica
Wen-Ching Winnie Li
National Center for Theoretical Sciences
Yuah-Chung Sheu
National Chiao Tung University
Chin-Lung Wang
National Taiwan University
Executive Committee Members -›› 6
Academic Committee Members
Committees
Affiliation
Gerard J. Chang
National Taiwan University
Jung-Kai Chen
National Taiwan University
Kuo-Chang Chen
National Tsing-Hua University
Shun-Jen Cheng
Academia Sinica
Liang-Chung Hsia
National Central University
Sze-Bi Hsu
National Tsing-Hua University
Ming-Chih Lai
National Chiao Tung University
Yng-Ing Lee
National Taiwan University
Tai-Chia Lin
National Taiwan University
Yuah-Chung Sheu
National Chiao Tung University
Chih-Wen Shih
National Chiao Tung University
Dong-Ho Tsai
National Tsing Hua University
Zhu Eugene Xia
National Cheng Kung University
Chia-Fu Yu
Academia Sinica
7 ‹‹- Academic Committee Members
Highlights of the Focus Programs
D.1 Algebraic Geometry
Coordinators: Jungkai Chen (National Taiwan University) and Ching-Lung Wang (National Taiwan University)
1. T
he long project of Chin-Lung Wang(NTU)
jointly with Yuan-Pin Lee (U. Utah) and HuiWen Lin(NTU) on quantum cohomology and
GW invariants is one of the main themes.
2. T
he birational geometry of higher dimensional
varieties circling around minimal model
program is another main topic.
he project on quantum cohomology keeps
producing many interesting results.
During the period, it is getting clear that one
might need to formulate the problem in larger
scale. Even though there are many technical
difficulties, the project keeps going in a good
pace.
The project of higher dimensional varieties has
turning its focus to dimension three, four or
higher. It is getting more complicated and difficult
to predict what to expect at this moment.
1-1 Local Algebraic Geometry Group
Jiun-Cheng Chen (NTHU), Jungkai Chen
(NTU), We-Yen Chuang (NTU), Tatsuki Hayama(
NTU), Hui-Wen Lin (NTU), Steven Lu* (UQAM/
NTU), Chin-Lung Wang (NTU), Eugene Xia
(NCKU) , Jeng-Daw Yu (NTU).
*Steven Lu from UQAM, Canada takes his
sabbatical leave to visit NTU for the academic
year 2010-2011 under the support of NSC.
Highlights of the Focus Programs -›› 8
1-2 Visitors
Y.P. Lee (Utah), Ican Cheltsov (Edinburgh,
UK), Miles Reid (Warwick, UK), V. Maillot (Paris
VI), Chen-Yu Chi , (Harvard)
2-1. Conference
The 3 rd Workshop on Higher Dimensional
Algebraic Geometry was held in NTU from Mar.
29 to Apr. 2, 2010. Invited speakers are either
well-established algebraic geometers or young
prospects. The organizers are Jungkai Chen,
Hélène Esnault, Eckart Viehweg, Chin-Lung
Wang.
The list of invited speakers is:
• Valery Alexeev (Univ. Georgia)
• Jungkai Alfred Chen (Nat'l Taiwan Univ.)
• Juan Cervino (Universität Duisburg-Essen)
• Andre Chatzistamatiou (Universität DuisburgEssen)
• Chen-Yu Chi (Harvard University)
• Hélène Esnault (Universität Duisburg-Essen)
• Georg Hein (Universität Duisburg-Essen)
• Stefan Kebekus (Universität Freiburg)
• R adu Laza (State University of New York,
Stony Brook)
• Mircea Mustata (University of Michgan, Ann
Arbor)
• Yukinobu Toda (IPMU, University of Tokyo)
• Huian-Hua Tseng (Ohio State University)
• Y
u-jong Tzeng (Stanford University)
• G erard van der Geer (Universiteit v a n
Amsterdam)
• Chin-Lung Wang (National Taiwan University)
• Takehiko Yasuda (Kagoshima University)
• Jeng-Daw Yu (National Taiwan University)
• De-Qi Zhang (National Univ. of Singapore)
We would like to emphasize that there are 6
Taiwanese speakers (Chen, Chi, Tseng, Tzeng,
Wang Yu). Two of them are organizers who are
relatively senior (Chen, Wang). Participants are
very impressed by the outstanding performance of
those four Taiwanse young algebraic geometers
(Chi, Tseng, Tzeng, Yu). This reflects the growth
of the group of algebraic geometry in Taiwan after
the consistent support of NCTS for the past ten
years. We are quite confident of the further
development of our group in the coming years
under the support of NCTS.
2-2 Seminars
The regular joint seminar with TIMS was
organized by Jungkai Chen and Chin-Lung Wang.
One of the main focuses of the seminar was on
recent breakthrough in higher dimensional
minimal model program. There are many more
improvements of presentation of the materials
developed by Birkar, Cascini, Hacon and
McKernan, such as Paun and Birkar’s work. Some
attempts to attack the problems of termination and
abundance was discussed in the seminar as well.
The other main focus was on the GromovWitten theory and quantum cohomology around
the joint project of Yuan-Pin Lee, Hui-Wen Lin
and Chin-Lung Wang.
There is also a regular student seminar
organized by Jungkai Chen. The participants
consist of NCTS research assistants and students
from NTU and some faculty members. The main
topic is on derived categories in birational
geometry. Some aspects of geometry of arc spaces
was discussed as well.
3. Accomplishments
Higher dimensional singularities and birational
geometry developed by Jungkai Chen(NTU) and
his coworkers Meng Chen(Fudan) and
Christopher Hacon(Utah, USA) keep making
significant progress.
a. J ungkai Chen and Mang Chen investigate some
further results on the theory of baskets in
dimension three. Together with their previous
results on threefolds (cf. [16,21,23]), an
ongoing project on geography of threefolds of
general type will be completed soon. This work
will improve some previous effective bound on
pluricanonical maps and canonical volumes
substantially.
b. J ungkai Chen and Christopher Hacon made a
progress on Ueno’s conjecture K and Iitaka’s
conjecture C. The conjecture K predicts that
varieties of Kodaira dimension zero consist of
products of Calabi-Yau varieties and abelain
varieties after suitable etale covering and
birational maps, in which the factorization is
realized by the canonical Albanese map. In
[27], they proved that the second part of
Ueno’s conjecture holds. They also find some
application to Iitaka’s conjecture C in the same
article.
(1) The long project of Chin-Lung Wang jointly
with Yuan-Pin Lee (U. Utah) and Hui-Wen Lin
(NTU) is continued and significant progress is
made. The analytic continuation of quantum
cohomology under a general ordinary flop
over a smooth base had received fundamental
progress during the summer visit of Lee to
NCTS, Hsinchu in 2008. Under joint support
by TIMS, Y.P. Lee visited NTU even often in
the last year. There are various important
results presented in [6,7,15,17,19,24,25]
respectively. The whole project is now
formulated in greater scale. It turns out that
investigation on higher genus GW invariants is
the essential and inevitable. This was started in
[17] and further pursued through an attempt to
understand and extend the fundamental works
by BCOV (Bershdsky-Cecotti-Oguri-Vafa).
(2) Investigation of MMP from the analytic side
was started in early 2009 following a course,
delivered by Wang at NTU in the fall of 2008,
on Siu’s theory in complex geometry with
9 ‹‹- Highlights of the Focus Programs
focus on the general case of invariance of
pluri-genera. With his student Sz-sheng Wang,
C.-L. Wang wrote the version of [26] on
extension of pluri-canonical forms from the
viewpoint of developing a multiple version of
the Ohsawa-Takegoshi extension theorem.
After a visit of C.Y Chi, they manage to work
out the important results in their preprint (cf.
[26]).
(3) There are some application of the technique in
Deligne-Mumford stack to the birational
geometry of higher dimensional geometry
developed by J.C Chen and his collaborator H.
H. Tseng. Previously, they obtained Cone
Theorem via Deligne-Mumford stacks (cf.
[12]). Chen and Tseng was the first groups to
use the notion of stacky point in studying
birational geometry. By using stacky curves to
obtain the sharp bound (n+1) for anticanonical degree. They used this technique to
obtained a characterization of projective
spaces. They can now use similar technique to
study Fano varieties with large pseudo-index
(cf. [20]).
4. P ublications (year 2008, 2009 and
preprints)
[1] J .A. Chen, C. D. Hacon, An example of a
surface of general type with pg=q=2 and
KX2=5 , Pacific Jour. Math., 233, (2006), 219228.
[2] J . A. Chen, M. Chen, D.Q. Zhang, The
5-canonical system on 3-folds of general type ,
J. Reine Angew. Math., 603, (2007), 165-181.
arXiv 0512617
[3] J .A. Chen, C.D. Hacon, Pluricanonical
systems on irregular 3-folds of general type ,
Math. Zeit, 255, (2007), 343-355.
[4] J. A. Chen, M. Chen, On projective threefolds
of general type. Elec. Res . Announc. Math.
Sci., 14, (2007), 69-73.
[5] J . C C h e n a n d H . H . Ts e n g N o t e o n
characterizations of projective spaces , Comm.
in Algebra, Volume 35 (2007), Issue 11, 38083819
[6] H .W. Lin, Quantum invariance of simple
flops , Proceedings of the forth International
Congress for Chinese Mathematicians, Higher
Education Press 2007.
Highlights of the Focus Programs -›› 10
[7] B
. Fu and C.L. Wang; Motivic and quantum
invariance under stratified Mukai flops , J.
Differential Geometry 80 (2008), no.2, 261–
280
[8] F. Campana, J. A. Chen, T. Peternell, On
strictly nef divisors , Math. Ann., 342, (2008),
565-585.
[9] J. A. Chen, M. Chen, An optimal boundedness
on weak $\bQ$-Fano threefolds , Adv. Math.,
219, (2008), 2086-2104.
[10] J.A. Chen, M. Chen, The canonical volume
of threefolds of general type with X<1 , J.
London Math. Soc., 78, (2008), 693-706.
[11] J .C. Chen and H. H. Tseng A note on
derived McKay correspondence ,
Mathematical Research Letters, Volume 15
(2008), Issue 3, 435-445
[12] J. C. Chen and H. H. Tseng Cone Theorem
via Deligne-Mumford stacks , Mathematische
Annalen, Volume 345 (2009), no. 3, 525-545
[13] J. A. Chen, C. D. Hacon, On the geography
of threefolds of general type , J. Alg., 321,
(2009), 2500-2507.
[14] J . A . C h e n , C . D . H a c o n , On Ueno’s
Conjecture K, Math. Ann ., 345, (2009), 287296
[15] C.L. Wang, Quantum invariance under flop
transitions , in “Proceeding of Geometric
Analysis: Present and Future, a conference in
honor of Professor Shing-Tung Yau’s 60th
birthday (Harvard University, Cambridge
2008)”, International Press 2009.
[16] J . A. Chen, M. Chen, Explicit birational
geometry of threefolds of general type , I,
Ann. Sci. École Norm. Sup (43) 2010, 365394
[17] Y.P. Lee, H.W. Lin and C.L. Wang; Flops,
motives and invariance of quantum rings ,
Annals of Mathematics, 172 (2010), no.1,
243-290
[18] C.S. Lin and C.L. Wang; Elliptic functions,
Green functions and the mean field
equations on tori , Annals of Mathematics,
172 (2010), no.2, 911-954
[19] H .W. Lin, Quantum invariance under P1
flops of type (k + 2, k) , Proceeding of 2008
East-Asia Conference in Algebraic
Geometry, Advanced Studies in Pure
Mathematics, 60 (2010), 271-300.
[20] J . C. Chen On Fano varieties with large
pseudo-index , Proceeding of 2008 East-Asia
C o n f e r e n c e i n A l g e b r a i c G e o m e t r y,
Advanced Studies in Pure Mathematics, 60
(2010)
[21] J . A. Chen, M. Chen, Explicit birational
geometry of threefolds of general type, II,
Jour. Diff. Geom, to appear.
[22] J. A. Chen, C. D. Hacon, Factoring 3-fold
flips and divisorial contractions to curves .
Jour. Reine Angew. Math., to appear
[23] J . J . C h e n , J . A . C h e n , M . C h e n , On
weighted complete intersections . J. Alg.
Geom, to appear
[24] Y
. Iwao, Y.P. Lee, H.W. Lin and C.L. Wang;
Invariance of Gromov-Witten theory under
simple flops , to appear in J. Reine. Angew.
Math. 29 pages
[25] Y.P. Lee, H.W. Lin, C.L. Wang, Invariance of
quantum rings under ordinary flops , preprint
[26] C.Y. Chi, C.L. Wang, S.S. Wang, Extensions
of multiply twisted pluri-canonical forms ,
preprint 2010.
[27] J. A. Chen, C. D. Hacon, Kodaira dimension
of irregular varieties , preprint.
D. 2 Discrete Mathematics
Coordinators: Gerard Jennhwa Chang (National Taiwan University) and Xuding Zhu (National Sun Yat Sen University)
iscrete mathematics is an active research
area in Taiwan. In the program of discrete
mathematics supported by the NCTS, we organize
various activities to broaden the spectrum of
research in Taiwan, to promote international
collaborations, and to provide training and
opportunities for young scholars and students. The
activities we have organized and related results
are as follows.
D.2.2 Workshops
D.2.1 Regular weekly seminar
• P
avol Hell, Variants of interval graphs.
• Andre Raspaud, Acyclic choosability of planar
graphs.
• Mickael Montassier, Decomposition of sparse
graphs, with application to game coloring
number.
• Weifan Wang, Linear coloring of graphs.
• Paul Dorbec, Power domination in graphs.
• Zdenek Dvorak, Sizes of embedded coloringcritical graphs.
• Matej Stehlik, Extensions of Gallai's theorem on
colour-critical graphs.
There is a weekly seminar every Tuesday from
13:30 to 16:30 in the National Taiwan University,
and a weekly seminar every Tuesday from 11:00
to 12:00 in the National Sun Yat-sen University.
They are platform for the center members,
visitors, post doctoral fellows and students to
share their research experiences. The contents of
the seminars could be talks on previous results as
well as current idea for a research topic.
There is a two-day workshop on Graph Theory
in March 19-20 of 2010 held at the Department of
Applied Mathematics, National Sun Yat-sen
University. The theme of this workshop is on
graph coloring. All eleven speakers, from Canada,
Czech Republic, France, mainland China and
Taiwan, are invited. The speakers and their topics
are as follows. The workshop attracted about
eighty participants.
11 ‹‹- Highlights of the Focus Programs
• H
ong-Gwa Yeh, The nullity and maximum
nullity of a graph.
• Hsin-Hao Lai, Acyclic list edge colouring of
planar graphs.
• L i - D a To n g , B l o c k i n g a n d c o l o r i n g i n
interconnection networks.
• Xuding Zhu, The nine dragon tree conjectures.
D.2.3 Hosting aboard visitors
The visitors from aboard in this year are as
follows.
• P
atrice Ossona de Mendez, Ecole des Hautes
Etudes en Sciences Sociales, Paris, France,
2010/02/06~2010/03/05.
• Shinya Fujita (Japan), 2010/02/24~2010/03/09.
• Andre Raspaud, Bordeaux University I, France,
2010/03/05~2010/03/25.
• M ickael Montassier, Bordeaux University I,
France, 2010/03/05~2010/03/25.
• Z denek Dvorak, Charles Univeersity, Czech
Republic, 2010/03/06~2010/03/21.
• Paul Dorbec, Bordeaux University I, France,
2010/03/07~2010/03/25.
• Pavol Hell, Simon Fraser University, Canada,
2010/03/09~2010/04/07.
• Weifan Wang, Zhejiang Normal University,
China, 2010/03/17~2010/08/18.
• L eonardo Sampaio Roc, INRIA, Spphia
Antipolis, France, 2010/07/15~2010/08/14.
• N athann Cohen, INRIA, Spphia Antipolis,
France, 2010/7/15~2010/08/14.
• WenXing Zhu, DIMACS, Fuzhou University,
2010/08/25~2010/08/29.
• G enghua Fan, DIMACS, Fuzhou University,
2010/08/25~2010/08/29.
• M inhua He, DIMACS, Fuzhou University,
2010/08/25~2010/08/29.
• Chuixiang Zhou, DIMACS, Fuzhou University,
2010/08/25~2010/08/29.
• R uofan Liu, DIMACS, Fuzhou University,
2010/08/25~2010/08/29.
• A n Chang, DIMACS, Fuzhou University,
2010/08/25~2010/08/29.
• D aqing Yang, DIMACS, Fuzhou University,
2010/08/25~2010/08/29.
• JianFeng Hou, DIMACS, Fuzhou University,
2010/08/25~2010/08/29.
Highlights of the Focus Programs -›› 12
• X
ue-Wen Bao, DIMACS, Fuzhou University,
2010/08/25~2010/08/29.
• Wenling Huang,University of Hamburg,
Germany, 2010/09/03~2010/09/30.
Some of them also take the chance of visiting
NCTS to visit other institutions in Taiwan. For
instance, Patrice Ossona de Mendez and Weifan
Wang also visited Institute of Mathematics,
Academia Sinica. The visitors have close
discussions with the Center members. Some join
work are done during their visiting, as will be
described below.
D.2.4 Research results
In this year, the research of the group concerns
several aspects of graph theory. Graph colouring
and graph labeling have always been a main area
of our research. There are problems in this area
that we have been working on for a long time.
1. Total coloring. Using the discharging
method, we obtained several interesting results on
total chromatic numbers and their choosablity
versions as follows: (1) Every planar graph with
maximum degree Δ≦8 is 11-totally choosable. (2)
If G is a 5-cycle-free planar graph with maximum
degree Δ≧8, then χ"_l(G) = Δ+1. (3) If G is a
graph with maximum degree Δ = 4 and maximum
average degree mad(G)<3, then G is 5-totally
choosable. (4) If G is a graph with maximum
degree Δ = 3 and maximum average degree
mad(G)<9/4, then G is 4-totally choosable. (5) If
G is a graph with maximum degree Δ = 4 and
maximum average degree mad(G)<10/3, then G is
6-totally choosable. (6) If G is a planar graph with
maximum degree Δ = 4 with no triangle adjacent
with a cycle of length at most five, then G is
7-totally choosable. (7) Suppose G is a planar
graph with maximum degree 7. If every vertex v
has an integer k_v □ {3;4;5;6} such that v is not in
any k_v-cycle, then χ"(G) = 8. (8) Let G be a
planar graph with maximum degree Δ≦6. If G
contains no cycles of length 4 and no incident
triangles, then G is 7-totally choosable. (9) Let G
be a planar graph with maximum degree Δ≦5. If
G contains no cycle of length from 4 to k and no
triangles at distance less than d_Δ, then G is
6-totally choosable for (k;d_Δ) = (5;2); (6;1);
(7;0). (10) Let G be a planar graph with maximum
degree Δ≦4. If G contains no cycle of length
from 4 to k and no triangles at distance less than
d_Δ, then G is 5-totally choosable for (k;d_Δ) =
(6;3); (7;2); (10;1).
2. Generalization of rainbow domination.
Previous result on the rainbow domination
problem is an algorithm on trees. We extend this
to k-rainbow domination. We first show that the
k-rainbow domination number of a strongly
chordal graph is equal to its weak {k}-domination
number. Using this we are able to give an
algorithm for the k-rainbow domination on block
graphs. Notice that strongly chordal graphs
include block graphs, which in turn include trees.
3. Generalization of power domination. We
introduce k-power domination as a generalization
of power domination (with k = 1) and the usual
domination (with k = 0). We prove that the
problem is NP-complete even for bipartite graphs
or chordal graphs; and then give a linear algorithm
for the problem in trees. We also prove that for a
connected graph G of order n≧k+2 its k-power
domination number is at most n/(k+2) and for a
connected claw-free graph G of order n≧k+3 its
k-power domination number is at most n/(k+3).
4. Strong chromatic index. The strong
chromatic index of a graph is the least number of
sets that partition the edge set such that each part
is an induced matching. Most previous upper
bound for the strong chromatic number of a graph
is square of its maximum degree. We prove that If
G is 2-degenerate (respectively, chordaless), then
its strong chromatic index is at most 10Δ−10
Respectively, 8Δ−6).
5. Thue choice number of trees are
unbounded. Thue Theorem is a classical result
which is viewed as the starting point of Formal
Language Theory or Automata Theory - these are
fundaments of Computer Science. Thue theorem
is easy to state and understand: there is an infinite
sequence S 1S 2S 3⋯ in three symbols, say 0,1,2,
(i.e., S i {0,1,2}) such that any two adjacent
blocks are distinct, i.e., for any i and n,
S iS i+1⋯S i+n+1 ≠ S i+nS i+n+1⋯S i+2n-1. The Thue choice
number of a graph asks the following question:
What is the smallest integer k for which the
following holds: If each vertex v is given a set
L(v) of k colours, then there is a colouring c of the
vertices of G so that c(v) belongs to L(v) for each
v, and for any path P of G, any two adjacent
blocks of colour sequence on this path are distinct.
Last year, we proved that the Thue choice number
of a path is at most 4. We asked the question
whether trees have bounded Thue choice number.
This year, we proved that the answer is no. This is
a joint work with three French mathematicians.
6. Entire colouring of plane graphs. We
proved that every simple plane graph has entire
chromatic number at most Δ+4, which is a more
than 30 year old conjecture.
7. Fractional chroamtic number of product
of graphs. We proved that the fractional
chromatic number of the categorical product is
equal to the minimum of the fractional chromatic
numbers of the factor graphs. This is the fractional
version of Hedetniemi’s conjecture. As a
consequence of this result, we proved Burr-ErdosLovasz conjecture, which is also more than 30
old.
8. On line list coloring of graphs. This is a
concept introduced not long time ago. We worked
on this concept last year, and proved that graphs
of chromatic number k and with n vertices has
on-line choosability at most k ln (n). This year, we
continued resarch in this area. We proposed
on-line version of Ohba’s conjecture and verified
some special cases. The proofs us polynomial
method. Some of the techniques used in the proof
are due to Tsai-Lien Wong and Po-Yi Huang,
which are interesting and might be useful
elsewhere.
9. Orientation of graphs. The study of
orientations of graphs is widely studied in graph
theory. An acyclic orientation of a graph is also a
useful tool for the investigation of structure and
property in graph theory; such as, cover graphs
and circular chromatic numbers. First, we study
the relations among dmin(G), the circular chromatic
numbers and fully orientable graphs. Second, we
discuss geodesic sets, hull sets, and convex sets in
the orientations of graphs.
13 ‹‹- Highlights of the Focus Programs
∍
10. Nonblocking problems of networks. We
find the necessary and sufficient conditions of the
rearrangeability, multi-cast rearrangeability and
the multirate rearrangeability in Banyan-type
networks with crosstalk constrains by graph
coloring method, and investigate related problems.
[11]
[12]
[13]
D.2.5 Publications
[1] W
.-H. Lin and G. J. Chang, Equitable
colorings of Kronecker products of graphs,
Disc. Appl. Math. 158 (2010), 1816-1826.
[2] G. J. Chang, J. Hou and N. Roussel, On the
total choosability of planar graphs and of
sparse graphs, Inform. Proc. Letters 110
(2010), 849-853.
[3] L.-H. Huang, G. J. Chang and H.-G. Yeh, A
note on universally optimal matrices and field
independence of the minimum rank of a
graph, Linear Algebra Appl. 433 (2010), 585594.
[4] L.-H. Huang, G. J. Chang and H.-G. Yeh, On
minimum rank and zero forcing sets of a
graph, Linear Algebra Appl. 432 (2010),
2961-2973.
[5] G . J. Chang, J. Wu and X. Zhu, Rainbow
domination on trees, Disc. Appl. Math. 158
(2010), 8-12.
[6] G. J. Chang, L.-H. Huang and H.-G. Yeh, A
characterization of graphs with rank 4, Linear
Algebra Appl.(accepted).
[7] Y. Z h a o a n d G . J . C h a n g , We i g h t e d
competition numbers of some graphs, Ars
Comb.(accepted).
[8] B .-J. Li and G. J. Chang, The competition
number of a graph with exactly two holes, J.
Combin. Optim.(accepted).
[9] G. J. Chang, C. Lu, J. Wu and R. Yu, Vertexcoloring edge-weightings of graphs, Taiwnese
J. Math.(accepted).
[10] C.-C. Lin, G. J. Chang and G.-H. Chen, The
degree-preserving spanning tree problem in
Highlights of the Focus Programs -›› 14
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
strongly chordal and directed path graphs,
Networks (accepted).
W.-H. Lin and G. J. Chang, Resource-sharing
systems and hypergraph colorings, J.
Combin. Optim.(accepted).
G. J. Chang, Near automorphisms of paths,
J. Graph Theory (accepted).
G . J. Chang and C. Lu, The L(2,1)-Flabeling problem of graphs, Taiwanese J.
Math. (accepted).
M. Montassier, A. Pecher, A. Raspaud, D. B.
West and X. Zhu, Decomposition of sparse
graphs with application to game coloring
number, Disc. Math. 310 (2010), 1520-1523.
L . C a i a n d W. Wa n g a n d X . Z h u ,
Choosability of toroidal graphs without short
cycles. J. Graph Theory 65 (2010).
N . Roussel and X. Zhu, Total coloring of
planar graphs of maximum degree eight,
Infor.Proc.Letters 110 (2010), 321-324.
H.-H., K.-W. Lih, C.-Y. Lin and L.-D. Tong,
When is the direct product of generalized
Mycielski graphs a cover graph, Ars
Combin. (accepted).
Y.-P. Chen, Y.-M. Huang and L.-D. Tong,
Rearrangeable nonblocking optical
interconnection network fabrics with
crosstalk constraints, IEEE/ACM Trans.
Networking (accepted).
W. Lin, D. Liu and X. Zhu, Multi-colouring
of Mycielski graphs, J. Graph Theory
(accepted).
W. Lin and X. Zhu, Game circular colouring
of Graphs, Disc. Math. (acceptd).
L. Esperet and X. Zhu, Game colouring of
the square of Graphs, Disc. Math. (accepted).
L . Esperet, M. Montassier and X. Zhu,
Adaptable list colouring of planar Graphs, J.
Graph Theory (accepted).
X . Zhu, Bipartite density of triangle free
subcubic graphs, Disc. Applied Math.
(accepted).
D.3 Dynamical System
Coordinators: K
uo-Chang Chen (National Tsing-Hua University), Cheng-Hsiung Hsu (National Central University),
Chih-Wen Shih (National Chiao Tung University)
he primary investigators of this focus
program are Kuo-Chang Chen (NTHU),
Jonq Juang (NCTU), Ming-Chia Li (NCTU),
Song-Sun Lin (NCTU), Chih-Wen Shih (NCTU),
Cheng-Hsiung Hsu (NCU)
Coordinators: Kuo-Chang Chen, ChengHsiung Hsu, Chih-Wen Shih
The other investigators include Jung-Chao Ban
(NDHU), Chang-Yuan Cheng (NPUE), Yi-Chuan
Chen (Academia Sinica), Wen-Chiao Chen
(CCUT), Shyan-Shiou Chen (NTNU), Bau-Sen
Du (Academia Sinica), Jin-Long Li ((NHCTC),
Ken Palmer (NTU), Jun-Hsiung Hsia (NTU),
Chen-Chang Peng (NCU), Shih-Feng Shieh
(NTNU), Li-Chin Yeh (NHCTC), Je-Chiang Tsai
(NCCU), Ting-Hui Yang (Tamkang), Tzi-Sheng
Yang (Tonghai), Suh-Yuh Yang (NCU)
Dynamical System is one of the major and
classical research areas in mathematics and
mathematical science. The discipline traces back
to Newton, Poincare, and Birkhoff. Current
interesting research topics in the field contain the
ones of classical origin: celestial mechanics,
Hamiltonian systems, the ones developed since
the sixties: chaotic dynamics and ergodic theory,
and the ones that attract increasing attention:
random dynamical systems. In addition to the
theoretical side, the application of dynamical
system is closely linked to the nonlinear dynamics
in Physics, both historically and contemporarily.
The range of applications crosses from physics,
biology, information science, engineering, to
economy and finance. There are more than
twenty active researchers in dynamical systems in
Taiwan. Their research topics include n-body
problem, homoclinic orbits, entropy, delayed
equation, chaotic saddle, synchronization, multidimensional perturbation, heterodimensional
cycles, noisy oscillators, anti-integrable systems,
geometric singular perturbation, monotone
dynamics, traveling waves, lattice dynamical
systems, and chaotic attractors. Regular seminars
have been held at a weekly base with talks given
by visiting scholars, and local researchers.
Summer school in dynamical systems was
arranged with focus on specific topic.
International conference or workshop is organized
every year here in NCTS. Some mini courses are
arranged in the workshops. These activities
broaden the spectrum of current research in
Ta i w a n , p r o m o t e t h e c o l l a b o r a t i o n w i t h
international scholars, and enhance the training of
graduate students. Both individual and group
researchers have delivered significant works in the
past few years. We also have joint activities with
the topical programs of mathematical biology and
scientific computation on some applications and
computational aspects of dynamical systems. The
activities this year are listed below.
D.3.1 Conference and Workshop
NCTS/CMMSC Dynamics Day A Workshop on
Dynamics for Coupled Systems, January 12, 2010
Organizers: J onq Juang (NCTU)
Ming-Chia Li (NCTU)
Wen-Wei Lin (NCTU)
Chih-Wen Shih (NCTU)
Invited Speakers:
• C
hi Keung Chan 陳志強 (Physics, Academia
Sinica)
15 ‹‹- Highlights of the Focus Programs
• Y
ing-Cheng Lai 來穎誠 (EE, Arizona State
Univ.), 2 talks
• Chu-Pin Lo 羅主斌 (Applied Math, Providence
Univ.)
• T s u n g-L u n g Ts a i 蔡宗龍 (M a t h e m a t i c s,
National Changhua Univ of Education)
• Feng-Sheng Tsai 蔡豐聲 (Mathematics, NTNU)
• Yu-Hao Liang 梁育豪 (Applied Math, NCTU)
• Jui-Pin Tseng 曾睿彬 (Applied Math, NCTU)
2010 NCTS Workshop on Calculus of Variations
and Related Topics, May 6-8, 2010
Introduction: The CTS Workshop on Calculus of
Variations and Related Topics will be held at the
National Center for Theoretical Sciences on May
6-8, 2010. Calculus of variations plays an
important role in the study of partial differential
equations, differential geometry, and dynamical
system, but there were few activities in Taiwan in
recent years which focus on this topic. The aim of
this mini workshop is to bring together leading
experts from overseas and domestic researchers
from related fields, and to provide a forum for
discussion over recent and prospective advances.
The workshop consists of three mini-courses and
several hour talks.
Invited Speakers:
•
•
•
•
•
•
•
•
•
•
•
•
Chiun-Chuan Chen (Nat'l Taiwan Univ., Taiwan)
Jann-Long Chern (Nat'l Central Univ., Taiwan)
Marc Chaperon (Universite Paris VII, France)
J ong-Shenq Guo (National Taiwan Normal
University, Taiwan)
Xijun Hu (Shandong University, China)
Shuichi Jimbo (Hokkaido University, Japan)
C hun-Chi Lin (National Taiwan Normal
University, Taiwan)
C hun-Kong Law (National Sun Yat-Sen
University, Taiwan)
Tai-Chia Lin (Nat'l Taiwan Univ., Taiwan)
Yiming Long (Nankai University, China) mini
course
Eric Séré (Universite Paris-Dauphine, France)
mini course
Vittorio Coti Zelati (University of Napoli, Italy)
mini course
Highlights of the Focus Programs -›› 16
Organizers:
• C
hao-Nien Chen (National Changhua
University of Education, Taiwan)
• Kuo-Chang Chen (Nat'l Tsing Hua Univ., Taiwan)
2010 NCTS Workshop on Dynamical Systems,
May 12-15, 2010
Introduction: The 2010 NCTS Workshop on
Dynamical Systems will be held at the National
Center for Theoretical Sciences on May 12-15,
2010.
The aim of this annual workshop is to bring
together active researchers from various fields of
dynamical systems, and discuss recent and
prospective advances in related areas. This year
we have arranged lectures and talks related to
ergodic theory, Hamiltonian systems, invariant
manifolds, and random dynamical systems. The
workshop will include four mini courses, several
invited talks and contributed talks.
Invited Speakers:
• J ung-Chao Ban (Nat'l Dong Hwa Univ., Taiwan)
• A lain Chenciner (Universite Paris VII and
IMCCE, France) mini course
• Marc Chaperon (Universite Paris VII, France)
mini course
• Shui-Nee Chow (Georgia Tech, USA)
• S hyan-Shiou Chen (National Taiwan Normal
University, Taiwan)
• Yi-Chiuan Chen (Academia Sinica, Taiwan)
• B o Deng (University of Nebraska-Lincoln,
USA)
• Xijun Hu (Shandong University, China)
• Ming-Chia Li (Nat'l Chiao Tung Univ., Taiwan)
• Bing Li (National Taiwan University, Taiwan)
• S hanzhong Sun (Capital Normal University,
China)
• T s u n g - L u n g Ts a i ( N a t i o n a l C h a n g h u a
University of Education, Taiwan)
• Claude Viterbo (Ecole Polytechnique, France)
mini course
• Qiu-dong Wang (University of Arizona, USA)
mini course
• Dongmei Xiao (Shanghai Jiao Tong University,
China)
• T
zi-Sheng Yang (Tung-Hai University, Taiwan)
• Haumin Zhou (Georgia Tech, USA)
• X iaoqiang Zhao (Memorial University of
Newfoundland, Canada)
Contributed talks:
• Wen-Guei Hu (Nat'l Chiao Tung Univ., Taiwan)
• Chi-Ru Yang (Nat'l Chiao Tung Univ., Taiwan)
Organizers:
• K
uo-Chang Chen (Tsing-Hua University)
• Cheng-Hsiung Hsu (Central University)
• Chih-Wen Shih (Chiao-Tung University)
D.3.2 Courses and Seminars
NCTS and NTHU-CMS Minicourse on
Compensated Compactness Method
Speaker: Prof. Tianhong Li 李天虹 教授
(Academy of Mathematics and Systems
Science, Chinese Academy of Sciences) Lecture 1: Introduction to Compensated
Compactness Method
Date: 1:30-3:00PM, Thursday, April 22
Lecture 2: The Riemann problem
Date: 1:30-3:00PM, Thursday, April 29
Lecture 3: The weak entropy
Date: 1:30-3:00PM, Monday, May 10
Lecture 4: Approximate solutions
Date: 1:30-3:00PM, Thursday, May 20
Lecture 5: Applications to System of Isentropic
Gas Dynamics
Date: 1:30-3:00PM, Thursday, June 3
NCTS Summer Course on Dynamical
Systems--Measures and Computations for
Dynamical Systems
Instructors:
• Prof. Jung Chao Ban (Nat’l Dong Hwa Univ.)
• Prof. Yun Zhao (SooChow Univ.)
• Prof. Wen-Chiao Cheng (Chinese Culture Univ.)
• Prof. Shu-Ming Chang (Nat’l Chiao Tung Univ.)
Dates of Course and Student Seminar:
7/6-8/26 Tuesdays and Thursdays from 2:00-4:00 pm
This summer course is intended for graduate
students and advanced undergraduate students
who are interested in dynamical systems. Students
are expected to have some basic knowledge about
measure theory and differential equations.
There will be three topics on measure theoretic
aspects of dynamical systems delivered by three
Instructors working in related fields, plus a topic
related to computational dynamics.
Topics to be covered include:
1. Measures in dynamical systems
(Jung Chao Ban, Nat’l Dong Hwa Univ.)
2. Measure-preserving transformations
(Yun Zhao, SooChow Univ.)
3. Measure-theoretic entropy
(Wen-Chiao Cheng, Chinese Culture Univ.)
4. Computational dynamical systems
(Shu-Ming Chang, Nat’l Chiao Tung Univ.)
References:
(1) P
eter Walters, An Introduction to Ergodic
theory, Cambridge University Press, 2000.
(2) K arl Peterson, Ergodic theory, Cambridge
University Press, 1983.
Prerequisite: Real Analysis
There will be several assignments for this
summer course. Students signed up for the asses
and supported classes and supported by the CTS
are required to present assigned materials or
problems during the student seminar. Details will
be available during the first week of classes. 2010 NCTS Course on Dynamical Systems-Countable Markov Systems and Phase
Transition Dynamics
Instructor: Prof. Jung-Chao Ban 班榮超 (NDHU)
Time: 9/24-12/3, Friday, from 10:00am to
12:00pm (10 Lectures)
The study of countable Markov systems
becomes a popular topic recently since for a
hyperbolic system, the well-known result shows
that it always admits a finite Markov partition, and
the investigation of statistic properties relates to
the study of the finite Markov system which lifts
the original one. However, the study of the nonuniformly hyperbolic dynamical system is more
subtle, the main reason is that it cannot conjugate
17 ‹‹- Highlights of the Focus Programs
to a finite symbols dynamical system but infinite
one instead. The main difference between finite
and infinite Markov systems is the phase
transition phenomena, To be precise, the famous
result presents that there always exists an unique
equilibrium measure for finite system, however, it
is no longer true for infinite systems, i.e., there
exists more than two equilibrium measures for
infinite dynamical system. So many interesting
systems, e.g., the Gauss map, Manneville-Pomeau
transformation and EMR transformation are
infinite dynamical systems.
We divide the lecture into two parts, in the first
part (around five weeks) some basic knowledge of
ergodic theory will be introduced in preparation
for the study of infinite systems. And we focus on
the recent development of the countable symbolic
system in the rest of this lecture, which includes
the finite approximation theory, variational
principle, Perron-Frobenius operator and phase
transition dynamics.
Prerequisite: Real analysis and some basic
knowledge of dynamical systems.
References:
(1) J . Aaronson: An introduction to infinite
Ergodic Theory, Math. Surv. and Mono. 50
(1997), AMS.
(2) B . P. Kitchens, Symbolic Dynamics: One
Sided, Two Sided and Countable State
Markov Shifts (Universitext). Springer
(1998).
(3) O . Sarig: Thermodynamic Formalism for
Countable Markov Shifts. Ergod. Th. Dynam.
Sys. 19 (1999), 1565-1593.
(4) O. Sarig: Thermodynamic formalism for null
recurrent potentials. Israel J. Math. 121
(2001), 285-311.
(5) P. Walters, An Introduction to Ergodic theory,
Cambridge University Press (2000).
2010 NCTS & CMMSC(NCTU) Seminar on
Dynamical Systems
(1) Speaker: Professor Wen-Xin Qin
(Suzhou Univ, China)
Time: PM 2:00-3:00, Tuesday, Jan. 26, 2010
Topic: M
onotonicity in the Frenkel-Kontorova
Model
(2) Speaker: Dr. Bing Li
(National Taiwan University)
Highlights of the Focus Programs -›› 18
Time: March 19, 2010
Topic: R ecurrence and Hitting Problems in
Dynamical Systems
2010 NCTS Seminar on Dynamical Systems
(1) Speaker: M
r. Chun-Hsien Hsiao (Ph D. NTHU)
Time: 11:10am-12:00pm, Fri., April 30, 2010
Topic: On Convex and Concave Central
Configurations (2) Speaker: D
r. Chi-Hua Chan (NTHU)
Time: PM 1:30-3:00, Friday, Oct. 15, 2010
Topic: S o m e E i g e n v a l u e P r o b l e m s f o r
Vectorial Sturm-Liouville Equations
with Eigenparameter Dependent
Boundary Conditions
2010 NCTS & CMMSC Joint Seminar on
Soft Matter Speaker: D
r. Yeng-Long Chen 陳彥龍
(Institute of Physics, Academia
Sinica)
Time: AM 10:10-12:00, Wed., June 9, 2010
Topic: P o l y m e r D y n a m i c s : f r o m S i n g l e
Molecule to Melt
2010 NCTS Seminar on Dynamical Systems
& Mathematical Biology
Speaker: P
rofessor LieJune Shiau
(University of Houston, Clear Lake)
Time: PM 3:30, Friday, July 2, 2010
Topic: Oscillations in An Adaptive Neuronal
Model
D.3.3 T he accomplished and the
anticipations
[1] J .-C. Ban and C.-H. Chang "Factor, Diamond
and Density of Pressure" Proc. Amer. Math.
Soc. to appear (2010).
[2] J.-C. Ban, Y.-L. Cao and H.-Y Hu "Hausdorff
Dimension and Variational Pronciple for
Repellers" Trans Amer. Math. Soc. vol. 362,
no.2, 727-751 (2010) (SCI)
[3] J.-C. Ban, C.-H. Chang, T.-J. Chen and M.-S.
Lin, "Dimension Spectrum for Sofic Systems"
Submit to Nonlinearity (2010)
[4] J.-C. Ban, C.-H. Chang, T.-J. Chen and M.-S.
Lin, "The Complexity of Permutive Cellular
Automata" Submit to J. Cellular Automata
(2010)
[5] J . - C . B a n a n d C . - H . C h a n g " F r a c t r a l
Dimension of One-Dimensional Cellular
Automata" Submit to Fractal (2010).
[6] J .-C. Ban, Y.-L. Cao and Y. Zhao "Multifractal Analysis for Products of Positive
Matrices Under Countable Symbol Spaces"
Submitted (2010).
[7] K.-C.Chen, X. Dong, On the barycenter of the
tent map. Proc. Amer. Math. Soc., 138, 40254035 (2010).
[8] K.-C.Chen, Variational constructions for some
satellite orbits in periodic gravitational force
fields. Amer. J. Math., 132, 681-709 (2010).
[9] K .-C. Chen, J.S. Hsiao, Convex central
configurations of the n-body problem which
are not strictly convex, preprint.
[10] J ohn M. Hong, Cheng-Hsiung Hsu and
Weishi Liu (2010), Inviscid and viscous
stationary waves of gas flow through
contracting-expanding nozzles, Journal of
Differential Equations 248, 50-76.
[11] J ohn M. Hong, Cheng-Hsiung Hsu and
Weishi Liu (2010), Viscous stan d i n g
asymptotic states of isentropic compressible
flows through a nozzle, Archive for Rational
Mechanics and Analysis 196, 575-597.
[12] C heng-Hsiung Hsu and Ting-Hui Yang
(2010), Traveling wave solutions of delayed
lattice differential system in Lotka-Volterra
type, Discrete and Continuous Dynamical
Systems-B 14, 111-128.
[13] Cheng-Hsiung Hsu, Suh-Yuh Yang, Ting-Hui
Yang and Tzi-Sheng Yang (2010), Stability
and bifurcation of a two-neuron network
with distributed time delays, Nonlinear
Analysis-Real World Applications 11, 14721490.
[14] C
heng-Hsiung Hsu, Chi-Ru Yang, Ting-Hui,
Yang and Tzi-Sheng Yang, Existence of
traveling wave solutions for diffusive
predator-prayer type model, submitted to
Journal of Differential Equations, (2010).
[15] C heng-Hsiung Hsu, Jian-Jhong Lin and
Ting-Hui Yang, Traveling wave solutions for
delayed lattice reaction diffusion system,
s u b m i t t e d t o J o u r n a l o f D i ff e r e n t i a l
Equations, (2010).
[16] Cheng-Hsiung Hsu, Chi-Ru Yang and TziSheng Yang, Bifurcation analysis of a neural
loop with distributed time delays, Discrete
and Continuous Dynamical Systems-B,
(2010), revised.
[17] C heng-Hsiung Hsu, Inviscid and viscous
stationary waves of gas flow through nozzles
of varying area, preprint, (2010).
[18] S . G o n c h e n k o a n d M . - C . L i , 2 0 1 0 ,
Shilnikov's cross-map method and
hyperbolic dynamics of three-dimensional
Henon-like maps, Regular and Chaotic
Dynamics, 15, 165-184.
[19] S . Kiriki, M.-C. Li and T. Soma, 2010,
Coexistence of invariant sets with and
without SRB measures in Henon family,
Nonlinearity, 23, 2253-2269
[20] M.-C. Li and M.-J. Lyu, 2010, Topological
dynamics for multidimensional perturbations
of maps with covering relations and
Liapunov condition, Journal of Differential
Equations, to appear.
[21] C hih-Wen Shih, Jui-Pin Tseng, Global
Synchronization and Asymptotic Phases for
a Ring of Identical Cells with Delayed
Coupling, submitted.
[22] Kang-Ling Liao, Chih-Wen Shih, Snapback
Repellers and Homoclinic Orbits for Multidimensional Maps, submitted.
19 ‹‹- Highlights of the Focus Programs
D.4 Geometric Analysis and Differential Geometry
Coordinators: S.-C. Chang (National Taiwan University), J.-H. Cheng (Academia Sinica),
R. Chiang (National Cheng Kung University), Y.-I. Lee (National Taiwan University),
D.-M Nhieu (National Central University), C.-J. Sung (National Tsing-Hua University),
D.-H. Tsai (National Tsing-Hua University),
eometry has many interesting different
aspects, and our focus group has a wide
spectrum which covers quite a few important
directions of them. We mostly concentrate on, but
not limited to: Geometric Evolution Equations,
Function and Map Theory, and Geometric
Structures. During the year, we have many regular
seminars and held quite a few conferences and
mini courses.
Main research focus of GADG group at
NCTS
• Geometric Evolution Equations:
(i) Mean curvature flow in higher co-dimension
(ii) T
he torsion flow and geometrization problem
of contact 3-manifolds
(iii) T
he curvature flow of curves and
hypersurfaces
(a) Expanding convex immersed closed plane
curves
(b) Evolving a convex closed curve to another
one via a length-preserving linear flow
(c) Contracting convex immersed closed plane
curves
• Function and Map Theory :
(i) F
unction theory on pseudohermitian
manifolds.
(ii) A
nalysis on sub-manifold in a subRiemannian manifold
(iii) H
armonic function Theory
(a) Minimal submanifolds
(b) Harmonic functions and harmonic forms on
manifolds
Highlights of the Focus Programs -›› 20
(c) H
eat flow of Harmonic Maps Heat flow of
Harmonic Maps
• Geometric Structures :
(i) S
pecial Lagrangian and Hamiltonian
stationary sub-manifolds
(ii) C
R structures in Cauchy-Riemann geometry
and topology of contact manifolds
(iii) The Calabi-Yau problems for CR manifolds.
• Other Topics :
The geometry research at Tainan ranges from
symplectic geometry to algebraic geometry to
geometric analysis. Research topics include:
moduli spaces of vector bundles, representation
varieties, moment maps in various geometries,
contact homology, Lagrangian submanifolds,
orbifold quantum cohomology, cohomological
crepant resolutions, local positivity and syzygies
of algebraic varieties, geometric flows and
harmonic maps.
D.4.1 Researcher in local focus group
PI: S
.-C. Chang (NTU), J.-H. Cheng (Sinica),
River Chiang (NCKU), Y.-I. Lee (NTU),
D.-M Nhieu (NCU),C.-J. Sung (NTHU) and
D.-H. Tsai (NTHU).
AI: J .-F. Hwang (Sinica), D.-C. Wu (Sinica), S.-J.
Kan (Sinica), C.-C. Hsieh (Sinica), R.-T.
Huwang (Sinica), T.-H. Chang (Sinica), A. N.
Wang (NTU), K.-W. Lee (NTU), K.-L, Lin
(NTU), C.-J. Liu (NTU), J-.N. Tsai (NTU), S.
Takanari (NTU), C.-C. Lin (NTNU), J.-T.
Chen (NTNU), M.-L. Yau (NCU), H-L.Chiu
(NCU), N.-K. Ho (NTHU),.D. Nauyen
(NTHU), Y.C. Lin (NTHU), L.-C. Chang
(NTHU), S.-C. Chu (NCCU), C.-C. Poon
(NCCU), S.-Y. Hsu (NCCU), R. Chen
(NCKU), K.-G. Chan (NCKU), R. Chen
(NCKU), W.-K. Cheong (NCKU), Y-J Hong
(NCKU), H. Sakai (NCKU), E. Z. Xia
(NCKU), N.-C. Wong (NSYU), H.-G. Chan
(NPUE), C.-T. Wu (NPUE),
D.4.2 Visitors
W. Y. Hsiang (University of California,
Berkeley, USA), Y.-H. Pang (National University
of Singapore, Singapore), S.-T. Yau (Harvard
University, USA), C. Y. Hsiao (Chalmers
University of Technology, Sweden), Q. S. Chi
(Washington University, USA), Dominic Joyce
(University of Oxford, UK), Saotome Takanari
(OCAMI, Japan), S.-H Wei (University of
Oklahoma, USA), Otto Van Koert (Seoul National
University, South Korea), Mao-Pei Tsui (The
University of Toledo, USA), Eric Grinberg
(University of New Hampshire, USA), Ben
We i n k o v e ( U C S D , U S A ) , A n d r e a F r a s e r
(Dalhousie University, Canada), Der-Chen Chang
(Georgetown University, USA), C-H. Chu 朱礎豪
(London), W. Kaup (Tübingen), G. Roos (St.
Petersburg), I. Shestakov (Brazil), Y.-M. Chiang
蔣翼邁 (Hong Kong), K. Koufany (France), K.-S.
Lau 劉家成 (Hong Kong), M. Neal (Ohio), C.-K.
Ng 吳志強 (Nankai), Mitsuru Sugimoto (Nagoya
University), John Erik Fornaess (University of
Michigan, Ann Arbor), Xianghong Gong
(University of Wisconsin, Madison), Xiaojun
Huang (Rutgers University, New Brunswick),
Song-Ying Li (University of California, Irvine),
Ngaiming Mok (University of Hong Kong), MeiChi Shaw (University of Notre Dame), Yum-Tong
Siu (Harvard University), Paul Yang (Princeton
University), Stephen S.T. Yau (University of
Illinois, Chicago), Sai-Kee Yeung (Purdue
University), Irina Markina (University of Bergen,
Norway), Alexander Vasilev (University of
Bergen, Norway), S. Yang (Univ. New England),
J . - K . Yu ( P u r d u e ) , M . A k a h o ( To k y o
Metropolitan), U. Frauenfelder (Seoul National),
O. van Koert (Seoul National), R. Sjamaar
(Cornell), V. Ginzburg (UC Santa Cruz), S. P. Tan
(National Univ. Singapore).
D.4.3 Workshops, Course and Seminars
NCTS Colloquium Jordan Theory and
Analysis, April 8-12, 2010
A series of introductory and advanced lectures
will be given on Jordon theory and its applications
in analysis, algebra and geometry. Together with
invited talks on recent progress and related topics,
the Colloquium aims to create a forum to discuss
research problems and new directions. The
introductory lectures are designed to suit laymen
and research students.
Organizers:
Cho-Ho Chu 朱礎豪 (University of London)、
Ngai-Ching Wong 黃毅青 (NSYU)
Invited Speakers:
C-H. C h u 朱礎豪 (L o n d o n), W. K a u p
(Tübingen), P.-H. Lee 李白飛 (Taiwan), G. Roos
(St. Petersburg), I. Shestakov (Brazil), H.-S. Chen
陳界山 (Taiwan), Y.-M. Chiang 蔣翼邁 (Hong
K o n g), C.-L. C h u a n g 莊正良(Ta i w a n), K.
Koufany (France), K.-S. Lau 劉家成(Hong
Kong), T.-K. Lee 李秋坤 (Taiwan), M. Neal
(Ohio), C.-K. Ng 吳志強 (Nankai), P.-Y. Wu 吳培
元 (Taiwan)
2010 NCTS/TPE-TIMS Mini-Course and
Workshop on Geometric and Complex
Analysis, June 21-July 2, 2010
Invited Speakers:
• Der-Chen Chang(Georgetown University, USA)
• Jih-Hsin Cheng(Academia Sinica, Taiwan)
• Jui-Tang Chen(Nat'l Taiwan Normal Univ.)
• River Chiang (NCKU, Taiwan)
• Eric Grinberg(University of New Hampshire, USA)
• Andrea Fraser (Dalhousie University, Canada)
• O tto van Koert (Seoul National University,
Korea)
• Takanari Saotome (OCAMI, Japan)
• Mei-Chi Shaw (University of Notre Dame, USA)
• Mao-Pei Tsui (University of Toledo, USA)
• Ben Weinkove (UCSD, USA)
• Chin-Tung Wu, (NPTUE, Taiwan)
• Shihshu Wei (University of Oklahoma, USA) 21 ‹‹- Highlights of the Focus Programs
Organizers:
• Der-Chen Chang (Georgetown University, USA)
• Shu-Cheng Chang(NTU, Taiwan)
• Mao-Pei Tsui (University of Toledo, USA)
2010 NCTS Workshop on Fourier Analysis
and Its Applications to PDEs, July 1, 2010
One of the main aims of this workshop is to
elaborate approaches in Fourier analysis to study
sharp estimates for partial differential equations. The crucial idea is to put ahead the CalderónZygmund-Stein theory as a general point of view
that has great value for many methods of
harmonic and complex analysis. In particular, we
shall investigate problems arise from complex
analysis, integral geometry, pseudo-differential
operators and function spaces.
Organizers: • Prof. Der-Chen Chang (Georgetown University
& NCTS)
• Prof. Chiung-Jue Sung (Nat'l Tsing Hua Univ.)
Invited Speakers:
• Der-Chen Chang (Georgetown Univ. & NCTS)
• Andrea Fraser (Dalhousie Unmiversity)
• Eric Grinberg (University of New Hampshire)
• Jin-Wen Lan (National Tsing Hua University)
• Ming-Yi Lee (National Central University)
• Mitsuru Sugimoto (Nagoya University)
• Hwaichiuan Wang (Nat'l Tsing Hua Univ.)
2010 NCTS International Conference on
Several Complex Variables and Complex
Geometry, July 9-11, 2010
The purpose of this conference is to bring
together both experts and novices in Several
Complex Variables with experts in geometric
analysis and complex geometry. The participants
will present their results and discuss further
developments of the frontier research exploring
the bridge between Complex, Harmonic Analysis,
PDE and Geometry. The conference will feature
invited expository 50 minutes lectures by
prominent mathematicians.
One of the goals of this meeting is to discuss
possibilities of further cooperation, networking
and promotion of mobility of senior and young
researchers in Taiwan and United States.
Highlights of the Focus Programs -›› 22
Organizers: • Prof. Der-Chen Chang (Georgetown University
& NCTS)
• Prof. Xiaojun Huang (Rutgers University, New
Brunswick)
• Prof. Ngaiming Mok (Univ. of Hong Kong)
• Prof. Chiung-Jue Sung (Nat'l Tsing Hua Univ.)
Invited Speakers:
Der-Chen Chang (Georgetwon University &
NCTS), Hong-Ling Chiu (National Central
University), Jih-Hsin Cheng (Academia Sinica),
John Erik Fornaess (University of Michigan, Ann
Arbor), Peter Greiner (University of Toronto &
Academia Sinica), Xianghong Gong (University
of Wisconsin, Madison), Xiaojun Huang (Rutgers
University, New Brunswick), Song-Ying Li
(University of California, Irvine), Ngaiming Mok
(University of Hong Kong), Mei-Chi Shaw
(University of Notre Dame), Yum-Tong Siu
(Harvard University), Chiung-Jue Sung (National
Tsing Hua University) , Paul Yang (Princeton
U n i v e r s i t y ) , S h i n g - T u n g Ya u ( H a r v a r d
University), Stephen S.T. Yau (University of
Illinois, Chicago), Sai-Kee Yeung (Purdue
University)
Algebraic Geometry Day at NCTS(south),
October 11, 2010.
The algebraic geometers at NCKU, Eugene Z.
Xia, Kungho Chan, Wan Keng Cheong, each gave
a talk in this one day event. This not only presents
the algebraic geometry development in the south,
but also provides an opportunity for research
interaction and future collaboration.
The First Taiwan Geometry Symposium,
November 20, 2010.
The purpose of the symposium is to foster
discussions and interactions within the geometry
community in Taiwan. It hopes to meet regularly
in the years to come, running on a Saturday from
late morning to late afternoon, with 3 speakers,
followed by dinner. The activity will rotate among
Taipei, Hsin-Chu and Tainan. Everyone interested
in geometry, in particular students, postdoctoral
fellows and young scholars are encouraged to
participate.
Organizers: Y.-I. Lee (NTU), R. Chiang (NCKU)
and N.-K. Ho (NTHU).
Speakers: Y
.-I. Lee (NTU), K.-W. Lee (NTU),
and D.M. Nhieu (NCU)
NCTS Course in Aspects of Analysis on
Model Domains in Cn+1
Speakers:
• P
rof. Der-Chen Chang 張德健(Georgetown
Univ. & NCTS)、
• Prof. Duy-Minh Nhieu 饒維明 (Nat'l Central Univ.)、
• Prof. Chiung-Jue Sung 宋瓊珠 (Nat'l Tsing Hua Univ.)
In this short course, we introduce fundamental
techniques of geometric analysis in of Cn+1. The
course will focus on more technicalities usually
only mentioned briefly in talks. Such techniques
will eventually propel students into more
advanced research into the subject. Two general
directions applied to two basic models that are
closely related in the setting of complex spaces
will be considered. The first one will take on
geometry from the complex point of view on the
unit sphere in C n+1 The topics of this part will
include: Sub-Riemannian geometry on the unit
s p h e r e S 2n+1: H a m i l t o n i a n a n d L a g r a n g i a n
formalisms, Heat kernels for the sub-Laplacian
and the Poisson summation formula, Li-Yau
estimates for the heat kernel on S3 The second part
will consider geometric problems from the point
of view of real analysis on the Heisenberg group. The topic of this part will cover the following
topics: Basic geometric quantities on surfaces in
H 1 , Horizontal surface measure, H-minimal
surfaces, Horizontal and Vertical integration by
parts formulae and their applications, First and
Second variations of the H-perimeter. After taking
the short course, we hope that students will gain a
deeper understanding and interests into problems
that arise from such settings and are equipped
with the necessary skills to investigate into such
problems.
Contents:
(1) S
ub-Riemannian geometry on the unit
sphere S 2n+1: Hamiltonian and Lagrangian
formalisms.
(2) H eat kernels for the sub-Laplacian and the
Poisson summation formula.
(3) Li-Yau type estimates for the heat kernel on S3.
(4) Basic geometric quantities on surfaces in H1.
(5) Horizontal surface measure and H-minimal
surfaces.
(6) H
orizontal and Vertical integration by parts
formulae and their applications.
(7) F i r s t a n d S e c o n d v a r i a t i o n s o f t h e
H-perimeter.
ymplectic & Contact Winter School,
S
February 24 – 27, 2010
Organizer: R. Chiang (NCKU)
This Winter School brings together the
geometry/topology oriented students and faculty
members and promotes symplectic and contact
topology and their interaction with other fields.
The program includes:
Lecture series:
• M
anabu Akaho (TMU) Lagrangian Floer theory
• U rs Frauenfelder (SNU) Rabinowitz Floer
homology
• Otto van Koert (SNU) Construction of contact
manifolds
Invited talks:
• S
hu-Cheng Chang (NTU) Geometric evolution
problems on contact 3-manifolds
• E u g e n e Z . X i a ( N C K U ) S y m p l e c t i c
construction of moduli spaces
D.4.4 Seminars and Student Seminars
We hold several regular seminars at Taipei,
Hsinchu and Tainan. In May 2010, we started a
biweekly reading seminar on symplectic geometry
between National Central University and National
Cheng Kung University. M.-L. Yau and R. Chiang
each gave a series of talks based on research
papers in the field. The activities are summarized
below:
NCTS/TPE & TIMS Joint Geometry
Seminar
This is a weekly seminar. The speakers include
our foreign visitors and local mathematicians.
NCTS/TPE & TIMS Joint Student Geometry
Seminar
This is a weekly seminar, and sometimes
several talks are scheduled a week. Students read
and present important papers in the directions of
CR manifolds, General Relatives, Mean Curvature
Flow, Ricci Flow, Kahler-Ricci Flow, Contact
23 ‹‹- Highlights of the Focus Programs
Structures, and other related Riemannian
properties.
2010 NCTS Summer Student Seminar on
Geometry
Speakers include: 張廷暉 Ting-Hui Chang, 張博
堯 Po-Yao Chang, 呂楊凱 Yang-Kai Lue, 樊彥
Yen-Wen Fan, 楊劼之 Jie-Zhi Yang, 李國瑋 KuoWei Lee, 郭庭榕 Ting-Jung Kuo, 陳裕元 Yu Yuan
Chen, 張世翰 Shih-Han Chang, 賴馨華 Sin Hua
Lai, 王以晟 Yi-Cheng Wang, 林乾 Chien Lin, 施
博閔 Po-Min Shih, 黃詠翔 Yung Hsiang Huang,
徐裕光 Yuguang Xu (Kunming University)。
Each gives several talks and some even speak
every three weeks.
Organizers: Prof. Shu-Jung Kao 高淑蓉 (NTHU)
NCTS/TPE-Sinica Geometry Seminar
Speakers include: Po-Min Shin 施博閔 先生(
NTHU 清大)、Yang-Hsain Huang 黃詠翔 先生
(NCTU 交大)、薛至倖 女士(中研院研究助理)
Topics include: Topological Space, The Topology
of Euclidean Space, The Geometry of Curves
Biweekly Reading Seminar on Symplectic
Geometry between National Central
University and National Cheng Kung
University.
This is also at weekly basis. The speakers
include our foreign visitors and local
mathematicians.
M.-L. Yau and R. Chiang each gave a series of
talks based on research papers in the field.
2010 NCTS Seminar on Geometry
We held geometry seminars throughout the
year. Some speakers gave more than one lecture.
Our speakers from 2009/11 to 2010/10 include:
Chiung-ju Liu (TIMS/NTU), Yen-lung Tsai
(NCCU), Hironori Sakai (NCKU), Kungho Chan
(NCKU), Eugene Z. Xia (NCKU), Huai-Liang
Chang (HKUST), Shing-Tung Yau (Harvard), JiuKang Yu (Purdue), Wu-Yen Chuang (Rutgers),
Reyer Sjamaar (Cornell), Chuu-Lian Terng (UC
Irvine), Viktor Ginzburg (UC Santa Cruz), Siye
Wu (UHK & Colorado), Yuguang Xu (Kunming
Unisersity), Mao-Pei Tsui (Toledo), Ser Peow Tan
(National U Singapore).
Topic: Computing Integrals Using Fixed Points
Speakers: Professor Loring Tu (Tufs Univ., USA)
2010 NCTS Student Seminar on Differential
Geometry
Organizers: Prof. Chiung-Jue Sung (National
Tsing Hua University)
Speakers include: Mr. Kuen-Lian Wu 吳昆聯
(N T H U)、M i s s L i a n g-C h u C h a n g 張喨筑
(NCCU)、Mr. Guan-Ho Lai 賴冠合 (NCTS)、
Miss Wen-Cheng Wu 巫玟錚 (NTHU)、Mr.
Chiou-Yung Li 李邱勇 (NTHU)
Topics include: The Heat Flow of Harmonic
Maps, Eigenvalues on Minimal Surfaces in
Hyperbolic Spaces, Volume Comparison Theorem
on Manifolds, The Formation of Singularities in
the Harmonic Map, Eigenvalues Estimates on
Surfaces, On the Continuous Spectra of Small
Potentials, Growth and Decay Properties of
Solution of Second Order Elliptic Equations,
Relative Volume Comparison Theorem in
Manifold, Some Results on Harmonic Maps,
Volume Comparison Theorem Without Jacobian,
On the Gap Between the First Eigenvalues of the
Laplacian on Functions and 1-Forms, Eigenvalues
of the Laplace-Beltrami Operator on P-Forms
with Arou-Preserving Metric Conformal
Deformations, Differential Forms, Eigenvalues of
the Laplacian on p-forms.
Highlights of the Focus Programs -›› 24
Geometry Seminar at NCTS (south)
D.4.5 Accomplishments
[1] K
ungho Chan, A lower bound on Seshadri
constants of hyperplane bundles on threefolds.
Math. Z. 264 (2010), no. 3, 497-505
[2] D er-Chen Chang, Dachun Yang and Yuan
Zhou, Boundedness of Sublinear Operators on
Product Hardy Spaces and Its Application, J.
Math. Soc. Japan 62 (2010), no. 1, 321-353.
[3] L .-C. Chang, C.-L. Guo and C.-J. Sung,
p-Harmonic 1-Forms on Complete Manifolds,
Archiv der Mathematik, Vol. 94 No 2 (2010)
p183-192.
[4] L .-C. Chang and C.-J. Sung, p-Harmonic
l-Forms on Complete Manifolds. (Preprint)
[5] Shu-Cheng Chang and Hung-Lin Chiu, The
Li-Yau-Hamilton inequality for Yamabe flow
on a closed CR 3-manifold, Transactions of
AMS, Vol 362 (2010), 1681-1698.
[6] Shu-Cheng Chang, Jingzhu Tie and C.-T. Wu,
Subgradient Estimate and Liouville-type
Theorems for the CR Heat Equation on
Heisenberg groups Hn, Asian J. Math., Vol. 14,
No. 1 (2010), 041-072.
[7] S .-C. Chang and C.-T. Wu, The Entropy
Formulas for the CR Heat Equation and its
Applications on Pseudohermitian (2n+1)Manifolds, Pacific Journal of Mathematicsol.
246 (2010), 1-29
[8] Jih-Hsin Cheng, Jenn-Fang Hwang, Andrea
Malchiodi, and Paul Yang, A Codazzi-like
equation and the singular set for C1 smooth
surfaces in the Heisenberg group, preprint.
[9] J ih-Hsin Cheng, Hung-Lin Chiu, Andrea
Malchiodi, and Paul Yang, An ADM-type
mass in CR geometry, in preparation.
[10] Wan Keng Cheong, Orbifold quantum
cohomology of the symmetric product of A_
r, preprint.
[11] R. Chiang, Y. Karshon, Convexity package
for momentum maps on contact manifolds,
Algebr. Geom. Topol. 10 (2010), 925-977.
[12] Sun-Chin Chu, The Ricci Flow: Techniques
and Applications, Part III: GeometricAnalytic Aspects. (With Bennett Chow,
David Glickenstein, Christine Guenther, Jim
Isenberg, Tom Ivey, Dan Knopf, Peng Lu,
Feng Luo and Lei Ni.) Mathematical
Surveys and Monographs. American
Mathematical Society, Providence, RI.
(2010.)
[13] William M. Goldman, Eugene Z. Xia, Action
o f t h e J o h n s o n - To r e l l i g r o u p o n
Representation Varieties, arXiv:1003.2825
[14] D. Joyce, Y.-I. Lee and R. Schoen, On the
Ex i s te n ce o f H a mil to n ian S ta tio n a r y
Lagrangian Submanifolds in Symplectic
Manifolds, to appear in Amer. Journal of
Math (2010).
[15] D . Joyce, Y.-I. Lee, and M.P. Tsui, Selfsimilar Solutions and Translating Solutions
for Lagrangian Mean Curvature Flow, J.
Diff. Geom. Vol. 84, no 1 (2010), p.127-161.
[16] Y.-I. Lee, The Existence of Hamiltonian
Stationary Lagrangian Tori in Kahler
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
Manifolds of Any Dimension, submitted,
available at arXiv:1001.3861.
Y.-I. Lee, Self-similar Solutions and
Translating Solutions, to appear in the
Proceeding of Complex and Differential
Geometry, Leibniz University, Hannover,
Germany (2010)
Y.-I. Lee, K.-W. Lee, Mean Curvature Flow
of the Graphs of Maps between Compact
Manifolds, to appear in Trans. Amer. Math.
Soc. (2010).
Y. - I . L e e , C . - S . L i n , a n d M . - P. Ts u i ,
(Editors,) Recent Advances in Geometric
Analysis, Advanced Lectures in Mathematics
(ALM) 11, Beijing: Higher Education Press
(2009), and Somerville, MA: International
Press (2010).
Y.-I. Lee, A.-N. Wang, and S.-W. Wei, A
Generalized 1-harmonic Equation and the
Inverse Mean Curvature Flow, to appear in
Journal of Geometry and Physics (2010).
Y.-I. Lee and M.-T. Wang, Hamiltonian
Stationary Cones and Self-similar Solutions
in Higher Dimension, Trans. Amer. Math.
Soc. Vol. 362, no.3 (2010), 1491-1503.
Y.-C. Lin and D.-H. Tsai Using Aleksandrov
Reflection to Estimate the Location of the
Center of Expansion, Proc. Amer. Math. Soc.
138 (2010), no. 2, 557-565.
Y.-C. Lin and D.-H. Tsai, Contracting
convex immersed closed plane curves with
fast speed of curvature. Comm. Anal. Geom.
18 (2010), no. 1, 23-75.
H ironori Sakai, The symplectic DeligneMumford stack associated to a stacky
polytope, arXiv:1009.3547
Publications in 2009 after 2009/10
[1] T
ai-Chia Lin, Chi-Cheung Poon, and DongHo Tsai, Expanding convex immersed closed
plane curves, Calculus of Variations & PDEs,
34, 153.178, 2009.
[2] Hironori Sakai, A construction of a Frobenius
manifold from the quantum differential
equation of a weighted projective space. In
Riemann Surfaces, Harmonic Maps and
Visualization, volume 3 of OCAMI Studies,
pages 137-148. Osaka Municipal Universities
Press, 2009
25 ‹‹- Highlights of the Focus Programs
[3] C
hin-Tung, Wu, Evolution of CR Yamabe
constant under the Cartan flow on a CR
3-manifold. Taiwanese J. Math. 13 (2009),
no. 5, 1433-1439
[4] M
e i - L i n , Ya u , C y l i n d r i c a l c o n t a c t
homology of a Dehn twist. Internat. J.
Math. 20 (2009), no. 12, 1479-1525
D.5 Mathematical Biology
Coordinators: Sze-Bi Hsu (National Tsing-Hua University), Chih Wen Shih (Natinal Chiao-Tung University)
he purpose of the topical program in
Mathematical Biology is to promote the
interdisciplinary interaction between
mathematicians, biologists, physicists, statisticians
and computer scientists on the new problems
arising from biology. In the past one year, we held
a weekly seminars in Infinite Dimensional
Dynamical System in Population Biology, an
summer course in Mathematical Modeling and
Analysis for the graduate students, a topics course
in Partial Differential Equations with application
to Mathematical Biology, An international
conference: A workshop in PDE models of
Biological Process. We also invite several
speakers to give talks in Neural Science,
Geometric singular perturbation and Traveling
Waves. We state as follows:
Local Group: Yu-Yun Chen(NTHU), Jann-Long
Chern (NCU), Sze-Bi Hsu (NTHU), Kuo-Chih
Hung (NTHU), Chih-Wen Shih (NCTU), FengBin Wang (NTHU), Shin-Hwa Wang (NTHU),
Chih-Jiang Tsai (NCCU)
D.5.1 Workshop / Course & Seminars
I. 2
010 NCTS Seminar on Dynamical
Systems & Math Biology
Speaker: P
rofessor Xiaoqiang Zhao (Memorial
University of Newfoundland, Canada)
Time: P M 2:30-4:30, every Wednesday, March
10-May 31, 2010
Topic: Infinite Dimensional Dynamical Systems
in Population Biology
Remark: Professor Zhao will give talk every
Wednesday (March 10-May 31) based on his book
Highlights of the Focus Programs -›› 26
"Dynamical System in Population Biology " (2003
Springer Verlag) and his recent work.
II. 2
010 NCTS Summer Course in Math.
Modeling and Analysis in Biological
Science
Dates: 7/12-8/9, Every Monday(7/12, 7/19, 7/26,
8/2, 8/9) 10:30am-12:00pm, 2:00pm-3:30pm.
Speakers:
• Prof.Sze-Bi Hsu 許世壁 (Nat'l Tsing-Hua Univ.)
• Prof.Ying-Hen Hsieh 謝英恆 (China Medical
University)
• D r.Yun-Huei Tzeng 曾雲輝 (Biodiversity
Research Center, Academia Sinica)
Titles:
• July 12 & 19, Prof. Sze-Bi Hsu 許世壁,Math.
Model in Population Biology
• July 26, Prof. Ying-Hen Hsieh 謝英恆, Math.
Model in Epidemiology
• A ug. 2 & 9, Dr. Yun-Huei Tzeng 曾雲輝,
Molecular Evolution
III. 2
010 NCTS Topical Program in
Mathematical Biology: Topics in PDE
with Application to Mathematical
Biology
Instructor: Professor Sze-Bi Hsu 許世壁 (NTHU)
Time: September 13, 2010 – Jan. 14, 2011
10:20-12:10 (M3, M4), 2:20-3:10 (M6)
In this seminar we shall study the following
topics:
(1) B
ifurcation Theorem of Crandall and
Rabinowitz and Exchange Stability Principle.
(2) D
egree Theory & Its Applications.
(3) K r e i n - R u t m a n T h e o r e m a n d P r i n c i p a l
Eigenvalue.
(4) M aximal Principle, Method of Upper and
Lower Solution.
(5) Application to Mathematical Biology
(i) L ogistic Equation in Heterogeneous
Environment.
(ii) Two Species Competition System in
H e t e r o g e n e o u s E n v i r o n m e n t , a n
Application of Monotone Dynamical
System.
(iii) N
onlocal PDE in Ecology.
IV. W
orkshop on PDE Models of Biological
Process
Mathematical Biology provides mathematical
methods to study the modern biology. There are
many mathematical ways to approach biological
problems, either by simple mathematical models
or computation biology. Partial differential
equation plays an important role in both
approaches. The main purpose of the workshop is
to attract the researchers of partial differential
equations to study the problems arising from
population dynamics, physiology and cell biology.
Modeling and mathematical analysis will be
emphasized in the talks of this workshop. The
workshop will be held at National Center of
Theoretical Science (NCTS), Hsinchu (located at
National Tsing Hua University) in Dec. 13-17,
2010. On the first two days, (Dec. 13 and Dec. 14)
the subjects of talks will be focused in
mathematical modeling in Cell Biology and
Physiology. Dec. 15 is off for Taipei city tour.
Then on Dec. 16 and Dec. 17, the theme of the
talks is Population Dynamics. Besides 50-minute
plenary talks, we shall have 30-minute invited
talks and 20-minute contributed talks. There is no
registration fee. We welcome people to participate
the workshop and to deliver a talk.
Scientific Committee
• S
ze-Bi Hsu (Nat'l Tsing-Hua Univ.), Chair
• Avner Friedman (Mathematical Bioscience
Institute, Ohio State Univ., USA)
• Yuan Lou (Mathematical Bioscience Institute ,
Ohio State University, USA)
• Jong Shenq Guo (Tamkang University)
• Chuin-Chuan Chen (Nat'l Taiwan Univ.)
• Chih-Wen Shih (Nat'l Chiao-Tung Univ.)
The following is the list of plenary, invited and
contributed speakers:
Plenary Speakers (50min)
(1) Xinfu Chen (University of Pittsburgh, USA)
(2) Yihong Du (Univ. of New England, Australia)
(3) Avner Friedman (MBI, Ohio State Univ., USA)
(4) James Grover (Univ. of Texas, Arlington, USA)
(5) Bei Hu (University of Notre Dame, USA)
(6) Thomas Hillen (Univ. of Alberta, Canada)
(7) C hristopher Klausmeimer (Michigan State
University, USA)
(8) James Keener (University of Utah, USA)
(9) Yuan Lou (MBI , Ohio State University, USA)
(10) Angela Stevens (Univ. of Heidelberg, Germany)
(11) Jonathan Sherratt (Heriot-Watt Univ., Scotland)
Invited Speakers (30min)
(1) Chiun-Chuan Chen (Nat'l Taiwan Univ., Taiwan)
(2) Jong-Shenq Guo (Tamkang Univ., Taiwan)
(3) Sze-Bi Hsu (Nat'l Tsing-Hua Univ., Taiwan)
(4) Tai-Chia Lin (Nat'l Taiwan Univ., Taiwan)
(5) Peter Hinow (University of Wisconsin, USA)
(6) Chun Liu (The Penn State University, USA)
(7) Masayasu Mimura (Meiji University, Japan)
(8) Tim Reluga (Penn State, USA)
(9) Chih-Wen Shih (Nat'l Chiao-Tung Univ., Taiwan)
(10) Junping Shi (College of William and Mary, USA)
(11) K
uni Sakamoto (Hiroshima Univ., Japan)
(12) Z hian Wang (Hong Kong Polytechnic
University, Hong Kong)
(13) Yoshio Yamada (Waseda University, Japan)
Contributed Speakers (20 min)
(1) J a n H a s k o v e c ( A u s t r i a n A c a d e m y o f
Sciences, Austria)
(2) Harsh Jain (MBI, USA)
(3) Peter Kim (University of Utah, USA)
(4) Yangjim Kim (University of Michigan, USA)
(5) Alicia Prieto Langarica (Univ. of Texas, USA)
(6) Chiu-Chang Lee (Nat'l Taiwan Univ., Taiwan)
(7) Yu-Yu Liu (UC Irvine, USA)
(8) L in Feng Mei (The University of New
England, Australia)
(9) Andrew Nevai (Univ. of Central Florida, USA)
(10) Joaquin Rivera-Cruz (Colgate Univ., USA)
27 ‹‹- Highlights of the Focus Programs
(11) F
eng-Bin Wang (Univ. of West Ontario, Canada)
(12) Shari Wiley (Howard University, USA)
(13) Shin-Hwa Wang (Nat'l Tsing-Hua Univ., Taiwan)
VI. Seminar
1. 2010 NCTS Seminar on Mathematical Biology Speaker: Professor Yue Xian Li (University of
British Columbia, Canada)
Time: PM 4:00-5:00, Thu., April 15, 2010
Topic: S
tationary and Oscillatory Fronts in a
Two-Component Genetic Regulatory
Network Model
2. C
MS and NCTS Joint Seminar in
Mathematical Biology
Speaker: Prof. Deng Bo, (University of
Nebraska, USA)
Topic: Trapper drove Hare to eat Lynx
Time: May 19, 2010 (Wednesday)
2:30pm - 3:30pm
3. 2 010 NCTS Seminar on Dynamical Systems &
Mathematical Biology
Speaker: Professor LieJune Shiau (University
of Houston, Clear Lake)
Topic: Oscillations in An Adaptive Neuronal
Model
Time: July 2, 2010 (Friday)
4. 2 010 NCTS & CMS Joint Seminar in PDE &
Mathematical Biology
Speaker: Professor Liang Xing (University of
Science and Technology of China)
Time: 11:00AM-12:00PM, Friday, July 23,
2010
Topic: R
earrangement Inequalities for
Principal Eigenvalues of Integral Operators and Applications
D.5.2 Accomplishments
[1] J . - C . Ts a i , R o t a t i n g s p i r a l w a v e s i n
λ—ωsystems on circular domains, Phys. D,
239 (2010), pp. 1007-1025.
[2] J.-C. Tsai and S. Petrovskii, Wave propagation
for a model of population dynamics with
density-dependent migrations and the weak
Allee effect. (preprint)
Highlights of the Focus Programs -›› 28
[3] J .-C. Tsai and J. Sneyd, Fast buffering effect
on traveling waves in the FHN System.
(preprint)
[4] Sze-Bi Hsu, Jifa Jiang and Feng-Bin Wang,
On a system of reaction–diffusion equations
arising from competition with internal storage
in an unstirred chemostat, J. Differential
Equations 248 (2010), pp. 2470-2496
[5] S z e - B i H s u a n d Yu a n L o u , S i n g l e
phytoplankton species growth with light and
advection in a water column, SIAM J. Applied
Math., Vol 70,No.8 (2010) pp.2942-2974
[6] Y. D u a n d S ze- B i H s u , O n a n o n lo cal
reaction-diffusion problem arising from the
modeling phytoplankton growth, SIAM J.
Math. Analysis 42 (2010), pp. 1305-1333
[7] S ze-Bi Hsu and Feng-Bin Wang, On a
mathematical model arising from competition
of phytoplankton species for a single nutrient
with internal storage: Steady state analysis,
DCDS, Ser. S, to appear.
[8] F e n g - B i n Wa n g , A s y s t e m o f p a r t i a l
differential equations modeling the
competition for two complementary resources
i n f l o w i n g h a b i t a t s , To a p p e a r i n J .
Differential Equations
[9] Sze-Bi Hsu, Feng-Bin Wang and Xiao-Qiang
Zhao, Dynamics of a Periodically Pulsed Bioreactor Model with a Hydraulic Storage Zone,
submitted to Journal of Dynamics and
Differential Equations
[10] Sze-Bi Hsu, Jifa Jiang and Feng-Bin Wang,
Reaction-Diffusion Equations of Two
Species Competing for Two Complementary
Resources with Internal Storage, submitted
to J. Differential Equations
[11] F
eng-Bin Wang, A Periodic ReactionDiffusion Model with A Quiescent Stage,
submitted to DCDS, Ser. B
[12] James P. Grover, Sze-Bi Hsu and Feng-Bin
Wang, Competition between microorganisms
for a single limiting resource with cell quota
structure, submitted to Journal of
Mathematical Biology.
[13] Sze-Bi Hsu and Xiaoqiang Zhao , A LotkaVolterra Competition Model with Seasonal
Succession, submitted to Journal of
Mathematical Biology
D.6 Number Theory and Arithmetic Geometry
Coordinators: W
en-Ching W. Li (Penn State University and NCTS), Liang-Chung Hsia (National Central University) and
Chia-Fu Yu (Academia Sinica)
s this year (2010) is a special year in
number theory at NCTS, there are more
number theory activities at NCTS including one
international conferences and one Taiwan-Korea
joint workshop in number theory. The main
themes cover the field of automorphic/modular
forms, Galois representaions, and related topics.
Besides the above mentioned topics, the existing
research topics – traditional algebraic number
theory, arithmetic geometry and Diophantine
geometry and arithmetic of algebraic function
fields are also the main focus of number theory at
NCTS. The scope of our number theory group is
broadening, several international cooperation
programs have been established this year. The
following is a list of the main research areas in
number theory.
Main Research Focus of the working group
Arithmetic and geometry of moduli spaces
Diophantine geometry
Modular forms
Automorphic Representations and zeta functions
Coding theory
Transcendence theory in positive characteristic
D.6.1 Local participating members
W. W.-C. Li (Director of NCTS), J. Yu (NCTS
and NTU), C.-Y. Chang (Post doc), Y.-M. J.Chen
(NCU), W.-C. Chi (NTNU), L.-C. Hsia (NCU),
Ming-Lun Hsieh (NTU), A. Li (Fu Jen U.), S.-Y.
Pan (NTHU), A. Schweizer (Academia Sinica),
Ki-Seng Tan (NTU), Cristian Virdol (NCTS,
visiting assistant professor), C.-J. Wang (NCU), I.
Longhi (post doctor), J. T.-Y. Wang (Academia
Sinica), W.-C. Yao (TMUE), Y. Yang (NCTU),
C.-F. Yu (Academia Sinica), J.-D. Yu (NTU), Y.-J.
Yu (N. Cheng-Chi U.). Presently there are also 15
Ph.D. students and research assistants in this
group, from NTHU, NTU, NCU, and NCTU.
There are also research assistants at NCTS and
Academia Sinica.
D.6.2 Visitors
The speaker for our distinguished lecture series
this year is Prof. Don Zagier, who is one of the
directors of the Max Plank Institute for
Mathematics in Bonn, Germany, and a professor
at the College de France, Paris, France. Prof.
Zagier won the Cole Prize in Number Theory in
1987 and the von Staudt Prize in 2001.
There are many short term visitors this year.
Vistors at Hsinchu:
W. Dale Brownawell (Penn State University),
Jianya Liu (Shandong University), Gebhard
Böckle (University Heidelberg), Zhi-Wei Sun
(Nanjing University), Don Zagier (Max Planck
Institute for Mathematics and College de France),
Silke Wimmer Zagier (Max Planck Institute for
Mathematics), Dihua Jiang (University of
Minnesota), Ben Kane (University of Cologne),
Wen-Wei Li (Universite Paris Diderot 7), JiuKang Yu (Purdue University), Wenzhi Luo (Ohio
State University), Jongryul Lim, Subong Lim and
Bumkyu Cho (POSTECH), Yoon Kyung Park,
YoungJu Choie and Yoonbok Lee (POSTECH,),
Lin Han (Inha Universityx), Bo-Hae Im (ChungAng University), Dong UK Lee (KIAS), Yoonjin
Lee (Ewha Womans University), Winfred Konen
(Ruprecht-Karls-Universitat Heidelberg),
Solomon Friedberg (Boston College), Michael A.
Tsfasman (Independent University of Moscow),
Jeffery Hoffstein (Brown University), Keqin Feng
(Tsinghua University Beijing), Ming-Deh Huang
(University of Southern California), M.-H. Kang
(Penn. State University), Hironori Shiga (Waseda
University), Pedram Hekmati (Royal Institute of
Technology), Patrick Sole (CNRS/LTCI).
29 ‹‹- Highlights of the Focus Programs
Vistors at Taipei:
D.6.4 Lecture Series
Kai-Wen Lan (Princeton University), Laurent
Fargue (CNRS and Universite Paris-Sud), Sophie
Morel (Harvard University), Wen-Wei Li
(Universite Paris 7), Ching-Li Chai (University of
Pennsylvania). Among them C.-L. Chai, , JiuKang Yu are frequent visitors.
There are many series of lectures given by
visitors from abroad and our visitors and local
research members. Listed below are highlights of
these activities.
D.6.3 I nternational Conferences and
Workshops
2010 NCTS International Conference on
Automorphic Forms and Related Topics
This conference was organized by Wen-Ching
W. Li (National Center for Theoretical Sciences)
and Jing Yu (National Taiwan University). It was
held during July 7-9, 2010.
The purpose of this conference is to gather
experts in this area so that the progress in this area
made in recent years, both on analytic and
algebraic sides of the subject can be discussed. In
this three day conference, many different aspects
of automorphic forms were exposed and most
recent advances were discussed. Fourteen invited
speakers from six foreign countries participated
the conference. The total number of participants
was over 60.
2010 Taiwan-Korea Workshop on Number
Theory
This is a continuation of our international
cooperation program with the Pohang
Mathematics Institute of POSTECH, Korea,
initiated in 2009. Organized by YoungJu Choie
(POSTECH, Korea) and Wen-Ching W. Li
(National Center for Theoretical Sciences), this
conference was held in July 5-6, 2010. The
purpose of this annual workshop was to enhance
communications among number theorists in
Taiwan and Korea, with the hope of leading to
collaborations between mathematicians of these
two countries. The invited speakers consisted of 7
mathematicians from Korea and 5 from Taiwan.
This workshop was attended by more than 50
people.
Highlights of the Focus Programs -›› 30
I. Distinguished Lectures on "Modular Froms,
Mock theta Functions, and Black Holes" by
Don Zagier: Topics of this Distinguished Lectures
cover number theory as well as physics. In the ten
hour lectures in two weeks, Zagier gave an
introduction to classical, Jacobi and Siegel
modular forms, emphasizing recent developments
on mock theta functions. He also described
applications of this theory to the quantum theory
of black holes. Open problems as well as
conjectures were discussed. His lectures have
drawn attention from many local researchers in
different disciplines, including number theorists
and physicists.
II. "Cohomological Theory of Crystals over
Function Fields and Applications" given by
Gebhard Böckle (University Heidelberg). This
series of lectures gave an introduction to the
cohomological theory developed jointly by the
speaker and Richard Pink. He also gave some
applications.
III. "Theory of Transcendental Numbers
Related to the Function Field Setting" given by
W. Dale Brownawell (Pennsylvania State
University). The major theme of this series of
lectures was transcendental number theory, from
the classical Siegel-Shidlovsky theory to its
analogue in function field.
I V. " F o n t a i n e ’ s T h e o r y i n E q u a l
Characteristic" given by a member of our focus
group C.-Y. Chang. The aim of this course is to
discuss the recent developments on Fontaine's
theory over function fields in equal characteristic.
The topics include Hodge-Pink theory over
function Fields, local shtukas and isocrystals and
analogue of Colmez-Fontaine theorem.
V. "Potential Modularity for l-representations
and Applications" given by Cristian Virdol
(Columbia University and NCTS/TPE).
Simultaneous potential modularity of a finite
number of l-adic representations coming from
Hilbert modular forms was shown, and various
applications were discussed.
VI. NCTS Seminar on "Frobenius Modules"
jointly lectured by C.-Y. Chang (NCTS postdoc)
and J.-D. Yu (NTU), 6 lectures spread from
October to December, 2010.
VII. "Abelian Varieties and Jacobian I-VIII"
given by Chia-Fu Yu (Academia Sinica) and YihJeng Yu (NCCU) in July and August 2010.
VIII. "Abelian Galois Cohomology of
Reductive Groups I-II" given by Wen-Wei Li
(Universite Paris Diderot 7, visiting NCTS July 7
to July 17, 2010).
I X . " H a r d e r- N a r a s h i m a n f i l t r a t i o n s i n
arithmetic geometry I, II" by Laurent Fargues
(CNRS, Univesite Paris-Sud, visiting TIMS for 2
weeks in July, 2010).
D.6.5 Seminars and Courses
NCTS Number Theory Seminar
This is regular weekly number theory seminar
during the academic year. It includes talks given
by visitors from abroad and reports on research
results obtained by members of the number theory
group at NCTS. There were 34 talks scheduled in
Hsinchu from January to October this year.
There is also Seminar on Arithmetic Geometry
and Representation Theory at NCTS Taipei, and
Seminar on Number Theory at Academia Sinica in
Taipei. From January to October of 2010 there are
about 30 talks scheduled in Taipei.
There are courses, student seminars aiming at
PhD students. The following are brief descriptions
of these courses.
2010 NCTS Student Seminar on Arithmetic
Algebraic Geometry organized by Wen-Ching Li.
This year long seminar focuses on p-adic Hodge
theory and its applications.
NCTS& NTHU Joint Course Noncongruence
Subgroups and Noncongruence Modular Forms
This is given by Wen-Ching Li and Andreas
Schweizer. This course consists of two parts. The
first part is to present Serre’s work which
determines when SL2 over a ring of S-integers of a
global field is a congruence subgroup. The second
part is to study modular forms for noncongruence
subgroups of SL2 (Z). The Atkin-Swinnerton-Dyer
congruences and Scholl’s work on l-adic Galois
representations associated to the space of cusp
forms of given weight for a given noncongruence
subgroup are discussed.
NCTS & NCTU Joint Course Topics in
Number Theory Modular forms -theory and
applications
This is given by Yifan Yang. Contents of the
course include: basic theory of modular forms,
construction of modular forms and applications in
number theory.
NCTS Student Seminar on Algebra and
Number Theory
This seminar is organized by Jing Yu. It aims at
Ph.D. students; speakers are students from NTHU,
NTU, NCU and NCTU. Topics discussed include
transcendence problems, Diophantine problems,
elliptic curves, and algebraic number theory, etc.
D.6.6 Summer Programs for Students
In summer 2010 there were three 6-week
summer programs for graduate as well as
undergraduate students, organized by Y. Yang and
Wei-Chen Yao at Hsin-Chu and by C.F. Yu at
Taipei respectively. The summer program at
Taipei provided opportunity for advanced
undergraduate students to learn basic materials in
algebraic number theory, while the programs at
Hsinchu were more research oriented. Several
research projects in number theory suitable for
graduate and undergraduate students were given in
order to provide students with research
experience.
D.6.7 Important Results, Breakthroughs
There are many progresses. Here we mention
only the following directions:
In the arithmetic of function fields of positive
characteristic, many results have been obtained in
this research area. The arithmetic of Shimura
curves defined over function has been studied. A
Gross-Zagier type formula for the central critical
value of L-series over imaginary quadratic
extension of rational function field F_q[t] is
obtained as well as theta series from quaternion
31 ‹‹- Highlights of the Focus Programs
algebra over function fields are studied. Using the
methods of t-motives, the algebraic independence
of the nonzero values of arithmetic Drinfeld
modular forms of positive weight at nonisogenous CM points is established. The joint
work of C.Y. Chang and M. Papanikolas on the
period conjecture for arbitrary rank Drinfeld
modules is one of the most advanced in this
direction. In their paper, they completely solved
the algebraic independence problem for Drinfeld
logarithms, and quasi-logarithms for an arbitrary
rank Drinfeld module.
Y. Yang works on the arithmetic of modular
forms. Together with his coauthors, he studied the
periods of cusp forms, determined the special
values of twisted L-function of cusp forms, and
obtained an analogue of the classical Jacobsthal
identity for the cases Q(sqrt(-2)) and Q(sqrt(-3)).
He proved new congruences for the partition
function using only modular forms of half-integral
weights without appealing to Shimura
correspondence and Galois representations. He
also discovered an explicit Shimura
correspondence for cusp forms of low level.
On the arithmetic of abelian varieties and
Siegel modular varieties, C.-F. Yu has obtained the
boundedness property of the p-exponents of the
co-indices of the endomorphism rings of abelian
varieties over a field of positive characteristic.
C.-F. Yu continued his joint work with Gortz in
investigating Siegel modular varieties in positive
characteristic with Iwahori level structure. They
completely described the Kottwitz-Rapoport strata
contained in the supersingular locus as disjoint
unions of Deligne-Lustig varieties. C. Virdol
extended the work of Shimura and Yoshida on
central values of L-functions of Galois
representations attached to Hilbert modular forms
to their arbitrary totally real base change.
M.-L. Hsieh works on Iwasawa theory. He
successfully constructed an ordinary p-adic
Eisenstein series with desired properties on the
unitary group U(3,1), which is the first step in his
pursuit of the general theory. J.-D. Yu works on
arithmetic geometry, specializing in Calabi-Yau
varieties and p-adic Hodge theory.
The application of Diophantine approximation
to Diophantine problems is one of the main topic
in the focus group. In particular, applying
Nevanlinna theory over nonarchimedea fields, J.Y.
Highlights of the Focus Programs -›› 32
Wang collaborated with Ta Thi Hoai An and
Aaron Levin to study certain Diophantine
problems over the ring of integers and the field of
rational numbers. They established a
correspondence between p-adic Nevanlinna theory
and certain statement of Diophantine problems
over the ring of integers or the field of rational
numbers. L.-C.Hsia and J.Silverman applying
results in Diophantine approximation to obtain a
quantitative results concerning the number of
integral points in the orbit of a given rational
numbers under the iterations of a rational function
of degree greater than of equal to 2 over the
rational numbers.
W. - C . L i c o n t i n u e d h e r s t u d y o n
noncongruence modular forms. In a joint work
with T. Liu and L. Long, they established the
modularity of degree 4 Scholl representations with
quaternion multiplications, and also proved the
Atkin-Swinnerton-Dyer congruences for the
underlying 2-dimensional space of noncongruence
forms. She also worked jointly with C.-J. Wang
and her Ph.D. student Y. Fang to successfully
obtain zeta function identity for complexes arising
from buildings of GSp(4, F).
D.6.8 Accomplishments
[1] T
a Thi Hoai An, Aaron Levin and J.-Y. Wang,
A p-adic Nevanlinna-Diophantine
correspondence, Acta Arithmetica(2010)(to
appear)
[2] A . O. L. Atkin, W.-C. W. Li, T. Liu and L.
Long, Galois representations with quaternion
multiplications associated to noncongruence
modular forms, submitted, 2010.
[3] C.-Y. Chang, M. A. Papanikolas, D. S. Thakur
a n d J . Yu , A l g e b r a i c i n d e p e n d e n c e o f
arithmetic gamma values and Carlitz zeta
values, Adv. Math. 223 (2010), 1137-1154.
[4] C.-Y. Chang, M. A. Papanikolas and J. Yu,
Geometric gamma values and zeta values in
positive characteristic, Int. Math. Res. Notices
(2010) vol. 8, 1432-1455.
[5] C.-Y. Chang, M. A. Papanikolas and J. Yu,
Frobenius difference equations and algebraic
independence of zeta values in positive equal
characteristic, to appear in Algebra & Number
Theory.
[6] C
.-Y. Chang, Transcendence of special values
of quasi-modular forms, to appear in Forum
Math.(DOI 10.1515/FORM. 2011. 072)
[7] C . - Y. C h a n g a n d M . A . P a p a n i k o l a s ,
Algebraic relations among periods and
logarithms of rank 2 Drinfeld modules, to
appear in Amer. J. Math.
[8] Heng Huat Chan, Ling Long, and Yifan Yang,
A cubic analogue of the Jacobsthal identity,
Amer. Math. Monthly, to appear.
[9] S hinji Fukuhara and Yifan Yang, Twisted
Hecke L-values and period polynomials, J.
Number Theory 130 (2010), 976-999.
[10] U . Görtz and C.-F.Yu, Supersingular
Kottwitz-Rapoport strata and Deligne-Lusztig varieties, to appear in J. Inst. Math.
Jussieu. 9 (2010), 357-390.
[11] U. Görtz and C.-F. Yu, On the supersingular
locus in Siegel modular varieties with
Iwahori level structure. arXiv:0807.1229, 27
pages. To appear in Math. Ann., 2011.
[12] L.-C. Hsia and J. Silverman, A quantitative
estimate for quasi-integral points in orbits,
Pacific Journal of Math., in press.
[13] M .-L. Hsieh Ordinary p-adic Eisenstein
series and p-adic L-functions for unitary
Groups. To appear in Annales de l’Institut
Fourier (Grenoble) 60 (2010).
[14] M .-L. Hsieh, The algebraic functional
equation of Selmer groups for CM fields, J.
Number Theory, 30 (2010), 1914-1924.
[15] A ristides Kontogeorgis and Yifan Yang,
automorphism groups of hyperelliptic
modular curves, LMS J. Comp. Math. 13
(2010), 144-163.
[16] M.-H. Kang and W.-C. Li, Zeta functions of
complexes arising from PGL(3), submitted
2010.
[17] M.-H. Kang, W.-C. Li and C.-J. Wang, The
zeta functions of complexes from PGL(3): a
representation theoretic approach, Israel J.
Math. Vol. 177, no. 1, 2010, 335-348.
[18] W.-C. Li, Modular curves and coding theory
: a s u r v e y, P r o c e e d i n g s o f t h e N i n t h
International Conference on Finite Fields
and Applications, Dublin, Contemporary
Math. vol 518, 301-313 (2010), Amer. Math.
Soc., Providence.
[19] W
.-C. Li, Zeta functions of group based
graphs and complexes. Fields
Communications Volume WIN - Women In
Numbers, Proceedings of the WIN
Workshop, Banff International Research
Station, Banff, Canada, to appear.
[20] W.-C. Li, Zeta functions in combinatorics
and number theory, Proceedings of the 4th
International Congress of Chinese
Mathematicians, Hangzhou, China, 2007,
AMS/IP Studies in Advanced Mathematics,
vol. 48 (2010), 351-366.
[21] A. Schweizer, Value-sharing of meromorphic
functions on a Riemann surface, Journal of
Mathematical Analysis and Applications 365
(2010), 220-228
[22] T . - Y. W a n g a n d C h i e n - W e i L i n ,
Generalizations of rigid analytic Picard
theorems, Proceedings of A.M.S., 138(2010),
133-139.
[23] W.-C. Yao and J. Yu, On primitive roots for
rank one Drinfeld modules, Journal of
Number Theory 130 (2), 2010.
[24] Yifan Yang, Congruences of the partition
function, Int. Math. Res. Not., in press.
[25] Y. Yang and W. Zudilin, On Sp4 modularity
of Picard-Fuchs differential equations for
Calabi-Yau threefolds, Contemporary Math
517, 381-413.
[26] Yifan Yang and Jeng-Daw Yu, structure of
the cuspidal rational torsion subgroups of
J_1(p^n), J. London Math. Soc 82 (2010),
203-228.
[27] Y. Yang and S. Fukurara, Twisted Hecke
L-values and period polynomials, to appear
in Journal of Number Theory.
[28] Y . Y a n g a n d A . K o n t o g e o r g i s ,
Automorphidsm groups of hyperelliptic
curves, to appear in LMS J. Comp. Math.
[29] Y. Yang, On congruence of the partition
function, Int. Math. Res. Not., in press.
[30] C.-F. Yu, Simple mass formulas on Shimura
varieties of PEL-type. Forum Math. 22
(2010), 565-582.
[31] C .-F. Yu, Kottwitz-Rapoport strata of the
S i e g e l m o d u l i s p a c e s . To a p p e a r i n
Taiwanese J. Math. 2011.
33 ‹‹- Highlights of the Focus Programs
[32] C
.-F. Yu, On finiteness of endomorphism
rings of abelian varieties. Math. Res. Let. 17
(2010), no. 2, 357-370.
[33] C.-F. Yu, Geometry of the Siegel modular
threefold with paramodular level structure.
arXiv:0907.5263, 10 pp. To appear in Proc.
Amer. Math. Soc.
[34] J .-D. Yu, Special lifts of ordinary K3
surfaces and applications. To appear in Pure
Appl. Math. Q. 2011.
D.6.9 E xchange programs and
international cooperations
An MOU with Pohang Mathematics Institute,
Postech, Korea was signed in July 2010. Another
MOU with the Independent University in Moscow
and the CNRS research group in Marseille on
arithmetic and applications are in the working.
This year NCTS has supported young
members, PhD students in our focus group to
attend conferences, schools as well as individual
visits for international collaborations. These
activities include (in terms of countries):
Canada: In March 2010, W.-C. Li organized
the Workshop on Graphs and Arithemetic at
Montreal, Canada. C.-J. Wang was invited to
speak in the workshop. This trip was under the
support of NCTS.
China: In June 2010, C.-Y. Chang was invited
to visit Tsing-Hua University at Beijing and give a
talk at the Morningside Center of Mathematics,
Beijing. In December 2010, several members
from our focus group will attend ICCM 2010 to be
held in Beijing as invited speakers.
Highlights of the Focus Programs -›› 34
Japan: In January~February, 2010, Y. Yang
has visited Ki-Ichiro Hashimoto at Waseda
University. He and two PhD. Students were
invited to attend the annual Number Theory
Conference held at Waseda University. In
February 2010, C.-Y. Chang was invited to visit
Univ. of Kyushu and give a talk at the number
theory seminar. In August~September 2010, Y.
Yang visited Shinji Fukuhara at Tsuda College. He
was invited to give a talk at Tokyo Metropolitan
University workshop and a talk at the Workshop
on number theory, geometry, and physics at the
crossroads held at Tsuda College.
USA: In February~March 2010, C.-Y. Chang,
under the support of NCTS, visited M.
Papanikolas at A&M University in Texas to
continue their joint work on the transcendence
problem in function fields. In March 2010, NCTS
supported two PhD. students and a research
assistant to attend the Arizona winter school in
arithmetic dynamical systems at Tucson.
Spain: In April 2010, C.-Y. Chang was invited
to give lectures in the Workshop on Drinfeld
modules and L-functions held at CRM, Spain. The
main theme of this workshop centered at the
recent development in transcendence theory,
Iwasawa theory, and L-functions in function
fields.
France: In July 2010, under the support of the
Franch-Taiwan joint research project –The Orchid
Program, L.-C. Hsia, W.-C. Yao and one PhD
student visited Jean-Yves Briend at C.M.I.,
University de Marseille France. During the visit,
they participated in discussions and seminar at
C.M.I.
D.7 Partial Differential Equations
Coordinators: J ong-Shenq Guo (Tamkang University), Tai-Chia Lin (National Taiwan University),
Jenn-Nan Wang (National Taiwan University), Jann-Long Chern (National Central University),
Yung-Fu Fang (National Cheng Kung University)
D.7.1 Research Goals and Contents
. Nonlinear Schrödinger equations
(1) B lowup ring profiles of two-component
systems of NLS Blowup solutions of nonlinear
Schrödinger equations (NLSEs) may describe
nonlinear wave collapse, which is universal to
many areas of physics including nonlinear
optics, plasma physics, and Bose-Einstein
condensates (BECs). The spatial profile of a
collapsing wave may evolve into a universal,
self-similar, circularly symmetric shape with a
single peak known as the Townes profile,
which has been observed experimentally by
amplified laser beams. In high-power laser
beams, different collapsing behaviors may
develop blowup ring profiles which break into
filaments with multi-Townes profiles under the
effect of noise. It would be naive to think that
ring profiles can be obtained by finding the
blowup solutions of NLS. One may find
blowup solutions of NLS with ring profiles but
those solutions have infinite L2 norm, so one
may not maintain the ring profile all the way
up to the singularity. It is still an open issue
whether there are H1 non-vortex blowup
solutions with ring profiles. In this
subprogram, we want to find H1 non-vortex
blowup solutions with ring profiles from twocomponent systems of NLS instead of single
NLS
(2) Orbital stability of bound states of NLS
ecently, optical lattices have created many
R
interesting phenomena in Bose–Einstein
condensates (BECs) and attracted a great deal
of attention. Two types of optical lattices are
considered: a linear optical lattice (OL) and a
nonlinear OL. A linear OL is a series of
potential wells having a periodic (in space)
intensity pattern which may confine atoms of
BECs in the potential minima. A nonlinear OL
can be obtained by inducing a periodic spatial
variation of the atomic scattering length,
leading to a periodic space modulation of the
nonlinear coefficient in GPE (a kind of NLS)
governing the dynamics of BECs.
Experimentally, bright solitons can be
observed in linear and nonlinear OLs,
respectively. One may find stable bright
solitons in three-dimensional linear OLs. On
the other hand, two-dimensional bright solitons
can also be investigated in two-dimensional
nonlinear OLs. Consequently, under the
influence of linear and nonlinear OLs, twodimensional bright solitons must have suitable
stability for experimental observations.
However, most theoretical results focus on the
orbital (dynamical) stability of only onedimensional single-spike bound states which
are steady state bright solitons in onedimensional nonlinear OLs without the effect
of linear OLs. To see how linear and nonlinear
OLs affect the stability of two-dimensional
single-spike bound states, we develop
mathematical theorems for the orbital stability
and instability of two-dimensional single-spike
bound states of GPE under different conditions
of linear and nonlinear OLs.
(3) W
e also study bilinear estimates for
Schrödinger waves, well posedness problem
for wave type problems, including a system of
coupled Schrödinger equations arose from a
problem of Bose-Einstein Condensation, and
scattering problems.
II. Parabolic equations
(1) Pattern formation and travelling waves
e are interested in the existence of entire
W
solutions defined for all time from negative
35 ‹‹- Highlights of the Focus Programs
infinity to plus infinity in reaction-diffusion
equations. In particular, the combination of two
fronts coming from two far sides of real line
gives the so-called 2-front entire solution. Also
we study the existence and uniqueness of
stabilized propagating wave segments in wave
front interaction model which is established by
Zykov and Showalter. For discrete lattice
dynamical systems, we have been studying the
existence of traveling fronts for different
settings, including homogeneous and
heterogeneous media. These models arise in,
for example, the study of competition of two
species when the habitat is divided into
discrete regions.
(2) Formation of singularity
here are many questions about blow-up (or
T
dead-core) behavior for parabolic equations.
Among them, we are interested in studying the
time asymptotic rate of the singularity and the
locations of singularity. It is know classically
that the self-similar singular rates are verified
in many cases. Recently, the non-self-similar
rate is found in many examples. One of them is
so-called type II singularity. For the locations
of singularity, we investigate whether a zero of
the potential can be a blow-up point, if the
solution blows up in finite time. This is an
on-going project. We have some interesting
results.
III. Inverse Problems
(1) We continue our study on the quantitative
estimates for elliptic type of partial differential
equations. Previously, we have successfully
derived quantitative estimates for second and
higher order elliptic equations. Those estimates
are extremely useful in other problems such as
inverse problems. Recently, we have extended
the method to a system of partial differential
equations combining second and fourth order
of elliptic equations. One of these systems is
the shallow shell system.
(2) We focus on uniqueness continuation theorem,
Carleman estimates, and related inverse
problems. We plan to extend the technique to
the Stokes system. The equations for the
velocity and the pressure are not symmetric. In
addition, we consider the same problem for the
parabolic equations.
Highlights of the Focus Programs -›› 36
IV. Nonlinear elliptic equations
(1) C
hern-Simons-Higgs model and Louville type
equation
(2) M
inimizers of Cafarelli-Kohn-Nirenberg
Problem: the Cafarelli-Kohn-Nirenberg
inequality is generalized to the functions with
singularities on the boundary of the domain.
(3) T
he uniqueness problem of Hamiltonian,
Liouville type and coorperative elliptic system
(4) P
roperties of nodal solution for elliptic
equations and Sturm-Liouville equations
(5) W
e also investigate homogenization problems,
stability of traveling waves, and integral
equation problems.
Local focus group:
Chiun-Chuan Chen (NTU), Chao-Nien Chen
(NCUE), I-Liang Chern (NTU), Jenn-Long Chern
(NCU), Yung-Fu Fang (NCKU), Jong-Shenq Guo
(TKU), Chun-Hsiung Hsia (NTU), Jiann-Sheng
Jiang (Tung Fang IT), Chun-Kong Law (NSYSU),
Jyh-Hao Lee (AS), Kuo-Ming Lee(NCKU), ChunChi Lin (NTNU), Ching-Lung Lin (NCKU),
Chang-Shou Lin (NTU), Tai-Chia Lin (NTU),
Dong-Ho Tsai (NTHU), Je-Chiang Tsai (CCU),
Jenn-Nan Wang (NTU), Tsung-fang Wu (NUK)
D.7.2 Conference and Workshop
• 2
010 Conference in Differential
Equations, January 08~09, 2010
Speakers:
Sze-Bi Hsu(許世壁) (National Tsing Hua
University), Yoh Iwasa (Kyushu University),
Chao-Nien Chen (陳兆年) (National Changhua
University), Chih-Wen Shih (石至文) (National
Chiao Tung University), Meng-Kai Hong (洪盟
凱) (National Central University), Ching-Lung
Lin (林景隆) (National Cheng Kung University),
Kwangseok Choe (Inha University), Keh-Ming
Shyue(薛克民) (National Taiwan University),
Wei-Cheng Wang (王偉成) (National Tsing Hua
University), Wen-Hann Sheu (許文翰) (National
Taiwan University), Jeng-Tzong Chen (陳正宗)
(National Taiwan Ocean University), Wei-Chih
L i u ( 劉 威 志 ) ( N a t i o n a l Ta i w a n N o r m a l
University), Chun Liu (柳春) (The Penn State
U n i v e r s i t y), J i n g-F a n g H u a n g (黃京芳)
(University of North Carolina at Chapel), Yoshio
Sone (Kyoto University), Yu-Lin Lin (林玉琳)
(Academia Sinica), Jin-Cheng Jiang (江金城)
(Academia Sinica), Chun-Hsiung Hsia (夏俊雄)
(National Taiwan University), I-Kun Chen (陳逸
昆)(Academia Sinica), Jong-Shenq Guo (郭忠勝)
(National Taiwan Normal University), Namkwon
Kim(Chosun University) , Ming-Chih Lai (賴明
治) (National Chiao Tung University), Tzyy-Leng
Horng (洪子倫) (Feng Chia University), ChinTi e n Wu (吳金典) (N a t i o n a l C h i a o Tu n g
University)
• F
ourth Workshop on Nonlinear Partial
Differential Equations: Analysis,
Computation and Applications, June
11~14, 2010
Speakers:
Hyeong-Ohk Bae (Ajou University, Korea),
Jose Antonio Carrillo (Universitat Autònoma de
Barcelona, Spain), Tong Keun Chang (Korea
Institute for Advanced Study), Li Chen (TsingHua
University, China) , Ching-Hsiao Cheng (National
Central University, Taiwan), Wai Sun Don (Hong
K o n g B a p t i s t U n i v e r s i t y ) , Yu n g - F u F a n g
(National Cheng Kung University, Taiwan),
Meng-Kai Hong (National Central University,
Taiwan) , Chun-Hsiung Hsia (National Taiwan
University, Taiwan), BumJia Jin (Mokpo National
University, Korea), Hyeonbae Kang (Inha
University, Korea), Shuichi Kawashima (Kyushu
University, Japan) , Chi-Kun Lin (National Chiao
Tung University, Taiwan), Tai-Chia Lin (NTU,
Taiwan), Yu-Lin Lin (Academia Sinica, Taiwan),
Jie Liu (National University of Singapore), TaiPing Liu (Academia Sinica, Taiwan), Tao Luo
(Georgetown University, USA), Yasunori
Maekawa (Kobe University, Japan), Takayoshi
Ogawa (Tohoku University, Japan), Yu Hin Pang
(National University of Singapore), Yosio Sone
(Kyoto University and Academia Sinica),
Athanasios Tzavaras (University of Maryland,
USA), Xiao-Ping Wang (Hong Kong University of
Technology), Zhou Ping Xin (Chinese University
of Hong Kong), ChuanJu Xu (Xiamen University,
China)
• 2
010 Taiwan-Japan Joint Workshop on
Inverse Problems, Nov. 20(Sat.) - 22(Mon.),
2010
Speakers:
Hitoshi Imai 今井 仁司 (The University of
To k u s h i m a), Yu u s u k e I s o 磯 祐介 (K y o t o
University), Hiroshi Fujiwara 藤原 宏志 (Kyoto
University), Naoki Wada 和田 尚樹 (Kyoto
University), Daiki Tanaka 田中 大毅 (Kyoto
University), Yoshihiro Sawano 澤野 嘉宏 (Kyoto
University), Yoko Hoshi 星 詳子 (Tokyo Institute
of Psychiatry), Nobuyuki Higashimori 東森 信就
(Hitotsubashi University), Hideki Takuwa 多久和
英樹 (Doshisha University), Gen Nakamura 中村
玄 (Hokkaido University), Chen, Jeng-Tzong 陳
正宗 (Taiwan Ocean University), Cheng-Hung
Huang 黃正弘 (Cheng Kung University), ChengChien Liu 劉正千 (Cheng Kung University),
Hong-Kun Xu 徐洪坤 (Sun Yat-Sen University),
Chun-Kong Law 羅春光 (National Sun Yat-sen
University), Ching-Lung Lin 林景隆 (Cheng
Kung University), Min-Hsiung Lin 林敏雄
(Chung Cheng University), Chin-Tien Wu 吳金典
(Chiao Tung University), Pengwen Chen 陳鵬文
(Taiwan University), Rulin Kuan 關汝琳 (Taiwan
University)
• 1
9th Workshop on Differential Equations
and Its Application, Jan. 14-17, 2011
Foreign Speakers:
Yoshio Tsutsumi (Kyoto University), Kenji
Nakanishi (Kyoto University), Tohru Ozawa
(Waseda University), Tetsu Mizumachi (Kyushu
U n i v e r s i t y ) , Ta k a y o s h i O g a w a ( To h o k u
U n i v e r s i t y ) , K o t a r o Ts u g a w a ( N a g o y a
University), Rainer Kress (University
Goettingen), Hideo Kozono (Tohoku University),
Sanghyuk Lee (Seoul National University), Hideo
Takaoka (Hokkaido Univerity), Gen Nakamura
(Hokkaido Univerity), Nobu Kishimoto (Kyoto
University), Masayasu Mimura (Meiji
University), Hideo Ikeda (Toyama University),
Hirokazu Ninomiya (Meiji University), Richard
Tsai (University of Texas, Austin), Do Young
Kwak (Korea Advanced Institute of Sci and Tech),
Tsorng-Whay Pan (University of Houston),
Daishin Ueyama (Meiji University), Yuusuke Iso
(Kyoto University)
• C
onference in Dynamical Systems: A
Celebration in honor of Kenneth James
Palmer on his Retirement
37 ‹‹- Highlights of the Focus Programs
Speakers:
Shui-Nee Chow (Georgia Institute of
Technology, USA), Peter Kloeden (J.W. Goethe
Universitaet, Germany), Huseyin Kocak
(University of Miami, USA), Sergei Pilyugin (St.
Petersburg State University, Russia), Yi-Chiuan
Chen (Academia Sinica), Chen-Chang Peng
(National Chiayi University), Jung-Chao Ban
(National Dong Hwa University), Ming-Chia
Li(National Chiao Tung University),
D.7.3 Important Results, Breakthrough
1. T
. C. Lin, J. Wei and W. Yao, Orbital stability
of bound states of nonlinear Schrodinger
equations with linear and nonlinear optical
lattices, JDE 249 (2010) 2111-2146.
e study the orbital stability and instability of
W
single-spike bound states of semi-classical
nonlinear Schrödinger (NLS) equations with
critical exponent, linear and nonlinear optical
lattices (OLs). These equations may model
two-dimensional Bose–Einstein condensates in
linear and nonlinear OLs. When linear OLs are
switched off, we derive the asymptotic
expansion formulas and obtain necessary
conditions for the orbital stability and
instability of single-spike bound states,
respectively. When linear OLs are turned on,
we consider three different conditions of linear
and nonlinear OLs to develop mathematical
theorems which are most general on the orbital
stability problem.
2. X
. Chen, T. C. Lin and J. Wei, Blowup and
solitary wave solutions with ring profiles of
two-component nonlinear Schrödinger systems,
Physica D 239 (2010) 613-626.
lowup ring profiles have been investigated by
B
finding non-vortex blowup solutions of
nonlinear Schrödinger equations (NLSEs) (cf.
Fibich et al. 2005 and Fibich et al. 2007).
However, those solutions have infinite L2
norm, so one may not maintain the ring profile
all the way up to the singularity. To find H1
non-vortex blowup solutions with ring profiles,
we study the blowup solutions of two
component systems of NLSEs with suitable
n o n l i n e a r c o e ff i c i e n t s . T h e n t h e t w o component system can be transformed into a
Highlights of the Focus Programs -›› 38
multi-scale system with fast and slow variables
which may produce H1 blowup solutions with
non-vortex ring profiles. We use the localized
energy method with symmetry reduction to
construct these solutions rigorously. On the
other hand, these solutions may describe steady
non-vortex bright ring solitons. Various types
of ring profiles including m-ring and ring-ring
profiles are presented by numerical solutions.
3. H
. Berestycki, T. C. Lin, J. Wei and C. Zhao,
On Phase-Separation Model: Asymptotics and
Qualitative Properties, Preprint.
4. J .-S. Guo, C.-T. Ling and P. Souplet, Non-selfsimilar dead-core rate for the fast diffusion
equation with strong absorption, Nonlinearity
23 (2010/03), 657-673
e study the dead-core problem for the fast
W
diffusion equation with strong absorption.
Unlike in many other related problems of
singularity formation, we show that the
temporal rate of formation of the dead-core is
not self-similar. We moreover obtain precise
estimates on rescaled solutions and on the
single point final dead-core profile. Results of
this type were up to now known only for
problems with linear diffusion. The proofs rely
on self-similar variables and a delicate use of
the Zelenyak method.
5. J .-S. Guo, H. Ninomiya, and J.-C. Tsai,
Existence and Uniqueness of stabilized
propagating wave segments in wave front
interaction model, Physica D: Nonlinear
Phenomena 239 (2010/02), 230-239.
e use the model of Zykov and Showalter in
W
2005 to study the existence of stabilized
propagating wave segments. In this model, a
stabilized propagating wave segment can be
described by two systems of ordinary
differential equations, one for the wave front
and one for the wave back. Although this
model is a reduction of two-component
reaction diffusion system, it can still reflect the
essential behavior of stabilized propagating
wave segments. Moreover, it is easier to handle
analytically, and only the key parameters are
involved in this model. Within this frame, we
have established that for each given size of the
wave segment, there exists a unique
excitability such that the stabilized wave
segment with the given size can propagate in
the corresponding medium. Our analysis also
shows that there are two types of the profiles of
stabilized wave segments, namely, convex and
non-convex types. In particular, the wave
profile is of convex type when the normalized
propagating velocity is small. However, it is of
non-convex type when the normalized
propagating velocity is close to 1.
6. T
he Liouville type equation with exponential
nonlinearity and delta measure source in two
dimension is closed related to the limit case of
Chern-Simon models and the electroweak
theory. We have completed the study of sharp
blowup behavior for this equation which has
been invited to publish in special issues to
celebrate the 85th birthday of Louis Nirenberg
edited by Luis Caffarelli and Yanyan Li.: Chen,
C.-C. and Lin, C.-S., Mean field equations of
Liouville type with singular data: sharper
estimate, Discrete and Continuous Dynamical
Systems Vol 28, No 3 (2010), 1237-1272.
7. J .-L. Chern, Z.-Y. Chen and C.-S. Lin,
Uniqueness of Topological Solutions and The
Structure of Solutions for the Chern-Simons
Equations with Two Higgs Particles, Commun.
Math. Phys. 296, 323–351 (2010).
he existence of topological solutions for the
T
Chern-Simons equation with two Higgs
particles has been proved by Lin, Ponce and
Ya n g [ 2 0 0 8 , J FA ] . H o w e v e r, b o t h t h e
uniqueness problem and the existence of nontopological solutions have been left open. In
this paper, we consider the case of one vortex
at origin. Among others, we prove the
uniqueness of topological solutions and give a
complete study of the radial solutions, in
p a r t i c u l a r, t h e e x i s t e n c e o f s o m e n o n topological solutions. We can also classify the
structure of all radial solutions as a clear
pictures.
8. J .-L. Chern and C.-S. Lin, Minimizers of
Cafarelli-Kohn-Nirenberg inequality with the
singularity on the boundary, Archive for
Rational Mechanics and Analysis 197 (2010),
401-432.
he Cafarelli-Kohn-Nirenberg inequality is
T
generalized to the functions with singularities
on the boundary of the domain.
9. J .-L. Chern, Z.-L. Chen, C.-S. Lin and Y.-L.
Tang, Uniqueness and structure of Solutions to
the Derichlet Problem for an Elliptic System,
Journal of Differential Equations 246 (2009).
iggs particle has been intensively studied in
H
the past twenty years. By investigating the
properties for the corresponding linearized
equations of solutions, and adopting the
Pohozaev identity and Implicit Function
Theorem, we show the uniqueness and the
structure of solutions.
• J .-L. Chern, Z.-Y. Chen, J. Shi and Y.-L.
Tang, On the Uniqueness and Structure of
Solutions to a Coupled Elliptic System, To
appear in Journal of Differential Equations,
2010.
In this paper, we consider a nonlinear elliptic
system which is an extension of the single
equation derived by investigating the
stationary states of the nonlinear Schrodinger
equation. We establish the existence and
uniqueness of solutions to the Dirichlet
problem on the ball. In addition, the
nonexistence of the ground state solutions
under certain conditions on the nonlinearities
and the complete structure of different types
of solutions to the shooting problem are
proved.
• J .-L. Chern, Z.-Y. Chen, Y.-L. Tang and
Z.-H. Chen, On the Classifications of
Standing Wave Solutions for the Schrodinger
Equation, Comm. in Partial Differential
Equations 35(2010), 275-301.
he entire structure of radial solutions is
T
clarified according to their behaviors at the
origin and infinity.
• J .-L. Chern, Z.-Y. Chen and Y.-L. Tang,
Uniqueness of Finite Total Curvature and
Structure of Radial Solutions for Nonlinear
Elliptic Equations, To appear in Transactions
of American Mathematical Society, 2010.
he relation between the structure of positive
T
radial solutions and the total curvature is
derived.
• J .-L. Chern, C.-S. Lin, J. Shi and Y.-L. Tang,
Existence, uniqueness and stability of
positive solution to sublinear elliptic
systems, To appear in P. Royal Society of
39 ‹‹- Highlights of the Focus Programs
Edinburgh: Section A Mathematics, 2010.
Reaction–diffusion systems are used to
model many chemical and biological
phenomena in the natural world, and systems
of coupled partial differential equations are
also used in other physical models such as
nonlinear Schrodinger systems in multicomponent Bose–Einstein condensates and
nonlinear optics. The steady-state solutions
or standing-wave solutions of such systems
of nonlinear partial differential equations
satisfy a nonlinear elliptic system with more
than one equation. Much effort has been
devoted to the existence of solutions of such
systems, but it is usually difficult to
determine whether or not the solution is
unique. The existence, stability and
uniqueness of positive solutions to a
sublinear elliptic system are proved. It is
shown that the precise global bifurcation
diagram of the positive solutions is a
monotone curve with different asymptotical
behaviour according to the form of the
nonlinearities. Equations with Holder
continuous nonlinearities are also
considered.
10. C
.K. Law (羅春光): We study an inverse
nodal problem, concerning the reconstruction
of a potential of a Sturm-Liouville operator
by using zeros of one eigenfunction as input.
We p r o p o s e t h r e e m e t h o d s f o r t h e
reconstruction, one of which is the Tikhonov
regularization method. The explicit error
bounds are calculated for all the three
methods. In case there is measurement error,
the Tikhonov regularization method is still
convergent. The study is motivated by
physical considerations.
11. Je-Chiang Tsai (蔡志強): λ–ω systems are
reaction–diffusion systems whose reaction
kinetics admits a stable limit cycle. It is known
that λ–ω systems can possess various types
of solutions. Among them, spiral waves are the
most fascinating pattern. However, the effects
of the diffusivity, the sizes of the domains, and
the reaction kinetics on spiral waves are
largely unknown. In this paper, we investigate
how these quantities affect the properties of
m-armed spiral waves in a generalized class of
λ–ω system on a circular disk with no-flux
boundary condition. First we derive a criterion
Highlights of the Focus Programs -›› 40
for the existence of m-armed spiral waves.
Specifically, we show that m-armed spiral
waves do not exist for, while for , there exists
an m-armed spiral wave if the twist parameter
q is small. Here d is the diffusivity for the
λ–ω system, R is the radius of the circular
disk, λ_0 is the value of the function λ(A) at
A=0, and jm is the first positive zero of the
first derivative of the Bessel function of the
first kind of order m. We also show that the
critical diffusivity is a bifurcation point. Next
we use the numerical simulation to show that,
for small twist parameter, the rotational
frequency increases with increasing domain
size, while for large twist parameter, the
dependence of the rotational frequency on the
domain size is not monotonic. Moreover, small
circular domains may change the properties of
spiral waves drastically. These numerical
results are in contrast to those in excitable
media. Finally, the stability of spiral waves is
investigated numerically.
12.Ching-Lung Lin (林景隆): We study the local
behavior of a solution to the Stokes system
with singular coefficients in Rn with n = 2; 3.
One of our main results is a bound on the
vanishing order of a nontrivial solution u
satisfying the Stokes system, which is a
quantitative version of the strong unique
continuation property for u. Different from the
previous known results, our strong unique
continuation result only involves the velocity
field u. Our proof relies on some delicate
Carleman-type estimates. We first use these
estimates to derive crucial optimal three-ball
inequalities for u. Taking advantage of the
optimality, we then derive an upper bound on
the vanishing order of any nontrivial solution u
to the Stokes system from those three-ball
inequalities. As an application, we derive a
minimal decaying rate at infinity of any
nontrivial u satisfying the Stokes equation
under some a priori assumptions.
13. Tsung-fang Wu(吳宗芳): We study a class of
semilinear elliptic equations in RN+ with
nonlinear boundary condition and signchanging weight function. By means of the
Lusternik- Schnirelman category, multiple
positive solutions are obtained.
D.7.4 Publications
[1] X
. Chen, T. C. Lin and J. Wei, Blowup and
solitary wave solutions with ring profiles of
two-component nonlinear Schrödinger
systems, Physica D 239 (2010) 613-626.
[2] T. C. Lin, J. Wei and W. Yao, Orbital stability
of bound states of nonlinear Schrodinger
equations with linear and nonlinear optical
lattices, JDE 249 (2010) 2111-2146.
[3] J .-S. Guo, C.-T. Ling and P. Souplet, Nonself-similar dead-core rate for the fast
diffusion equation with strong absorption,
Nonlinearity 23 (2010/03), 657-673
[4] J .-S. Guo, H. Ninomiya, and J.-C. Tsai,
Existence and Uniqueness of stabilized
propagating wave segments in wave front
interaction model, Physica D: Nonlinear
Phenomena 239 (2010/02), 230-239.
[5] C hen, C.-C. and Lin, C.-S., Mean field
equations of Liouville type with singular data:
sharper estimate, Discrete and Continuous
Dynamical Systems Vol 28, No 3 (2010),
1237-1272
[6] Ching-Lung Lin, Gunther Uhlmann, and JennNan Wang, Optimal Three-Ball Inequalities
and Quantitative Uniqueness For The Stokes
System, Discrete and Continuous Dynamical
Systems, Vol. 28, No 3, November 2010,
1~XX
[7] X infu Chen, Y.H. Cheng, and C.K. Law,
Reconstructing Potentials From Zeros Of One
Eigenfunction, to appear in Transactions of
the American Mathematical Society.
[8] Jann-Long Chern, Z.-Y. Chen and C.-S. Lin,
Uniqueness of Topological Solutions and The
Structure of Solutions for the Chern-Simons
E q u a t i o n s w i t h Tw o H i g g s P a r t i c l e s ,
Commun. Math. Phys. 296, 323-351 (2010).
(29 Pages)
[9] Jann-Long Chern and C.-S. Lin, Minimizers
of Cafarelli-Kohn-Nirenberg inequality with
the singularity on the boundary, Archive for
Rational Mechanics and Analysis 197 (2010),
401-432. (32 Pages)
[10] J ann-Long Chern, Z.-Y. Chen, Y.-L. Tang
and Z.-H. Chen, On the Classifications of
Standing Wave Solutions for the Schrodinger
Equation, Comm. in Partial Differential
Equations 35 (2010), 275-301. (27 Pages)
[11] J ann-Long Chern, Z.-Y. Chen and Y.-L.
Tang, Uniqueness of Finite Total Curvature
and Structure of Radial Solutions for
Nonlinear Elliptic Equations, To appear in
Transactions of American Mathematical
Society, 2010. (25 Pages)
[12] J ann-Long Chern, Z.-Y. Chen, J. Shi and
Y.-L. Tang, On the Uniqueness and Structure
of Solutions to a Coupled Elliptic System, To
appear in Journal of Differential Equations,
2010. (29 Pages)
[13] Jann-Long Chern, C.-S. Lin, J. Shi and Y.-L.
Tang, Existence, uniqueness and stability of
positive solution to sublinear elliptic
systems, To appear in Proc. Royal Society
of Edinburgh: Section A, 2010. (20 Pages)
[14] Z.-Y. Chen, Jann-Long Chern and Y.-L.Tang,
Erratum to "On the Classification of
Standing Wave Solutions for the Schrodinger
Equation", Comm. in Partial Differential
Equations 35 (2010), 1920-1921.
[15] Je-Chiang Tsai (2010), Rotating spiral waves
in λ–ω systems on circular domains,
Physica D: Nonlinear Phenomena, Vol. 239,
Issue 12, 1007-1025
[16] Tsung-fang Wu (2010), Multiplicity of
Positive Solutions for A Semilinear Elliptic
Equation In Rn+ with Nonlinear Boundary
Condition, Communications on Pure And
Applied Analysis, Vol. 9, No 6, 1675-1696
[17] C. Hsia, Bifurcation of Binary Systems with
t h e O n s a g e r M o b i l i t y, J o u r n a l o f
Mathematical Physics, 2010
[18] J . L. Bona, C. Hsia, T. Ma and S. Wang,
Hopf bifurcation for two-dimensional
doubly-diffusive convection, Applicable
Analysis, 2010.
[19] C . Hsia, T. Ma and S. Wang, Rotating
Boussinesq equations: dynamic stability and
transitions, Discrete and Continuous
Dynamical Systems. Series A, 2010
41 ‹‹- Highlights of the Focus Programs
D.8 Probability Theory & Related Topics
Coordinators: Yuan-Chung Sheu (National Chiao Tung University) and Narn-Rueih Shieh (National Taiwan University)
A. Research Goals and Contents
(I) T
he Probability Focus Program of NCTS
at Hsinchu
he yearly project on the topic of finite
Markov chains is to explore the
L2-mixing of reversible Markov processes. Under
the measurement of the sup-L2-distance
(maximum over all initial distributions), there is
an equivalent condition on the L2-cutoff, a sharp
phase-transit phenomenon, for families of Markov
processes using the product of the L2-mixing time
and the spectral gap. But, however, this condition
can fail if the underlying distance has specified
initial distribution instead of the maximal one.
Our goal is to find out an equivalence of cutoff
and determine the cutoff time, which is also the
mixing time if a cutoff happens. We have
successfully found out the equivalent condition
for the L2-cutoff and obtain a formula on the
corresponding mixing time. The theoretical results
have been published in an academic journal.
Our main objective on Lévy processes and
Applications is to derive explicit solutions for the
functionals of a suitable class of Markov
processes. In particular, we consider functionals of
the first exit of a matrix-exponential L\’evy
process from an open set. By transforming the
corresponding integro-differential equation into an
ODE, we show that the functional can be written
as a linear combination of known functions. In
particular, when the jump-distribution is a twosided generalized hyper-exponential distribution,
we characterize the coefficients for the functionals
in terms of a system of linear equations. As an
example of applications of our results, combining
with the smooth pasting principal, we solve the
option pricing problem for perpetual straddle and
strangle options. Our method give an alternative
approach to compute prices in jump-diffusion
models and can be used to solve a number of
Highlights of the Focus Programs -›› 42
problems from the theory of optimal stopping, the
theory of insurance ruin and risk, the theory of
credit risk, and the theory of options pricing.
As for computational finance, one of our
objectives is to investigate asymptotic behaviors
of the lower tail probability and its variance (first
and second moment) for some rare events
occurring from financial applications. We use
Monte Carlo simulation to estimate the joint
default probability and improve its accuracy by
developing an importance sampling method. We
have designed several importance sampling
algorithms to estimate lower tail probabilities in
high dimension. The optimal efficiency of these
algorithms is validated by means of large
deviation theory. This result is an alternative to the
interacting particle systems proposed by Carmona,
Fouque, and Vestal (2009). We are currently
working on variant algorithms and their
applications on computational finance and risk
management. The design of measure change for
optimal importance sampling is typically
nonstandard in the current literature, so this topic
is still under investigation.
For biological applications, we have gathered
scholars and students in the fields related to
Mathematics, Statistics, Physics, Biology, and
Engineering to discuss interdisciplinary studies for
the challenging problems in biology. As a result,
we have an international conference at NCTS in
the period of July 14-16, 2010, to invite leading
experts in Taiwan, Japan and USA to exchange
research experiences and establish collaboration
plans. For scholars and students participated in
this focus group, we have built up supporting
network in NCTS for this challenging area with
international collaborations. Hence, we have
completed the goal of this focus group in this year.
(II) T
he Probability Focus Program of
NCTS at Taipei-NTU
The Probability Focus Program of NCTS at
Taipei-NTU is on NCTS/TPE and TIMS joint
Activity in Analysis/Probability/Applications; and
toward various applications, Mathematical
Physics in particular.
B. I mportant Research Results and
Achievements
(I) T
he Probability Focus Program of NCTS
at Hsinchu
demonstrate how the criterion works, we
consider Ehrenfest processes and birth-anddeath chains with constant rates on births and
deaths. Regardless of the heavy requirements
to work out the theorem, this is the first time
that a cutoff is determined theoretically and the
cutoff time is formulated.
he result mentioned above should be regarded
T
as a frontier on the mixing of Markov
processes since currently there is indeed no
similar results developed in the related fields.
For more details, see Guan-Yu Chen and
Laurent Saloff-Coste, The L 2 -cutoff for
reversible Markov process, . J. Funct. Anal.
258 (2010), 2246-2315.
(A) I n the past year, we are trying to find an
equivalent condition on the L 2-cutoff for
families of reversible Markov processes with
specified initial distribution without knowing
exactly the L 2-mixing times. At the ARCC
workshop "Sharp Thresholds for Mixing
Times" in 2004, Yuval Peres arose a heuristic
idea on cutoffs under the measurement of
supremum (over all starting states) total
variation. His conjecture is that the total
variation cutoff exists if and only if the
product of the spectral gap and mixing time
tends to infinity. This conjecture has been
disproved by David Aldous and Igor Pak
using different type of counterexamples, but,
however, holds in the case of the supremum
LP-distance. When the initial distribution is
fixed, the conjecture fails again. To compose a
possible condition on the L2-cutoff, we start
from the finite case and write the L2-distance
in terms of the eigenvalues and eigenvectors.
By replacing the spectral gap with a modified
constant, we derive an equivalent condition on
the L2-cutoff and the form is very similar to
Peres’ conjecture. This criterion does give a
way to investigate the L2-cutoff but does not
completely solve the cutoff problem since the
L2-mixnig time is still a puzzle.
(B) M r. Yu-Ting Chen was kindly invited by
Professor Jean-Franc\c{o}is Delmas to visit
\'Ecole des Ponts ParisTech during Jan. 27 to
Feb. 3 in 2009. Besides giving a talk at the
nearby Universit\'e Paris-Est Marne-la-Vall\'ee
on our past research work in the first-passage
functionals of matrix-exponential L\'evy
processes, he also worked on a project with
Professor Delmas in mathematical biology
during this visit. In this project, they consider
a population model of stationary size given by
a weightless immortal particle and Poissonian
arrivals of continuous state branching
processes. They compute the distributions of
various variables related to the most recent
common ancestor (MRCA). Many interesting
results are reported in their recent preprint:
Yu-Ting Chen and Jean-Francois Delmas,
Smaller population size at the MRCA time for
stationary branching processes(2010).
(Professor Delmas visited NCTS in 2008 and
Yu-Ting Chen is now a Ph.D. student of UBC,
Canada.)
o find out a formula on the L2-mixing time,
T
we rewrite the L 2-distance as the Laplace
transform of the spectral measure using the
spectral decomposition. Applying the realanalyticity of Laplace transforms, we are able
to keep the equivalent condition on the
L 2-cutoff obtained before and express the
L 2 -mixng time in terms of the spectral
information. This means that we can not only
check the L 2 -cutoff without knowing the
L 2- m i x i n g t i m e b u t a l s o d e t e r m i n e t h e
threshold once the L 2 -cutoff exists. To
(C) For financial applications, we have gathered
scholars and students in the fields related to
Mathematics, Statistics, and Social Science to
discuss interdisciplinary studies for the
challenging problems in finance. For example,
we have invited Academician Jin-Chuan Duan
to give excellent lectures and suggestions on
mathematical finance. Consequently, these
activities have help a Ph. D. trained at NCTU,
Dr. Wei-fang Niu, to get a chance to work as a
Research Fellow in the Risk Management
Institute of the National University of
43 ‹‹- Highlights of the Focus Programs
Singapore (NUS). This is a great step to help
s t u d e n t s t r a i n e d i n Ta i w a n t o g a i n
international experience.
(II) T
he Probability Focus Program of
NCTS at Taipei-NTU
Accomplished papers in 2009/2010 (Narn-Rueih
Shieh (PI))
• T
he exact packing measure of Brownian double
points. Probability Theory and Related Fields
143, 2009, pp 113-136. Joint work with P.
M¨orters.
• O
n the exponentials of fractional OrnsteinUhlenbeck Processes. Electronic Journal of
Probability 14, 2009, Paper no. 23, 594-611.
Joint work with M. Matsui.
• M
ultifractal products of stationary diffusions.
Stochastic Analysis and Applications 27, 2009,
pp 475-499. Joint work with V. Anh and N.N.
Leonenko.
• Multifractal moment-scalings in geometric birth
and death processes. Bernoulli 15, 2009, pp 508531. Joint work with V. Anh and N.N. Leonenko.
• Hausdorff and Packing dimension results for the
images ofrandom fields. Bernoulli, under
revision. Joint work with Y.M. Xiao.
C. H
ighlights of NCTS International
Conference on Probability and
Statistics (July 14-16, 2010)
The NCTS International Conference on
Probability and Statistics with Applications in
Biology is a very unique conference that focuses
on this specialized topic with leading experts from
in Taiwan, Japan and USA. It is very successful to
stimulate more collaboration between researchers
in Asia and North America.
For instance, Academician Wen-Hsiung Li has
presented an inspiring talk regarding modern
sequencing technologies and their applications
that summarized the pioneering research works by
his laboratories at Academia Sinica in Taiwan and
University of Chicago in USA. Professor Satoru
Miyano and his two colleagues presented their
leading research results related to cancer studies in
his laboratory at University of Tokyo in Japan.
Highlights of the Focus Programs -›› 44
Professor Shaw-Hwa Lo and his colleague
presented their leading research results related to
genomic studies in his group at Columbia
University in USA.
We have also invited local researchers to
present their research results. For instance,
Professor Wen-Ping Hsieh in Institute of Statistics
at National Tsing Hua University presented a talk
related to the integration of array based SNP and
expression data towards biomarker identification
for oral cancer. Professor Guan-Hua Huang in
Institute of Statistics at National Chiao Tung
University presented a talk of gene expression
microarray data generator. Meanwhile, Professor
Henry Horng-Shing Lu in Institute of Statistics at
National Chiao Tung University presented a talk
for the inference of biological pathway from gene
expression profiles by time delay Boolean
networks.
Other outstanding researchers also presented
their leading results and the details of this
conference are post at the conference web page
hosted in the web site of NCTS (http://math.cts.
nthu.edu.tw/Mathematics/2010PSAB0714-16.
htm). As a result, we have built up the supporting
network in NCTS for this challenging area with
international collaborations.
D. S eminars/Courses/Workshops/
Visitors
(a) Workshops
(1) O ne-Day Workshop on Stochastics and
Finance / December 28, 2009 / NCTS /
Taiwan, Germany, USA
Speakers: Prof. Brice Franke (Ruhr University,
B o c h u m , G e r m a n y ) , D r. H i r o a k i H a t a
(Academia Sinica), Wei-Chung Miao (National
Ta i w a n U n i v e r s i t y o f S c i e n c e a n d
Technology), Shuenn-Jyi Sheu (Academia
Sinica), Ju-Yi Yen (Vanderbilt University),
Dr.張華平 (Taiwan Ratings Corporation)
(2) M ini-Workshop on Applied Analysis and
P r o b a b i l i t y, M a r c h 2 4 , D e p a r t m e n t o f
Mathematics, National Taiwan University,
2010
S peakers: Prof. Ben T. Nohara (Tokyo City
University), Prof. Jenn-Nan Wang (National
Taiwan University), Prof. Akio Arimoto
( To k y o C i t y U n i v e r s i t y ) , P r o f . S h u y a
Kanagawa (Tokyo City University), Prof.
Narn-Rueih Shieh (National Taiwan University).
(b) Courses
(1) N CTS& NCTU Joint Course on Stochastic
Processes: Markov Chains and Mixing Times
Instructor: Professor Guan-Yu Chen (NCTU)
(2) NCTS & NCTU Joint Course on Stochastic
Portfolio Theory
I nstructor: Professor Yuan-Chung Sheu
(NCTU))
(3) S ummer Course on Lévy Processes with
Applications in Finance
Instructor: Yuan-Chung Sheu (NCTU)
(c) Seminar on Probability and Statistics
with Applications in Biology Speakers in this series of seminars are: Prof.
B o r- S e n C h e n ( D e p a r t m e n t o f E l e c t r i c a l
Engineering, NTHU), Prof. Sing Kiong
Nguang(EE/CE, The University of Auckland),
Prof. Cheng-Hung Chang (Institute of Physics,
NCTU), Prof. Wen-Hsiung Li(Academia Sinica,
Taiwan and University of Chicago, USA), Prof.
Cheng-Hung Chang (Institute of Physics, NCTU),
Dr. Trees-Juen Chuang (Genomics Research
Center, Academia Sinica), Prof. I-Shou Chang
(National Health Research Institutes, Zhunan),
Prof. Michael Fuchs (Department of Applied
Mathematics, National Chiao Tung University),
Dr. Chen-Hsiang Yeang (Institute of Statistical
Science, Academia Sinica), Prof. Cheng-Ying
Chou(Department of Bio-Industrial Mechatronics
Engineering, National Taiwan University), Prof.
Chuan Yi Tang (CS, NTHU), Prof. Jung-Hsin
Lin, Dr. Shu-Chun Chen(Institute of Mathematics,
Academia Sinica), Prof. Chen-Hsiang
Yeang (Institute of Statistical Science, Academia
Sinica)
(d) S
eminars on Probability Theory and
Related Topics
Speakers in this series of seminars are Prof.
Xiaowen Zhou(Concordia University, Canada)
Prof. Jin-Chuan Duan (Director of Risk
Management Instituteand Cycle & Carriage
Professor of Finance, National University of
Singapore), Professor Kanta NAITO (Shimane
University, Japan) ,Prof. Lung-Chi Chen (Fu-Jen
University), Professor Zenghu Li (School of
Mathematical Science, Beijing Normal, Prof.
Masayoshi Takeda (Tohoku University, Japan),
Professor Albert Fannjiang (University of
California at Davis)
(e) Regular Seminar Activity at NTU
Speakers are students, faculty, and visitors;
each talk is 90 minutes, 2010, 17 meeting, 2010,
01.31 – 2010, 10.31. The speakers’ names and
lecture titles can be seen in the files of NCTS
Taipei Office
(f ) Foreign Visitors (NTU, Taipei)
M a s a m i O k a d a ( To k y o M e t r o p o l i t a n
University) Hiroshi Takahashi(Tokyo City
University), Shuya Kanagawa(Tokyo City
U n i v e r s i t y ) , A k i o A r i m o t o ( To k y o C i t y
U n i v e r s i t y ) , B e n T. N o h a r a ( To k y o C i t y
University), Albert Fannjiang (University of
California at Davis)
E. Accomplishments
(I) T
he Probability Focus Program of NCTS
at Hsinchu
[1] G
uan-Yu Chen and Laurent Saloff-Coste, The
L2-cutoff for reversible Markov processes. J.
Funct. Anal. 258 (2010), 2246-2315.
[2] Guan-Yu Chen, An iterative scheme on the
spect ral gap of birth-and-death chains.
Preprint.
[3] Y. T. C h e n a n d Y. C . S h e u , A n o t e o n
$r$-balayages of matrix-exponential Lévy
processes, Elect. Comm. Probab. 14(2009),
165-175.
[4] Yu-Ting Chen and Yuan-Chung Sheu , Exit
Times for Matrix-Exponential Lévy Processes
with Two-Sided Jumps, Preprint(2010)
[5] Yu-Ting Chen and Jean-Francois Delmas,
Smaller population size at the MRCA time for
stationary branching processes(2010)
[6] Ming-Chi Chang and Yuan-Chung Sheu, Twosided optimal and perpetual straddle and
strangle options, Preprint(2010).
45 ‹‹- Highlights of the Focus Programs
[7] L
u, H. H.-S., and Wu, H.-M., "Visualization,
Screening, and Classification of Cell CycleRegulated Genes in Yeast". International
Journal of Systems and Synthetic Biology.
2010, In Press.
[8] C hueh, T.-H., and Lu, H. H.-S., "Boolean
Networks". Handbook of Computational
Statistics: Statistical Bioinformatics, 2010, In
Press.
[9] C.H. Han and Y. Lai: A Smooth Estimator for
MC/QMC Methods in Finance, Mathematics
and Computers in Simulation, in press.
[10] C.H. Han and Y. Lai: Generalized Control
Variate Methods for Pricing Asian Options,
Journal of Computational Finance, in press.
[11] C .H. Han, W.H. Liu, and T.Y. Chen: An
I m p r o v e d P r o c e d u r e f o r Va R / C Va R
Estimation under Stochastic Volatility
Models, Submitted.
[12] C.H. Han and C.T. Wu: Efficient Importance
S a m p l i n g f o r E s t i m a t i n g L o w e r Ta i l
Probabilities under Multivariate Gaussian
and Student T Distributions. Preprint(2010).
(II) T
he Probability Focus Program of
NCTS at Taipei-NTU
[1] P
. Mörters and Narn-Rueih Shieh, The exact
packing measure of Brownian double points.
Probability Theory and Related Fields v. 143,
2009, 113-136.
[2] Narn-Rueih Shieh and Y.M. Xiao, Hausdorff
and Packing dimension results for the images
of random fields. Bernoulli, under revision.
D.9 Representation and Geometric Group Theory
Coordinators: Shun-Jen Cheng (Academia Sinica) and Ching Hung Lam (Academia Sinica)
his research group investigates the
representation theory of groups, Lie
algebra, Lie superalgebras and vertex operator
algebras. Research topics include the use of group
theoretic methods in geometry and applying the
underlying algebraic structures to representation
theory and mathematical physics, the
investigations of the relationship between the
representation theories of classical Lie algebras
and Lie superalgebras and the structure theory of
vertex operator algebras and their relationship
with certain sporadic simple groups.
Investigators: Shun-Jen Cheng (Academia
Sinica), Meng-Kiat Chuah (NTHU), Wan-Keng
Cheong (NCKU, since August 2010), Nan-Kuo
Ho (NTHU), Po Yi Huang (NCKU), Shih-Chang
Huang (NCKU), Wen Fong Ke (NCKU), Ching
Hung Lam (Academia Sinica), Ngau Lam
(NCKU), Chu-Feng Nien (NCKU), Shu-Yen Pan
(NTHU), J. H. Teh (NTHU), Shih-Wei Yang
(NCKU, since August 2010).
Highlights of the Focus Programs -›› 46
Visitors: Bob Griess (Michigan, USA), Weiqiang
Wang (Virginia, USA), Jae-Hoon Kwon (Seoul,
Korea), Hiroshi Yamauchi (Tokyo, Japan),
Tomoyuki Arakawa (Nara, Japan), Hiromichi
Yamada (Tokyo, Japan), Hiroki Shimakura (Aichi,
Japan), Takao Yamazaki (Tohoku, Japan), Hubert
Kiechle (Hamburg, Germany), KeQin Feng
(Tsinghua University, Beijing), Dihua Jiang
(Minnestoa, USA), Johannes Meyer
(Bloemfontein, South Africa), Bin Shu (East
China Normal University), Edmund Puczylowski
(Warsaw, Poland), Guenter Pilz (Linz, Austria),
Siye Wu (Hong Kong University).
S.-J. Cheng, C.H. Lam, together with MengKiat Chuah (National Tsinghua University) and
Ngau Lam (National Cheng-Kung University)
organized the Academia Sinica-NCTS/TPE
summer school on infinite dimensional Lie
algebras from August 16-27, 2010. The summer
school consists of 30 hours of lectures and 10
hours of tutorial. Its purpose is to introduce the
subject of representation theory of symmetrizable
Kac-Moody Lie algebras. It was held in Academia
Sinica and was attended by 25-30 students, postdocs, and faculty members.
In Sep 2010, C.H. Lam organized a miniworkshop infinite dimensional Lie algebras and
related topics. There were 4 speakers from Japan.
C.H. Lam and N. Lam also plan to organize a
summer school in July 2011.
A student seminar was run by King Fai Lai,
Wen Fong Ke and Po Yi Huang at weekly basis at
Tainan. This seminar primarily aims at graduate
students. The main subject is Quantum
Information in 2009/2010.
Another bi-weekly seminar on p-adic
representation is run by King Fai Lai and ChuFeng Nien in Tainan for 2010/2011.
J.H. Teh organized an "Open problem seminar"
in Hsin Chu in which he invited experts to talk
about famous open problems in their fields.
Problems include Clay Institute 6 unsolved
millennium problems. The goal was to broader
students’ view of mathematics. During the
summer of 2010, he organized student seminar to
discuss Feynman integral, Hodge theory, algebraic
geometry and complex geometry. There were 10
students participated in this seminar. J. H. Teh also
organized one seminar in the spring semester
2010. It is a weekly student seminar on geometry.
There are altogether 4 strong undergraduate and 4
graduate students who participate.
S. Y. Pan gave a series lectures on linear
algebraic group of a total 8 hours in NCTS
summer school in 2009. He also gave a talk in the
Open Problem seminar on the Langlands program
in May, 2010. He gave a 3 hours lecture in NCTS
(Taipei) on Introduction to Bruhat-Tits building
over local fields in June 2010.
N. K. Ho invited Siye Wu (HKU) for a twoweek visit and Siye Wu gave two lectures on the
moduli space of Higgs bundles. N.K. Ho is
co-organizing an international conference between
Taiwan and France "NCTS (Taiwan)-CPT(France)
Joint Workshop on Symplectic Geometry and
Quantum Symmetries in Mathematical Physics "
which will be held at the National Center for
Theoretical Sciences on February 21-25, 2011.
There are 13 invited speakers from France,
Luxembourg and some other places and 10 invited
speakers from Taiwan. Moreover, N.K. Ho is
teaching a graduate course this Fall on symplectic
geometry intended to equip the students with
some background for this upcoming NCTS-CPT
Joint workshop in Feb 2011. Right now there are
regularly 10 graduate students attending the class.
S.J. Cheng and Weiqiang Wang (University of
Virginia) plan to have the Taipei Winter School in
Representation Theory from December 16-19. The
two main speakers of the winter school are Olivier
Schiffmann (Paris 6) and Mark Shimozono
(Virginia Tech). The winter school will be
f o l l o w e d b y t h e Ta i p e i C o n f e r e n c e o n
Representation Theory from December 20-23.
Among the invited speakers of the conference are
George Lusztig (MIT), David Vogan (MIT), Eric
Vasserot (Paris 7), Minoru Wakimoto (Kyushu),
and Claus Ringel (Bielefeld). The main sponsor of
these two events is Academia Sinica. However,
the NCTS-TPE will also provide a very
substantial amount of financial and in particular
logistic support. This enables us to provide limited
support many students and junior mathematicians
from Singapore, China, France and the US.
C.H. Lam was an invited speaker for a
program on Quantum field theory, String Theory
& Mathematical Physics in Beijing
from 07-19 to 08-07, 2010. He also visited
University of Michigan on Mar, 2010 for one
month.
S.J. Cheng was invited to attend the 23rd
Khwarizmi International Award ceremony in
Tehran and visited University of Isfahan (Iran) in
February 2010. He visited Tokoku University in
February 2010, and the University of Virginia in
April 2010. He was an invited participant in the
KITPC program Quantum field theory, String
Theory & Mathematical Physics in Beijing in July
2010. He was an invited speaker in the ICM
Satellite conference Combinatorial Methods in
Representation Theory in the Tata Institute in
Bangalore (India) in August 2010.
N. Lam participated in the KITPC program
Q u a n t u m f i e l d t h e o r y, S t r i n g T h e o r y &
Mathematical Physics in Beijing in July 2010.
Nien will attend the International Congress of
Chinese Mathematicians, held in Beijing,
December 17-22, 2010.
47 ‹‹- Highlights of the Focus Programs
Important Results, Breakthrough
Over the past several years, S.-J. Cheng has
been studying the relationship between
representation theories of Lie algebras and Lie
superalgebras. The original motivation is to solve
the irreducible character problem in the BGG
category O for Lie superalgebras of classical
types, which has been a long outstanding problem
in theory of Lie superalgebras. His works, some of
them jointly with N. Lam, over several years led
to a conjectural relationship between the
representation theories of Lie algebras and Lie
superalgebras, called the super duality conjecture,
which for type A case was formulated in joint
works with Wang and Zhang in 2008. Recently,
S.J. Cheng and N. Lam proved this super duality
conjecture for this type A in [C3]. In the case of
the ortho-symplectic Lie superalgebras
homological data have been shown to be directly
related to those of the classical Lie algebras of
types B, C, D in [C2], which provide strong
evidence for a super duality in types B, C, D. S.-J.
Cheng and N. Lam, in collaboration with Wang,
then solved the irreducible character problem for
Lie superalgebras of classical types for a fairly
general parabolic subcategory of the BGG
category in [C1] by formulating and proving the
super duality conjecture in the types B, C, D. The
subcategory includes all finite dimensional
modules and in particular this solves the finite
dimensional irreducible character problem which
has been an outstanding problem for the orthosymplectic Lie superalgebras since the early
eighties.
S.C. Huang has been working on the Dade
conjecture for past years. Recently, together with
co-authors, he proved the Dade conjecture for
some families of simple groups: Sp(4, pn) (p = 2),
SU(4, p2n) (p = 2), GU(4, p2n) (p odd) and Sp(4, pn)
(p odd).
Wen-Fong Ke and Po Yi Huang are interested
in combinatorial structures related to
representation theory. In [K1], W.-F. Ke and K. F.
Lai, together with R.B. Zhang, constructed
quantum codes using Hadamard matrices.
C.H. Lam has continued his program on
classifying holomorphic vertex operator algebras
of central charge 24. The classification of c = 24
holomorphic vertex operator algebras is one of the
Highlights of the Focus Programs -›› 48
central problems in the theory of vertex operator
algebras. In 1993, Schellekens classified possible
partition functions of c = 24 holomorphic models
based on characters of representations of affine
Lie algebras. There are 71 inequivalent candidates
of c = 24 holomorphic vertex operator algebras up
to character level, and he conjectured that there
exist exactly 71 inequivalent models. However,
only 39 of them are constructed so far. There is a
work of Montague that applying Z2 and
Z3-orbifold constructions sequentially, one can
obtain 70 of proposed models from known ones.
His argument involves conjectural orbifold
constructions and is not a rigorous one. Recently,
C.H. Lam and H. Shimakura have constructed
many new models by using Virasoro frames. In
particular, the candidate No. 10 in Schellekens’
list is constructed, which is missed in Montague’s
proposal. Moreover, they are very close to a
complete classification of a special class of
holomorphic vertex operator algebras (called
framed VOA) of central charge 24. These results
are the only breakthrough in the classification in
the last 10 years and would provide a substantial
inroad into the complete classification. In
addition, C.H. Lam has studied the structure codes
of the famous moonshine VOA. He and his
collaborators have determined all structure codes
of the moonshine VOA which is isomorphic to
certain doublings. As a continuation of his work
on some mysterious relationship between affine
Dynkin diagrams and the Monster group, C.H
Lam and R.L. Griess (Univeristy of Michigan)
have obtained several partial results (3C and 5A
cases) related to McKay-Glauberman-Norton’s
theory on certain centralizers of the Monster
group.
Over the past years, Chu-Feng Nien has been
steadily making progress in her understanding of
models of p-adic representations of groups. In her
works, C.F. Nien summarized the basic structures
and properties of irreducible symplectic
supercuspidal representations of GLn (F) over a
p-adic local field F with characteristic zero,
showed the uniqueness of Shalika model of
GL(2n,F), generalized Shalika model on
SO(4n,F), and Klyachko models for irreducible
unitary representations of GL(5, F), for various
field F.
S. Y. Pan studies pairs of reductive Lie groups,
and uses the method of theta correspondences in
representation theory. He obtained some results on
the Nilpotent orbit correspondence for real
reductive dual pairs of symplectic and orthogonal
groups.
J.H. Teh developed a theory to study algebraic
varieties parametrized by the closed points of the
scheme of rings of continuous functions. The goal
is to prove a Grothendieck-Riemann-Roch
theorem in morphich cohomology along the line
of Grothendieck's. The main difficulty in this
approach is that rings of continuous functions are
not Noetherian in general. He is able to use this
theory to define many new invariants like semitopological cobordism groups and semitopological motives. In his another project, he
defined almost Noetherian rings and generalized
several classical results like Hilbert
Nullstellensatz and Serre's theorem to these rings.
He and his student Hsuan-Yi Liao introduced the
notion of splitting covering and showed that it
correspondences exactly to the notion of splitting
field. They proved a Galois correspondence and
used it to study the inverse Galois problem.
N. K. Ho uses surface group representations
and Morse theory to study the topology and
geometry of the moduli space of flat connections
over compact orientable or nonorientable surfaces.
She and Melissa Liu introduced the notion of
Anti-prefect Morse stratification and used it to
study the topology of moduli spaces of flat unitary
connections over a nonorientable surface and gave
conjectural formulas on the Poincare polynomials
for the moduli space and have since been verified
to be correct.
Accomplishments
Shun-Jen Cheng and Ngau Lam
[C1] S.-J. Cheng, N. Lam, and W. Wang, Super
Duality and Irreducible Characters of the
ortho-symplectic Lie Superalgebras,
Inventiones Mathematicae (2011) to appear.
DOI: 10.1007/200222-020-0277-4.
[C2] S .-J. Cheng, J.-H. Kwon and W. Wang,
Kostant Homology Formulas for Oscillator
Representations of Lie Superalgebras,
Advances in Mathematics, 224 (2010), No.
4, 1548-1588.
[C3] S .-J. Cheng and N. Lam, Irreducible
Characters of General Linear Superalgebra
and Super Duality, Communications in
Mathematical Physics, 298 (2010), No. 3,
645-672.
M. K. Chuah
[Ch1] M
. K. Chuah and J. S. Huang, Double
Vogan diagrams and semisimple symmetric
spaces, Transactions of the American
Mathematical Society 362 (2010), 17211750.
N. K. Ho
[Ho1] N
. K. Ho, C.C. Melissa Liu Anti-perfect
Morse Stratification, to appear in Selecta
Methematica.
S. C. Huang
[Hu1] J . An, S. C. Huang and H. Yamada, "Uno's
invariant conjecture for the finite
symplectic group Sp 4 (q) in defining
characteristic", to appear in
Communications in Algebra, Vol. 38,
Issue10.
[Hu2] J. An, F. Himstedt and S. C. Huang, Dade's
invariant conjecture for the symplectic
group Sp4(2n) and the special unitary group
S U 4( 2 2n) i n d e f i n i n g c h a r a c t e r i s t i c ,
Communications in Algebra 38 (2010), no.
6, 2364-2403
[Hu3] J. An and S. C. Huang, Dade's invariant
conjecture for the general unitary group
G U 4( q 2) i n d e f i n i n g c h a r a c t e r i s t i c ,
International Journal of Algebra
Computation 20 (2010), no. 3, 357-380.
[Hu4] F. Himstedt and S. C. Huang, Character
tables of the maximal parabolic subgroups
of the Ree groups 2F4(q2), LMS Journal of
Computation and Mathematics, 13 (2010),
90-110.
Wen-Fong Ke
[K1] K
e, Wen-Fong; Lai, Kingfai; Zhang, Ruibin
Quantum codes from Hadamard matrices.
Linear and Multilinear Algebra 58 (2010),
847-854.
49 ‹‹- Highlights of the Focus Programs
[K2] K e, Wen-Fong; Pilz, Guenter F. Abstract
algebra in statistics. Journal of Algebraic
Statistics 1 (2010), 6-12.
[K3] K e, Wen-Fong; Meyer, Johan H.; Wendt,
Gerhard. Matrix maps over planar nearrings. Proceedings of the Royal Society of
Edinburgh: Section A Mathematics 140
(2010), 83-99.
[K4] Huang, Po-Yi; Ke, Wen-Fong; Pilz, Guenter
F. The cardinality of some symmetric
differences. Proc. Amer. Math. Soc. 138
(2010), 787-797.
Ching Hung Lam
[L1] C
. Dong, C. H. Lam, Q. Wang and H.
Yamada, The structure of parafermion vertex
operator algebras, Journal of Algebra 323
(2010), 371-381.
[L2] C . H. Lam and Robert L. Griess Jr., A
moonshine path for 5A and associated
lattices of ranks 8 and 16, preprint.
[L3] C . H . L a m , O n t h e c o n s t r u c t i o n s o f
holomorphic vertex operator algebras of
central charge 24, to appear in
Communications in Mathematical Physics.
[L4] C . H. Lam and R.L. Griess Jr., Dihedral
groups and Sums of EE8-lattices, Pure and
applied mathematics quarterly 7 (2011), no.
3, 621-743.
[L5] C.H. Lam and R. L. Griess, A moonshine
path from E8 to the Monster, to appear in
Journal of Pure and Applied Algebras.
[L6] G . Hoehn, CH. Lam and H. Yamauchi,
McKay's E7 observations on the
Babymonster, preprint.
[L7] G . Hoehn, CH. Lam and H. Yamauchi,
McKay's E6 observations on the largest
Fischer group, preprint.
Highlights of the Focus Programs -›› 50
Chu-Feng Nien
[N1] D
. Jiang , C.F. Nien, and Y. Qin, Symplectic
supercuspidal representations and related
problems, SCIENCE CHINA Mathematics,
Special Issue Dedicated to Professor Yang
Lo on the Occasion of his 70th Birthday,
Volume 53, Number 3, 2010, 533-546)
[N2] C
.F. Nien, Local Uniqueness of Generalized
Shalika model for SO(4n). Journal of
Algebra 323, Issue 2, 2010, 437-457
[N3] D
. Jiang , C.F. Nien, and Y. Qin, On
Symplectic Supercuspidal Representations
of GL(2n) over p-adic Fields, Pacific
Journal of Mathematics, Vol. 245 (2010),
No. 2
S. Y. Pan
[P1] S
. Y. Pan, Nilpotent orbit correspondence
for real reductive dual pairs of symplectic
and orthogonal groups, to appear in Pacific
J. Math.
J.H. Teh
[T1] J .H. Teh, A homology and cohomology
theory for real projective varieties, Indiana
University Mathematics Journal, no.1,
59(2010), 327-384.
[T2] J .H. Teh, Semi-topological algebraic
geometry and Riemann-Roch Theorem,
arXiv:1001.2355.
[T3] J .H. Teh, Almost algebraic geometry,
arXiv:1001:2371.
[T4] J.H. Teh, H.Y. Liao, Semi-topological Galois
theory and the inverse Galois problem,
arXiv:1006:1166.
[T5] J . H . Te h , S t r i n g y m i r r o r s y m m e t r y,
arXiv:1007.4448.
D.10 Scientific Computation at NCTS
Coordinators: M
ing-Chih Lai (National Chiao Tung University), Wen-Wei Lin (National Chiao Tung University),
Wei-Cheng Wang (National Tsing Hua University), Soon-Yi Wu (National Cheng Kung University)
ue to the development of computer
technology and mathematical science,
Scientific Computation (SC) has become an
indispensable means for solving problems in both
theoretical sciences and engineering disciplines.
Numerical simulation tools have increasingly
become a vital component in the research as well
as application of modern technologies ranging
from environment, aerospace, materials, biology,
to electrical engineering. Based on the support of
NCTS, Scientific Computation has gradually
received proper attention among the mathematics
c o m m u n i t y. I n a d d i t i o n t o p r o m o t i n g
interdisciplinary research activity with other
sciences, the Scientific Computation program at
NCTS also cooperates well with the PDE,
Mathematical Biology, and Dynamical Systems
programs in Mathematics Division.
We now report the activities of SC group in
this year. We have organized one international
conference and three workshops. Meanwhile, we
also have invited a number of distinguished
researchers to offer some short courses and to
conduct cooperative research with our community.
Activities of this year can be summarized as
follows.
D.10.1 Visiting Scientists
1. P
rofessor Biswa Nath Datta (Nothern
Illinois University), Jan. 27-Feb. 12, 2010
Prof. Datta visited NCTS and gave a speech on
"Recent developments on computational
aspects of quadratic inverse eigenvalue
problems in active vibration control and model
updating".
cooperated with Wen-Wei Lin, Tsung-Min
Huang and Wei-Qiang Huang to finish a paper
"Efficient Arnoldi-Type Algorithms for
Rational Eigenvalue Problems Arising in
Fluid-Solid Systems".
3. P
rofessor Moody Ten-Chao Chu (North
Carolina State University), Mar. 29-Apr. 09,
2010
rof. Chu vis ited N CTS and g ave five
P
speeches on
(1) " Semi-definite Programming Techniques
for Structured Quadratic Inverse
Eigenvalue Problems"
(2) "Linear Algebra Algorithms as Dynamical
Systems: Orthogonal Polynomials,
Moments, Measure Deformation,
Dynamical Systems, and SVD Algorithm"
(3) "Data Mining and Applied Linear Algebra"
(4) "Nonnegative Matrix Factorization"
(5) " Group Theory, Linear Transformations,
and Flows: Dynamical Systems on
Manifolds"
4. P
rofessor Eric King-Wah Chu (Monash
University), May 24-Jun. 16, 2010
rof. Chu visited NCTS about one month this
P
year. He gave a speech on "On the numerical
solution of rational Riccati equations in
stochastic optimal control" and, in addition, he
continued doing further work with our group.
In the mean time, he finished three joint works
as follows.
2. P
rofessor So-Hsiang Chou (Bowling Green
State University), Feb. 25-Jun. 24, 2010
(1) " A S t r u c t u r e - P r e s e r v i n g D o u b l i n g
Algorithm for Quadratic Eigenvalue
P r o b l e m s A r i s i n g f r o m Ti m e - D e l a y
Systems", Tiexiang Li, Eric King-Wah Chu
and Wen-Wei Lin.
rof. Ghou visited NCTS four months this year
P
and gave a course on "Numerical Methods for
Partial Differential Equations". In addition, he
(2) " The Rayleigh-Ritz Method Refinement
and Arnoldi Process for Periodic Matrix
Pairs", Eric King-Wah Chu,, Hung-Yuan
51 ‹‹- Highlights of the Focus Programs
Fan, Zhongxiao Jia, Tiexiang Li and WenWei Lin.
5. P
rofessor Tien-Yien Li (Michigan State
University), Jun. 19-Jun. 27, 2010
rof. Li visited NCTS and give a speech on
P
"Solving Some Ill-Posed Problems".
6. P
rofessor Weizhu Bao (National University
of Singapore), Oct. 19-Oct. 30, 2010
rof. Bao visited NCTS and give a speech on
P
"Analysis and Efficient Computation for
Nonlinear Eigenvalue Problems in Quantum
Physics and Chemistry".
7. P
rofessor Zhilin Li (North Carolina State
University), Dec. 1-Dec. 21, 2010
8. P
rofessor Tsung-Ming Huang (National
Taiwan Normal University)
rof. Huang visited NCTS six months this year
P
and finished four joint papers as follows.
(1) " Preconditioning bandgap eigenvalue
problems in three dimensional photonic
crystals simulations", Tsung-Ming Huang,
Wei-Jen Chang, Yin-Liang Huang, WenWei Lin, Wei-Cheng Wang and Weichung
Wa n g , To a p p e a r i n J o u r n a l o f
Computational Physics
(2) " Efficient Arnoldi-Type Algorithms for
Rational Eigenvalue Problems Arising in
Fluid-Solid Systems", Wen-Wei Lin,
Tsung-Min Huang and Wei-Qiang Huang to
finish a paper
(3) " A null space free Jacobi-D av id s o n
iteration for Maxwell's operator", TsungMing Huang, Yin-Liang Huang, Wen-Wei
Lin and Wei-Cheng Wang.
9. P
rofessor Jian-Wen Peng (Chongqing
Normal University), Aug. 10, 2009 -Jul. 31,
2010
10. Professor Donghui Li (Hunan University),
Jan. 2-Jan. 25, 2010
rof. Li visited NCTS and gave one or more
P
speeches on "Methods in Optimization and
Nonlinear Equations".
11. Professor Chong Li (Zhejiang University),
Feb. 14-Feb. 28, 2010
Highlights of the Focus Programs -›› 52
12. P rofessor Shunsuke Hayashi (Graduate
School of Informatics), Aug. 13-Sep. 12,
2010
rof. Hayashi visited NCTS and gave one or
P
more speeches on "Optimality conditions and
regularized exchange method for semi-infinite
programs with infinitely many conic
constraints" , "Explicit exchange method for
convex semi-infinite programs with secondorder cone constraints" and "SDP
reformulation for robust LPs and SOCPs
based on nonconvex QP duality".
13. P ro f e s s o r C h a n g z h i Wu ( C h o n g q i n g
Normal University), Aug. 6-Oct. 31, 2010
rof. Wu visited NCTS and gave one or more
P
speeches on "Approaching Optimal Control
Problems by Infinite-dimensional Problems".
14. P ro f e s s o r M a s a k a z u K o j i m a ( To k y o
Institute of Technology), Nov. 21-Nov. 27,
2010
rof. Wu visited NCTS and gave one or more
P
speeches on "Introduction to Semidefinite
Programming", "SOS and SDP Relaxation of
Polynomial Optimization Problems", and
"Recent Topics (I)(II) - Exploiting Sparsity in
Linear and Nonlinear Matrix Inequalities via
Positive Semidefinite Matrix Completion"
D.10.2 Regular Seminar
1. W
eekly and NCTS Seminar on Scientific
Computation: Oct. 3-Dec. 26, 2009 & Mar.
6-Oct. 31, 2010.
Subjects:
(1) Rank Reduction
(2) Boundary Value Problems
(3) P alindromic Polynomial Eigenvalue
Problems
(4) Iterative Methods for Linear System
(5) Riccati Equations
(6) The Quadratic Eigenvalue Problem
(7) The Rational Eigenvalue Problem
(8) Arnoldi and Arnoldi-type Methods
(9) Jacobi-Davidson Methods
(10) Photonic Crystals
(11) GPU
(12) Acoustic Wave
(13) Stochastic Differential Equations
(14) Symplectic Runge-Kutta Schemes
2. S
eminar in Computational Optimization and
Applications was organized by Soon-Yi Wu
(NCKU). Totally, 15 talks are presented. We
list here these talks in the following:
(1) T
he Optimality Conditions for Fuzzy
Optimization Problems, by Prof. Hsien-Chung
Wu, National Kaohsiung Normal University,
January 5, 2010.
(2) Conjugate Gradient Methods in Optimization
and Nonlinear Equations, by Prof. Dong-HuiLi, January 8, 2010.
(3) Periodic step-size adaptation in second-order
gradient descent for single-pass on-line
learning, by Prof. Yuh-Jye Lee, National
Taiwan University of Science and Technology,
January 12, 2010.
(4) Group Theory, Linear Transformations, and
Flows: Dynamical Systems on Manifolds, by
Prof. Moody T. Chu, North Carolina State
University, USA, April 8, 2010.
(5) P erturbation Analysis for Palindromic
Polynomial Eigenvalue Problems, by Prof.
Chen-Shu Wang, National Cheng Kung
University, June 10, 2010.
(6) P rojection and contraction methods for
convex optimization and monotone
variational inequalities, by Prof. Bingsheng
He, Nanjing University, China, June 11, 2010.
(7) R egularity of the Lyapunov exponent for
quasi-periodic cocycles, by Prof. Yiqian
Wang, Nanjing University, China, August 13,
2010.
(8) Explicit exchange method for convex semiinfinite programs with second-order cone
constraints, by Prof. Shunsuke Hayashi,
Kyoto University, Japan, August 24, 2010.
(9) O ptimality conditions and regularized
exchange method for semi-infinite programs
with infinitely many conic constraints, by
Prof. Shunsuke Hayashi, Kyoto University,
Japan, August 31, 2010.
(10) S DP reformulation for robust LPs and
SOCPs based on nonconvex QP duality, by
(11)
(12)
(13)
(14)
(15)
Prof. Shunsuke Hayashi, Kyoto University,
Japan, September 7, 2010.
R
elaxed Cutting Plane Method with
Convexification to Solve Nonlinear SemiInfinite Programming Problems, by Mr.
Ting-Jang Shiu, National Cheng Kung
University, September 10, 2010.
Approaching Optimal Control Problems by
Infinite-dimensional Problems (I), by Prof.
C h a n g z h i Wu , C h o n g q i n g N o r m a l
University, September 14, 2010.
Approaching Optimal Control Problems by
Infinite-dimensional Problems (II), by Prof.
C h a n g z h i Wu , C h o n g q i n g N o r m a l
University, September 16, 2010.
Approaching Optimal Control Problems by
Infinite-dimensional Problems (III), by Prof.
C h a n g z h i Wu , C h o n g q i n g N o r m a l
University, September 21, 2010.
Approaching Optimal Control Problems by
Infinite-dimensional Problems (IV), by Prof.
C h a n g z h i Wu , C h o n g q i n g N o r m a l
University, September 23, 2010.
D.10.3 Schools and Short Courses
1. N
umerical Methods for PDEs, So-Hsiang Chou
(Bowling Green State University), Feb. 25-Jun.
24, 2010.
2. L
inear System and Eigenvalue Problems, WenWei Lin (National Chiao Tung University),
Mar. 12, 19, 26; Apr. 2, 16, 23, 30, 2010.
3. S
ummer Course on Scientific Computation
Introduction to Fluid Mechanics, Models and
Computations, Ming-Chih Lai (National Chiao
Tung University), Aug. 30-Sep. 1, 2010.
4. N
CTS Short Course on Applied Mathematics
in Biophysics, Bo Li (University of California,
San Diego) and Hong Qian (University of
Washington), Dec. 15-16, 2010.
D.10.4 Conferences and Workshops
1. F
ourth Workshop on Nonlinear Partial
Differential Equations: Analysis,
Computation and Applications, June 11-14,
2010
53 ‹‹- Highlights of the Focus Programs
The main purpose of this workshop is to bring
together researchers from diverse fields in
nonlinear PDE to share their new ideas and to earn
benefit from others’ different viewpoints. Topics
include, but are not limited to conservation laws,
fluid mechanics, kinetic theory, quantum
hydrodynamics, semiconductor modeling and
simulation, nonlinear Schrodinger equations,
plasma physics and electromagnetics.
Speakers:
Hyeong-Ohk Bae (Ajou University, Korea),
Jose Antonio Carrillo (Universitat Autònoma de
Barcelona, Spain), Tong Keun Chang (Korea
Institute for Advanced Study), Li Chen (TsingHua
University, China), Ching-Hsiao Cheng (National
Central University, Taiwan), Wai Sun Don (Hong
K o n g B a p t i s t U n i v e r s i t y ) , Yu n g - F u F a n g
(National Cheng Kung University, Taiwan),
Meng-Kai Hong (National Central University,
Taiwan), Chun-Hsiung Hsia (National Taiwan
University, Taiwan), BumJia Jin (Mokpo National
University, Korea), Hyeonbae Kang (Inha
University, Korea), Shuichi Kawashima (Kyushu
University, Japan), Chi-Kun Lin (National Chiao
Tung University, Taiwan), Tai-Chia Lin (National
Ta i w a n U n i v e r s i t y, Ta i w a n ) , Yu - L i n L i n
(Academia Sinica, Taiwan), Jie Liu (National
U n i v e r s i t y o f S i n g a p o r e ) , Ta i - P i n g L i u (Academia Sinica, Taiwan), Tao Luo (Georgetown
University, USA), Yasunori Maekawa (Kobe
University, Japan), Takayoshi Ogawa (Tohoku
University, Japan), Yu Hin Pang (National
University of Singapore), Yosio Sone (Kyoto
University and Academia Sinica), Athanasios
Tzavaras (University of Maryland, USA), XiaoP i n g Wa n g ( H o n g K o n g U n i v e r s i t y o f
Technology), Zhou Ping Xin (Chinese University
of Hong Kong), ChuanJu Xu (Xiamen University,
China)
Organizers
Weizhu Bao (National University of Singapore)
I-Liang Chern (National Taiwan University)
Seung-Yeal Ha (Seoul National University)
Jian-Guo Liu (Duke University)
Hisashi Okamoto (Kyoto University)
Wei-Cheng Wang (Nat'l Tsing Hua Univ.)
Zhou Ping Xin (Chinese Univ. of Hong Kong)
Highlights of the Focus Programs -›› 54
D.10.5 Important Results, Breakthrough
In this year there are 20 published papers and
13 accepted papers in SCI journals for our group.
We describe the important research achievements
such as the following:
(1) W
e present an immersed boundary (IB)
method that takes into account the nonequilibrium fluid mechanics of the gas to
simulate a dry foam. Dry foam dynamics
involves the interaction between a gas and a
collection of thin liquid-film internal
boundaries that partition the gas into discrete
cells or bubbles. The liquid film boundaries
are flexible, contract under the influence of
surface tension, and are permeable to the gas,
which moves across them by diffusion at a
rate proportional to the local pressure
d i ff e r e n c e a c r o s s t h e b o u n d a r y. S u c h
problems are conventionally studied by
assuming that the pressure is uniform within
each bubble. To model gas diffusion across
the internal liquid-film boundaries, we allow
normal slip between the boundary and the gas
at a velocity proportional to the (normal) force
generated by the boundary surface tension.
We implement this method in the twodimensional case, and test it by verifying the
von-Neumann relation, which governs the
coarsening of a two-dimensional dry foam.
The method is further validated by a
convergence study, which confirms its firstorder accuracy.
(2) W
e develop an immersed boundary (IB)
method to simulate the dynamics of
inextensible vesicles interacting with an
incompressible fluid. In order to take into
account the inextensibility constraint of the
vesicle, the penalty immersed boundary (pIB)
method is used to virtually decouple the fluid
and vesicle dynamics. As numerical tests of
our current pIB method, the dynamics of
single and multiple inextensible vesicles
under shear flows have been extensively
explored, and compared with the previous
literature. The method is also validated by a
series of convergence study, which confirms
its consistent first-order accuracy on the
velocity field, the vesicle configuration, the
vesicle area and the perimeter errors. In
addition, the method is also applied to study a
binary component vesicle problem.
(3) W
e propose a simple finite difference scheme
for Navier-Stokes equations in primitive
formulation on curvilinear domains. With
proper boundary treatment and interplay
between covariant and contra-variant
components, the spatial discretization admits
exact Hodge decomposition and energy
identity. As a result, the pressure can be
decoupled from the momentum equation with
explicit time stepping. No artificial pressure
boundary condition is needed. In addition, it
can be shown that this spatially compatible
discretization leads to uniform inf-sup
condition, which plays a crucial role in the
pressure approximation of both dynamic and
steady state calculations. Numerical
experiments demonstrate the robustness and
efficiency of our scheme.
(4) W
e present a fast Poisson solver on spherical
shells. With a special change of variable, the
radial part of the Laplacian transforms to a
constant coefficient differential operator. As a
result, the Fast Fourier Transform can be
applied to solve the Poisson equation with
O(N3logN) operations. Numerical examples
have confirmed the accuracy and robustness
of the new scheme.
(5) W
e propose a new exchange method for
solving convex semi-infinite programming
(CSIP) problems. We introduce a new
dropping-rule in the proposed exchange
algorithm, which only keeps those active
constraints with positive Lagrange multipliers.
Moreover, we exploit the idea of looking for
η-infeasible indices of the lower level
problem as the adding-rule in our algorithm.
Hence the algorithm does not require to solve
a maximization problem over the index set at
each iteration; it only needs to find some
points such that a certain computationallyeasy criterion is satisfied. Under some
reasonable conditions, the new addingdropping rule guarantees that our algorithm
provides an approximate optimal solution for
the CSIP problem in a finite number of
iterations. For the FIR filter design problem,
we show that our algorithm solves the
problem better than some algorithms that were
technically established for the problem.
(6) W
e consider a semismooth reformulation of
the KKT system arising from the semi-infinite
programming (SIP) problem. Based upon this
reformulation, we present a new smoothing
Newton-type method for the solution of SIP
problem. The main properties of this method
are: (a) it is globally convergent at least to a
stationary point of the SIP problem, (b) it is
locally superlinearly convergent under a
certain regularity condition, (c) the feasibility
is ensured via the aggregated constraint, and
(d) it has to solve just one linear system of
equations at each iteration. Efficient and
reliable numerical results are reported.
(7) W
e propose a structure-preserving doubling
algorithm for a quadratic eigenvalue problem
arising from the stability analysis of timedelay systems. We are particularly interested
in the eigenvalues on the unit circle, which are
difficult to estimate. The convergence and
backward error of the algorithm are analyzed
and three numerical examples are presented.
Our experience shows that our algorithm is
efficient in comparison to the few existing
approaches for small to medium size
problems.
(8) I n studying the vibration of fast trains, we
encounter a palindromic quadratic eigenvalue
problem (QEP) (λ 2 A T+λQ+A)z, where
nxn
A, ▋ and QT=Q. Moreover, the matrix is
block tridiagonal and block Toeplitz, and the
matrix A has only one nonzero block in the
upper-right corner. So most of the eigenvalues
o f t h e Q E P a r e z e r o o r i n f i n i t y. I n a
linearization approach, one typically starts
with deflating these known eigenvalues for
the sake of efficiency. However, this initial
deflation process involves the inverses of two
potentially ill-conditioned matrices. As a
result, large error might be introduced into the
data for the reduced problem. Here, we
propose using the solvent approach directly
on the original QEP, without any deflation
process. We apply a structure-preserving
doubling algorithm to compute the stabilizing
solution of the matrix equation X+ATX-1=Q,
whose existence is guaranteed by a result on
the Wiener–Hopf factorization of rational
matrix functions associated with semi-infinite
block Toeplitz matrices and a generalization
55 ‹‹- Highlights of the Focus Programs
of Bendixson’s theorem to bounded linear
operators on Hilbert spaces. The doubling
algorithm is shown to be well defined and
quadratically convergent. The complexity of
the doubling algorithm is drastically reduced
by using the Sherman–Morrison–Woodbury
formula and the special structures of the
problem. Once the stabilizing solution is
obtained, all nonzero finite eigenvalues of the
QEP can be found efficiently and with the
automatic reciprocal relationship, while the
known eigenvalues at zero or infinity remain
intact.
D.10.6 Publications
[1] S
.-L. Chen, T.-T. Hwang, S.-M. Chang and
W.-W. Lin, A Fast Digital Chaotic Generator
for Secure Communication, Int. J. Bifurcation
Chaos, accepted (2010).
[2] K . - C . C h e n , C . - S . Wa n g , C . - C . Ye n ,
Numerical Algorithms for estimating the
Largest Structured Singular Value of a
mu-Synthesis System, Taiwanese Journal of
Mathematics, 14(3A):973-998, (2010).
[3] R .-B. Chen, W. Wang, and C.-F. Jeff Wu.
Building Surrogates with Overcomplete Bases
in Computer Experiments with Applications to
Bistable Laser Diodes. IIE Transactions
(Quality and Reliability Engineering), to
appear (2010).
[4] C.-H. Guo and W.-W. Lin, Convergence Rates
of Some Iterative Methods for Nonsymmetric
Algebraic Riccati Equations Arising in
Transport Theory, Lin. Alg. Appl., Vol. 432,
No. 1, 283-291 (2010).
[5] T.-M. Huang, W.-J. Chang, Y.-L. Huang,
W.-W. Lin, W.-C. Wang, and W. Wang.
P re c o n d i t i o n i n g B a n d g a p E i g e n v a l u e
Problems in Three Dimensional Photonic
Crystals Simulations. Journal of
Computational Physics, to appear (2010).
[6] Y.-L. Huang, J.-G. Liu and W.-C. Wang, An
FFT based Fast Poisson Solver on Spherical
Shells. Communications in Computational
Physics, to appear (2010).
[7] Yukai Hung and W. Wang. Accelerating
Parallel Particle Swarm Optimization via
GPU. Optimization Methods and Software, to
appear (2010).
Highlights of the Focus Programs -›› 56
[8] T
.-M. Huang, W. Wang, and C.-T. Lee. An
Efficiency Study of Polynomial Eigenvalue
Pro b le m S o lve r s fo r Q u a n tu m D o t
S i m u l a t i o n s . Ta i w a n e s e J o u r n a l o f
Mathematics, 14(3A):999-1021, (2010).
[9] F.-N. Hwang, Z.-H. Wei, T.-M. Huang, and W.
Wa n g . A P a r a l l e l A d d i t i v e S c h w a r z
Preconditioned Jacobi-Davidson Algorithm
for Polynomial Eigenvalue Problems in
Quantum Dot Simulation. Journal of
Computational Physics, 229(8):2932-2947
(2010).
[10] S. Ito, S.-Y. Wu, T.-J. Shiu and K.-L. Teo, A
Numerical Approach to Infinite-Dimensional
Linear Programming in L1 Spaces, Journal
of Industrial and Management Optimization,
Vol. 6, 15-28 (2010).
[11] Y. Kim and M.-C. Lai, Simulating the
dynamics of inextensible vesicles by the
penalty immersed boundary method, Journal
of Computational Physics, vol 229, 48404853 (2010).
[12] Y. K i m , M . - C . L a i a n d C . S . P e s k i n ,
Numerical simulations of two-dimensional
foam by the immersed boundary method,
Journal of Computational Physics, vol 229,
5194-5027 (2010).
[13] Y.-C. Kuo, W.-W. Lin, S.-F. Shieh and W.
Wa n g , A H y p e r p l a n e - C o n s t r a i n e d
Continuation Method for Near Singularity in
Coupled Nonlinear Schrödinger Equations,
Appl. Num. Math., to appear (2010).
[14] Y.-C. Kuo, W.-W. Lin, S.-F. Shieh, and W.
Wang. Exploring Bistability in Rotating
Bose-Einstein Condensates by a Quotient
Transformation Invariant Continuation
Method. Physica D: Nonlinear Phenomena,
to appear (2010).
[15] M.-C. Lai, C.-Y. Huang and Y.-M. Huang,
Simulating the axisymmetric interfacial
flows with insoluble surfactant by immered
boundary method, International Journal of
Numerical Analysis and Modeling, vol 8,
105-117, (2011).
[16] M .-C. Lai, Y.-H. Tseng and H. Huang,
Numerical simulation of moving contact
lines with surfactant by immersed boundary
method, Communications in Computational
Physics , vol 8, 735-757 (2010).
[17] Z
. Li, M.-C. Lai, G. He and H. Zhao, An
augmented method for free boundary
p ro b l e m s w i t h m o v i n g c o n t a c t l i n e s ,
Computers and Fluids, vol 39, 1033-1040
(2010).
[18] C. Ling, Q. Ni, L. Qi and S.-Y. Wu, A New
Smoothing Newton-Type Algorithm for SemiInfinite Programming, Journal of Global
Optimization, Vol. 47, 133-159 (2010).
[19] T. Li, C.-Y. Chiang, E. K.-W. Chu and W.-W.
L i n , T h e P a l i n d ro m i c G e n e r a l i z e d
Eigenvalue Problem A*x=λAx : Numerical
Solution and Applications, Lin. Alg. Appl.,
to appear (2010).
[20] T. Li, E. K.-W. Chu and W.-W. Lin, A
Structure-Preserving Doubling Algorithm for
Quadratic Eigenvalue Problems Arising
from Time-Delay Systems, J. Comp. Appl.
Math., Vol. 223, 1799-1745 (2010).
[21] T. Li, E. K.-W. Chu, C.-S. Wang, Asymptotic
Perturbations of Palindromic Eigenvalue
P r o b l e m s , Ta i w a n e s e J o u r n a l o f
Mathematics, 14(3A):781-793, (2010).
[22] R .-C. Li, W.-W. Lin and C.-S. Wang,
Structured Backward Error for Palindromic
Polynomial Eigenvalue Problems, Numer.
Math., Vol. 116, No. 1, 95-12 (2010).
[23] M. López, S.-Y. Wu, C. Ling and L. Qi, A
Mathematical Programming Approach to
Strong Separation in Normed Spaces,
Journal of Convex Analysis, Vol. 17, 211227 (2010).
[24] J.-W. Peng, S.-Y. Wu, and J.-C. Yao, A New
Iterative Method for Finding Common
Solutions of a System of Equilibrium
Problems, Fixed-Point Problems, and
Variational Inequalities, Abstract and
Applied Analysis, Vol. 2010, Article ID
428293, 27 pages (2010).
[25] X.-J. Tong, L. Qi and S.-Y. Wu, A Smoothing
SQP Method for Nonlinear Programs with
[26]
[27]
[28]
[29]
[30]
[31]
[32]
Stability Constraints Arising from Power
Systems , to appear in Computational
Optimization and Applications (2010).
X.-J. Tong, S.-Y. Wu and R.-J. Zhou, New
Approach for the Nonlinear Programming
with Transient Stability Constraints Arising
f ro m P o w e r S y s t e m s , C o m p u t a t i o n a l
Optimization and Applications, Vol. 45, 495520 (2010).
C .-T. Wu, Z. Li and M.-C. Lai, Adaptive
mesh refinement for elliptic interface
p ro b l e m s u s i n g t h e n o n - c o n f o r m i n g
immersed finite element method,
International Journal of Numerical Analysis
and Modeling, accepted.
L.-P. Zhang and S.-Y. Wu, A New Approach
to Supply Chain Network Equilibrium
Models, to appear in Acta Mathematica
Scientia (2010).
L.-P. Zhang and S.-Y. Wu, Robust Solutions
to Euclidean Facility Location Problems
with Uncertain Data, to appear in Journal of
Industrial and Management Optimization
(2010).
L.-P. Zhang and S.-Y. Wu and S.-C. Fang, An
Entropy-Based Central Cutting Plane
Algorithm for Convex Min-Max problems
with Infinite Constraints, to appear in
Journal of Computational and Applied
Mathematics (2010).
L .-P. Zhang, S.-Y. Wu and S.-C. Fang,
Convergence and Error Bound of a D-gap
Function Based Newton-type Algorithm for
Equilibrium Problems, Journal of Industrial
and Management Optimization, Vol. 6, 333346 (2010).
L . P. Zhang, S. Y. Wu and M. A. Lopez
(2010), A New Exchange Method for Convex
Semi-Infinite Programming, SIAM Journal
on Optimization, Vol. 20, 2959-2977.
57 ‹‹- Highlights of the Focus Programs
Highlights of the Regional Programs
E.1 Regional Programs on Statistics at Hsinchu
Coordinators: C.-D. Fuh (National Central Univ. and Academia Sinica), S.-T. Tseng (National Tsing-Hua University),
H. Wang (National Chiao-Tung University), N.-J. Hsu (National Tsing-Hua University)
his is the second year of this statistics
program and we have a great year with
successful events and significant progress on
developing the research group. First of all, we had
a very successful winter course on multivariate
time series analysis given by R.S. Tsay. There
were more than 100 participates coming from
more than 10 universities around Taiwan in this
winter course. This course covers a lot of updated
research topics and the impact of this course is
clear and significant. The short course on
experimental design given by C.-S. Cheng is an
advanced and theoretic topic in statistics. It
inspires young researchers (P-W, Tsai and C-Y
Peng) and generates actual collaborations. In this
summer, the program held an international
conference on Probability and Statistics with
Applications in Biology. There are 17 invited
speakers presented in this event, in particular the
world famous scholar Professor Wen-Hsiung Li
gave the plenary speech on modern sequencing
technologies and their applications. More than 60
people from USA, Hong Kong, Japan and Taiwan
participated in this event and it was a very
successful conference. Regarding the research
group, the Industrial Statistics Research Group
(ISRG) operated by S.-T. Tseng is well developed
and functioned in this year. The primary goal of
ISRG is to promote frontier research of statistical
methods that can be efficiently applied to improve
the quality and productivity of high-tech industry.
In this year, ISRG had held monthly seminars and
discussions to generate interactions between
academic researchers and industrial engineers. It
usually takes time for collaborations among multi-
Highlights of the Regional Programs -›› 58
disciplines. We satisfy the current accomplishment
and we are very confident on the enhancement
and improvement of the program in the future.
The activities held by the statistics program
this year are summarized in the following:
Regular Seminars Industrial Statistics
Research Group (ISRG)
The ISRG runs a one-day regular seminar
monthly. This year (up to October), we have
invited 15 speakers to introduce contemporary
research topics in industrial statistics. The topics
include run to run process control, Bayesian
inference in screening experiment, degradation
modeling and inference, profile monitoring, fault
detection and classification. The seminar activities
are listed below and more information can be
found at the website:
http://stat.web.nthu.edu.tw/files/11-1017-428.php.
(1) Speaker: S
-K Fan (Dept. of Industrial
Engineering and Management, YuanZe University)
Title: The Enhanced dEWMA and RLS-LT
Controller to Compensate for Timevarying Metrology Delay
Time: Oct. 22, 2010
(2) Spearker: K
evin Tu 凱文 (旺宏電子工程資
料分析處副處長)
Title: S
tatistics Engineering: Mxic
Experiences on Statistics
Time: Oct. 22, 2010
(3) Spearker: I.-T. Yu 俞一唐 (Department of
Statistics, Tung Hai University)
Title: A Bayesian Approach to Identifying the
Active Factors in a Screening
Experiment
Time: Sep. 24, 2010
(10) Spearker: C
hin-Yuan Chen 陳志遠 (Quality
Manufactory Supervisor, ASEMC,
Ltd)
Title: Taguchi Method and SPC System in
Semiconductor acturing
Time: Apr. 30, 2010
(4) Spearker: C.-Y. Peng 彭健育 (Institute of
Statistical Science, Academia
Sinica)
Title: S
tatistical Lifetime Inference with
Skew-Wiener Linear Degradation
Models
Time: Sep. 24, 2010
(11) S
pearker: Su-Fen Yang 楊素芬 (Statistics
Department, National Cheng-Chi
University)
Title: I mprovement Inconsistency of the
Metallic Film Thickness of Computer
Connectors
Time: Mar. 26, 2010
(5) Spearker: P. C. Wang 王丕承 (Department of
Industrial and Business
Management, Chang Gung
University)
Title: U
se Orthogonal Arrays to Plan
Experiments
Time: June 25, 2010
(12) Spearker: Tzu-Cheng Lin 林資程 (Advanced
Control Program Integrated
Interconnect & Packaging
Division/ R&D, Taiwan
Semiconductor Manufacturing Co.)
Title: S
tatistical Process Control
Implementation in Semiconductor
Manufacturing
Time: Mar. 26, 2010
(6) Spearker: T. H. Fan 樊采虹 (Graduate Institute
of Statistics, National Central
University)
Title: An Overview of Accelerated Life-testing
Reliability Experiments for Various
Types of Data
Time: June 25, 2010
(7) Spearker: Arthur B. Yeh (Department of
Applied Statistics and Operations
Research, Bowling Green State
University)
Title: S
tatistical Control, Profile Monitoring
and Other Recent Developments
Time: May 28, 2010
(8) Spearker: Kwok-L. Tsui (Manufacturing
Engineering & Engineering
Management, City University of
Hong Kong)
Title: R
ecent Research in System Informatics,
Prognostics, and Health Management
Time: May 21, 2010
(9) Spearker: Mong-Na Lo Huang 羅夢娜
(Department of Applied
Mathematics, Sun Yat-sen
University)
Title: O
ptimal Experimental Designs for
Regression
Time: Apr. 30, 2010
(13) Spearker: Argon Chen 陳正剛 (Industrial
Engineering, National Taiwan
University)
Title: Temporal and Spatial Variation Analysis
and Its Applications to Semiconductor
Engineering Data Analysis
Time: Feb. 26, 2010
(14) Spearker: C
. M. Ke 柯志明 (Taiwan
Semiconductor Manufacturing Co.)
Title: C
hallenges of Semiconductor
Manufacturing Control for
Technologies below 45nm
Time: Feb. 26, 2010
(15) Spearker: N
. Balakrishnan (McMaster
University, Hamilton Ontario,
Canada)
Title: S
ystem Signatures and Their Properties
Time: Dec. 11, 2009
Conference and Course
2010 NCTS & NTHU Special Course
Topic: Analysis of Multivariate Time Series
Speaker: Ruey S. Tsay (University of Chicago)
59 ‹‹- Highlights of the Regional Programs
Dates: Jan 17-30, 2010 (total 30 hours)
Course Descriptions: This course studies the
dynamic relationships between multiple time
series. It starts with linear relationships between
two variables, especially when one of the variable
is the input variable and the other the output
variable. The course then introduces various
econometric/statistical models for multivariate
time series, including stationarity conditions and
properties of the model. The concepts of unit-root
nonstationarity and co-integration are discussed.
The models considered include transfer function
models, vector autoregressive models, vector
autoregressive and moving-average models, errorcorrection models, state-space models, dynamic
factor models, and, if time permits, multivariate
volatility models. The course also discusses a
model building procedure such as model
specification, estimation, and model checking. The
usefulness of exact likelihood estimation is
shown. Specific attention is then given to
structural specification to overcome the difficulty
of model identifiability. In particular, we study the
Kronecker index and scale component models for
modeling multivariate time series. The course also
introduces seasonal time-series models.
Applications with empirical data analysis are an
integral part of the course. The software packages
R and SCA will be used through out. Some
FORTRAN programs will also be used to specify
the scale component models. Students are required
to analyze real multivariate time series.
2010 NCTS & NTHU Special Course
Topic: M
inimum Aberration and Some Related
Criteria for Fractional Factorial Designs
Speaker: C -S. Cheng (University of California,
Berkeley)
Dates: M
ay 27, June 3, 10, 17, 2010 (total 12
hours)
Course Description: Minimum aberration and
some other criteria have been proposed for
choosing fractional factorial designs that can
better estimate lower-order effects, albeit with
different interpretations of such capability. The
differences in the interpretations sometimes lead
to inconsistencies or even contradictions among
the different criteria, and one should not expect
any criterion to work in all circumstances. I will
Highlights of the Regional Programs -›› 60
discuss these criteria, clarify their relationship,
and present some results on the construction of
optimal designs. The following topics will be
included: minimum aberration, clear two-factor
interactions, estimation capacity, complementary
design theory, structures of resolution IV designs
(including results on doubling, maximal and
second-order saturated designs), extensions (such
as generalized minimum aberration and criteria
for choosing multi-stratum fractional factorial
designs) if time permits.
NCTS International Conference on Probability
and Statistics with Applications in Biology
Time: July 14-16, 2010.
Conference Description: Numerous fascinating
breakthroughs in biotechnology have generated
l a rg e v o l u m e s a n d d i v e r s e t y p e s o f h i g h
throughput data. The data demand the
development of efficient and appropriate tools in
probability and statistics integrated with biological
knowledge and computational algorithms. This
conference invites leading researchers to survey
many active research topics and promote the
visibility of this research area. This conference is
intended to provide interaction for researchers
who are interested in the recent developments of
probability and statistics in biology.
Publications
[1] C
heng, C. S. and Tsai P. W. (2010). Multistratum fractional factorial design. Statistica
Sinica. In press.
[2] C hueh, T.-H., and Lu, H. H.-S. (2010).
Boolean networks. Handbook of
Computational Statistics: Statistical
Bioinformatics, In press.
[3] Deng, L.-Y. , Lu, H. H.-S., and Chen, T.-B.
(2010). 64-Bit and 128-bit DX random
number generators. Computing, 89, 1, 27-43.
2010.
[4] Emura, T. and Wang, H. (2010). Approximate
tolerance limits under log-location-scale
regression models in the presence of
censoring, Technometrics, 52, 313-323.
[5] H su, N-J, Chang, Y-M and Huang, H.-C.
(2010). A group lasso approach for
nonstationary spatial-temporal covariance
estimation. Manuscript.
[6] L u , H . H . - S . , a n d Wu , H . - M . ( 2 0 1 0 ) .
Visualization, screening, and classification of
cell cycle-regulated genes in yeast".
International Journal of Systems and
Synthetic Biology. 2010, In press.
[7] Tsai, C. C. Tseng, S. T., and Balakrishnan, N.
(2010). Optimal burn-in policy for highly-
reliable products using gamma degradation
process. Forthcoming in the December issue
of IEEE Transactions on Relability.
[8] Tseng, S. T., Tsai, C. C. and Balakrishnan, N.
(2010). Optimal sample size allocation for
Weiner accelerated degradation model.
Engineering Handbook will be published by
Wiley.
E.2 Regional Programs on Multiscale Modeling, Analysis and Computation at Taipei
Coordinators: I-Liang Chern (National Taiwan University), Chien-Cheng Chang (National Taiwan University),
Din Ping Tsai (National Taiwan University), Tony W. H. Sheu (National Taiwan University),
Keh-Ming Shyue (National Taiwan University), Wei-Chung Wang (National Taiwan University)
E.2.1 Background and Description
he rapid growth of high performance
computers has transformed the
methodology of scientific investigation.
Computing is nowadays joined experiment and
theory as one of the fundamental tools of
investigation. It is safe and cheap. Further, in
many cases, it can go beyond experiments or
observation, as those in astrophysics or
m e t e o r o l o g y, e t c . T h e d e v e l o p m e n t o f
computational science needs integration of
researchers from different disciplines:
mathematics, physics, chemistry, biology,
geoscience, engineering, computer science, etc.
The funding of NCTS provided opportunities to
bring researchers from different disciplines
together. In the year 2009/8-2010/7, we focus on
three interdisciplinary topics: (1) multi-scale
analysis and computation, (2) GPU and matrix
computation, (3) computational mechanics, and
(4) image processing. Multiscale analysis and
computation focuses on interface problems,
especially on computing surface plasmon
polariton appeared in nano-optics. The matrix
computation focuses on large-scale eigenvalue
problem solver on parallel computers. We
develop a parallel Jacobi-Davidson approach for
finding a partial set of eigenpairs of large sparse
polynomial eigenvalue problems with application
in quantum dot simulation. The computational
mechanics studies phase preserving and volume
preserving for two phase flows. The image
processing is a new subject. We host short course
for faculties and students to enter into this subject.
E.2.2 Local focus group
I-Liang Chern, Chien-Cheng Chang, Tony W.
H. Sheu, Keh-Ming Shyue,Wei-Chung Wang
E.2.3 Short Term Visitors
Hyeong-Ohk Bae (Ajou University), Jose
Antonio Carrill (Universitat Autònoma de
Barcelona), Tong Keun Chang (Korea Institute for
Advanced Study), Li Chen Tsinghua University),
WaiSun Don (Hong Kong Baptist University),
Maria Pia Gualdani (The University of Texas at
Austin), BumJa Jin (Mokpo National University),
Jie LIU(National University of Singapore),
Shuichi Kawashima (Kyoto University),
Hyeonbae Kang (Inha University), Chiu-Yen Kao
61 ‹‹- Highlights of the Regional Programs
(Ohio State University), Lek-Heng Lim
(University of California, Berkeley), Yasunori
MAEKAWA (Kobe University), Takayoshi Ogawa
(Tohoku University), Yu-Hin Pang (National
University of Singapore), William W. Symes
(Rice University), Yoshio Sone (Kyoto University
and sinica), Yen-Hsi Richard Tsai (The University
of Texas at Austin), Athanasios Tzavaras
(University of Crete), Shouhong Wang (Indiana
University, Bloomington), Xiaoping Wang (Hong
Kong University of Science and Technology),
Zhouping Xin (The Chinese University of Hong
Kong), ChuanJu Xu (Xiamen University)
computed tomography (CT), Positron emission
tomography (PET) and Magnetic resonance
imaging (MRI). In this serial lectures, we shall
also help students to focus on a specific topics and
give an oral report at the end of this course. The
lectures are in the morning, the computer practices
are in the afternoon. Our goal is to give students
an overview, a mathematical background and
computer tools as well as a subject to focus.
Organizer: Prof. I-Liang chern (Nat'l Taiwan Univ.)
web page:
http://homepage.ntu.edu.tw/~r97221026/
There are 38 students attending this course.
E.2.4 Seminars, Short courses and
workshops
I. W
eekly seminar on imaging, image
processing and inverse problems on every
Friday (2009,9-2010,6).
II. Short courses and schools
(1) Summer Course on Image Science in 2010
Speakers:
orng-Shing Lu (Nat'l Chiao Tung Univ.)
H
TZENG, JENG-NAN (Nat'l ChengChi Univ.)
Ting-Li Chen (Academia Sinica)
Chin-Tu Chen (University of Chicago, USA)
Chien-Min Kao (University of Chicago, USA)
Wen-Yih Tseng (National Taiwan University)
Fa-Hsuan Lin (National Taiwan University)
I-Liang Chern (National Taiwan University)
Kao Chiu-Yen (Ohio State University, USA)
Wen-Liang Hwang (Academia Sinica)
Weichung Wang (National Taiwan University)
Place: R
oom 638, Astro-Math. Building, National
Taiwan University
Time: 2 010/7/5~2010/8/20 Monday to Friday
10:00~12:00 (Lecture), 2:00-4:00 (Lab)
Abstract: Imaging science is a important growing
subject in Applied Mathematics. This course will
give a series lectures on this subject with focus on
medical image reconstruction. We will start from
basic image processing and mathematical
preliminaries. Then we will introduce the
Highlights of the Regional Programs -›› 62
(2) S
hort course on Large Linear Systems and
Eigenvalue problems.
Speaker: Wen-Wei Lin (Nat'l Chiao Tung Univ.)
Place: R
oom 401, Shin-Sheng Building, National
Taiwan University
Time: every Friday 2:20-5:20 (2010/3/12, 3/19,
3/26, 4/2, 4/16, 4/23, 4/30)
Abstract: Matrix computing is a core tool in
scientific computing. This course will study the
linear solver and eigensolvers for large linear
systems. The main topics will be the
preconditioned conjugate gradient method and
Arnodi method.
Organizer: Prof. Weichung Wang (National
Taiwan University), Prof. Tsung-Min Hwang
(National Taiwan Normal University)
Web page: h ttp://www.math.ntu.edu.tw/~wwang/
mtxcomp2010/index.html
(3) Short course on GPU and Matrix computation.
Speakers:
Yu-Kai Hong (National Taiwan University)
Wei-Jen Chang (National Taiwan University)
Vasily Volkov (University of California,
Berkeley, USA)
Place: R
oom 401, Shin-Sheng Building, National
Taiwan University
Time: e very Fr iday 2:20-5:20 (2010/5/7 2010/6/25)
Abstract: Due to the rapid growth of Graphic
Processing Unit (GPU) and distributed parallel
computer, it is expected that they will bring
scientific computing to another higher era. This
course will start from basic parallel algorithms,
the operation of GPU and eventually learn how to
develop GPU programs for solving large linear
systems.
Organizers:
Prof. Weichung Wang (Nat'l Taiwan Univ.)
Prof. Tsung-Min Hwang (Nat'l Taiwan Normal Univ.)
Web Page: http://www.math.ntu.edu.tw/~wwang/
mtxcomp2010/parallel_mtx_comp/
index.htm
(4) High performance computing
Speakers:
Chin-Tu Chen (University of Chicago, USA)
Chien-Min Kao (Univ. of Chicago, USA)
Weichung Wang (National Taiwan University)
Time: 2010/7/12-2010/8/6
Place: R
oom 307, New Mathematics Building,
National Taiwan University
Organizer: Weichung Wang (Nat'l Taiwan Univ.)
III. Workshops
Background:
The main purpose of this workshop is to bring
together researchers from diverse fields in
nonlinear PDE to share their new ideas and to earn
benefit from others’ different viewpoints. Topics
include, but are not limited to conservation laws,
fluid mechanics, kinetic theory, quantum
hydrodynamics, semiconductor modeling and
simulation, nonlinear Schrodinger equations,
plasma physics and electromagnetics.
Invited Speakers:
Hyeong-Ohk Bae (Ajou University, Korea),
Jose Antonio Carrillo (Universitat Autònoma de
Barcelona, Spain), Tong Keun Chang (Korea
Institute for Advanced Study), Li Chen (TsingHua
University, China), Ching-Hsiao Cheng (National
Central University, Taiwan), Wai Sun Don (Hong
K o n g B a p t i s t U n i v e r s i t y ) , Yu n g - F u F a n g
(National Cheng Kung University, Taiwan),
Meng-Kai Hong (National Central University,
Taiwan), Chun-Hsiung Hsia (National Taiwan
University, Taiwan), BumJia Jin (Mokpo National
University, Korea), Hyeonbae Kang (Inha
University, Korea), Shuichi Kawashima (Kyushu
University, Japan), Chi-Kun Lin (National Chiao
Tung University, Taiwan), Tai-Chia Lin (National
Ta i w a n U n i v e r s i t y, Ta i w a n ) , Yu - L i n L i n
(Academia Sinica, Taiwan), Jie Liu (National
U n i v e r s i t y o f S i n g a p o r e ) , Ta i - P i n g L i u (Academia Sinica, Taiwan), Tao Luo (Georgetown
University, USA), Yasunori Maekawa (Kobe
University, Japan), Takayoshi Ogawa (Tohoku
University, Japan), Yu Hin Pang (National
University of Singapore), Yosio Sone (Kyoto
University and Academia Sinica), Athanasios
Tzavaras (University of Maryland, USA), XiaoP i n g Wa n g ( H o n g K o n g U n i v e r s i t y o f
Technology), Zhou Ping Xin (Chinese University
of Hong Kong), ChuanJu Xu (Xiamen University,
China).
Organizing Committees:
Weizhu Bao (NUS), I-Liang Chern (NTU),
Seung-Yeal Ha (SNU), Jian-Guo Liu (Duke),
Hisashi Okamoto (Kyoto), Wei-Cheng Wang
(NTHU), Zhou Ping Xin (CUHK)
E.2.5 S elect publications of the local
focus group
[1] R
aymond H. Chan, I-Liang Chern, Li-Wei
Kuo, Chi-Kin Tai and Wen-Yih Isaac Tseng,
"Reconstruction of high-resolution magnetic
resonance images using total variation
regularization reconstruction techniques
,"preprint 2010.
[2] R en-Hao Chen, I-Liang Chern, Weichung
Wang, "Exploring Ground States and Excited
States of Spin-1 Bose-Einstein Condensates
by Continuation Methods", Journal of
Computational Physics, 2010 (accepted).
[3] I -Liang Chern and Chun-Hsiung Hsia,
"Dynamic phase transition for Cahn-Hilliard
equations in cylindrial geometry,"Discrete and
Continuous Dynamical System, B, 2010
(accepted).
[4] Yu-Chen Shu, Chiu-Yen Kao, I-Liang Chern,
Chien C. Chang, "Augmented Coupling
Interface Method for Solving Eigenvalue
Problems with Sign-changed
Coefficients,"Journal of Computational
Physics, accepted under revision, 2010
(accepted).
[5] Daomin Cao, I-Liang Chern, Jun-Cheng Wei,
"On Ground State of Spinor Bose-Einstein
Condensates,"preprint, 2010.
63 ‹‹- Highlights of the Regional Programs
[6] Y
u-Chen Shu, Yi-Cheng Hsu, Chien C.
Chang, I-Liang Chern, "Hybrid Optimization
Method for Complete Band-Gaps of Photonic
Crystals,"preprint, 2010.
[7] Feng-Nan Hwang, Zih-Hao Wei, Tsung-Ming
Huang, and Weichung Wang (2010). "A
Parallel Additive Schwarz Preconditioned
Jacobi-Davidson Algorithm for Polynomial
Eigenvalue Problems in Quantum Dot
Simulation," Journal of Computational
Physics, 229(8):2932-2947. (SCI)
doi:10.1016/j.jcp.2009.12.024
[8] Yueh-Cheng Kuo, Wen-Wei Lin, Shih-Feng
Shieh, and Weichung Wang (2010). "A
Hyperplane-Constrained Continuation Method
for Near Singularity in Coupled Nonlinear
Schrödinger Equations," Applied Numerical
Mathematics, 60:513-526. (SCI) doi:10.1016/
j.apnum.2009.11.007
[9] Tsung-Ming Huang, Weichung Wang, and
Chang-Tse Lee (2010). "An Efficiency Study
of Polynomial Eigenvalue Problem Solvers
for Quantum Dot Simulations," Taiwanese
Journal of Mathematics, 14(3A):999-1021.
(Special Issue for Recent Advances in
Numerical Methods for Eigenvalue
Problems).
[10] Ray-Bing Chen, Weichung Wang, and C. F.
Jeff Wu (2010). "Building Surrogates with
Overcomplete Bases in Computer
Experiments with Applications to Bistable
Laser Diodes." IIE Transactions (Quality and
Reliability Engineering), to appear.
[11] Yukai Hung and Weichung Wang (2010).
"Accelerating Parallel Particle Swarm
Optimization via GPU," Optimization
Methods and Software, to appear. (SCI) doi:1
0.1080/10556788.2010.509435
[12] Tsung-Ming Huang, Wei-Jen Chang, YinLiang Huang, Wen-Wei Lin, Wei-Cheng
Wa n g , a n d We i c h u n g Wa n g ( 2 0 1 0 ) .
"Preconditioning Bandgap Eigenvalue
Problems in Three Dimensional Photonic
Crystals Simulations." Journal of
Computational Physics, (229):8684-8703.
(SCI) doi:10.1016/j.jcp.2010.08.003
[13] Yueh-Cheng Kuo, Wen-Wei Lin, Shih-Feng
S h i e h , a n d We i c h u n g Wa n g ( 2 0 1 0 ) .
"Exploring Bistability in Rotating Bose-
Highlights of the Regional Programs -›› 64
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
Einstein Condensates by a Quotient
Transformation Invariant Continuation
Method," Physica D: Nonlinear Phenomena,
to appear. doi:10.1016/j.physd.2010.08.008
K .-M. Shyue (2010). A high-resolution
mapped grid algorithm for compressible
multiphase flow problems, J. Comput. Phys.,
229, 8780-8801.
K.-M. Shyue (2010). A cavitation tracking
method for elastic-plastic flow in solids, AIP
Conference Proceedings, Vol. 1233, 620625.
K .-M. Shyue (2010). A moving-mesh
relaxation scheme for one-dimensional
barotropic two-phase flow with cavitation
(submit for publication)
P. H. Chiu, Long Lee, Tony W. H. Sheu
(2010), A sixth-order dual preserving
algorithm for the Camassa-Holm equation,
Journal of Computational and Applied
Mathematics Vol. 233, pp 2267-2278 (SCI)
C. M. Ho, R. K. Lin, S. F. Tsai, P. C. Liang,
To n y W. H . S h e u , P. H . L e e ( 2 0 1 0 ) ,
Simulation of portal hemodynamic changes
in a donor after right hepatectomy, Journal of
Biomechanical Engineering Vol. 132, issue
4, 04112-04117 , April (SCI)
P. H. Chiu, R. K. Lin, Tony W. H. Sheu
(2010) , A differentially interpolated direct
forcing incompressible Navier-Stokes
equations in time-varying complex
geometries, Journal of Computational
Physics , Vol. 229 , pp. 4476-4500
J. H. Li, Y. W. Cheng, Y. C. Chue, C. H. Lin,
Tony W. H. Sheu (2010), Influence of
propagating and evanescent waves for
focusing properties in zone plate structures,
Optics Express, Vol. 229, pp. 4476-4500
(SCI)
M axim A. Solovchuk, Tony W. H. Sheu
(2010), Exploration of shock structure by
bimodal distribution function method,
Physical Review E, 81, 056314 (SCI)
Tony W. H. Sheu, Y. W. Hung, M. H. Tsai, J.
H. Li (2010), On the development of a triplepreserving Maxwell's equations solver in
non-staggered grids, International Journal for
Numerical Methods in Fluids, Vol.63, pp.
1328-1346 (SCI)
[23] R
oberto Camassa, P. H. Chiu, Long Lee,
Tony W. H. Sheu (2010), Viscous and
inviscid regularizations in a class of
enolutionary partial differential equations,
Journal of Computational Physics, Vol. 229,
pp. 6676-6687
[24] T. W. H. Sheu, R. K. Lin, G. Y. Huang
(2010), Three-dimensional wake structure
around a square-back vehicle, Computational
Fluid Dynamics Journal (CFD J) (accepted)
[25] Tony W. H. Sheu, C. H. Yu, P. H. Chiu
(2010) , Development of a level set method
with good area preservation to predict
interface in two phase flows, International
Journal for Numerical Methods in Fluids (in
print)
[26] R oberto Camassa, P. H. Chiu, Long Lee,
Tony W. H. Sheu (2010), A particle method
and numerical study of a quasilinear partial
differential equation, Discrete and
Continuous Dynamics Systems-Series S
(accepted)
[27] T o n y W. H . S h e u , C . H . Yu ( 2 0 1 0 ) ,
Development of an incompressible NavierStokes solver involving symplectic and nonsymplectic time integrators, Numerical Heat
Transfer, Part A: Fundamentals (accepted)
[28] Tony W. H. Sheu, S. H. Kuo, Prediction of
temperature-dependent electroosmotically
driven microchannel flows with the Joule
heating effect, International Journal of
Numerical Methods for Heat & Fluid Flow
(accepted)
[29] T o n y W. H . S h e u , R . K . L i n , T h r e e dimensional bifurcations in a cubic cavity
due to buoyancy-driven natural convection,
Int. J. Heat and Mass Transfer (accepted)
E.3 Regional Programs on Statistics at Tainan
Coordinators: Tiee-Jian Wu (National Cheng-Kung University)
e state our activities in 5 different focus
areas (I-V below):
I. Probability Program
Coordinator: Wen-Jang Huang
The main goal is to generate some common
research interest among members and to learn
some new topics.
The activities from mid-April, 2010 to the
present time are as follows:
Mathematics, NSYSU) will give a talk in Applied
probability theory on Dec. 2, 2010 at NCKU.
2. Visitor
There was one visitor Prof. Jigao Yan, School
of Mathematical Sciences, Suzhou University (蘇
州大學), China, from August 16-29, 2010. He
gave a lecture entitled: "Some Limit Theory for
Weighted Sums and Levy Processes” at NCKU.
He has also discussed joint research work with T-J
Wu and has written the preliminary version of a
manuscript.
1. Seminar
Prof. Guan-Yu Chen陳冠宇(Department of
Applied Mathematics, National Chiao Tung
University)will give a seminar talk in probability/
stochastic process on Oct. 28, 2010 at NCKU.
Prof. May-Ru Chen 陳美如 (Department of
II. Statistical Methods
Coordinator: Tiee-Jian Wu
The activities from mid-April, 2010 to the
present time are as follows:
65 ‹‹- Highlights of the Regional Programs
1. Seminar
1. Seminar
Prof. Shang-Ying Shiu 須上英 (Department of
Statistics, National Taipei University) gave a
lecture entitled: ” A Clustering Algorithm by SelfUpdating Process” on April 22, 2010 at NCKU.
Prof. Ying-Chao Hung 洪英超(Department of
Statistics, National Chengchi University) gave a
talk entitled: ” Optimal Bayesian Strategies for
Bandit Problems with Infinitely Many Arms” on
April 29, 2010 at NCKU.
Prof. Yu-Jen Cheng of Institute of Statistics,
National Tsing Hua University gave a talk
entitled: "Causal Estimation for The Proportional
Hazard Model with Prevalent Sampling” on
4/15/2010. Prof. Kuang-Fu Cheng鄭光甫(China
Medical University Biostatistics Center, Taiwan)
gave a seminar lecture entitled: "Exploiting
Interaction Information in Detecting Loci That
Influence Complex Diseases” on 5/27/2010 at
NCKU. Prof. Chen-Hsiang Yeang楊振翔of
Institute of Statistical Sciences, Academia Sinica
will give a lecture in Bioinformatics/Genetics on
10/21/2010.
2. Visitors
Professor P-Y. Chen (陳平雲) of Syracuse
University visited NCTS (South) from 7/4/2010 to
7/11/2010 and gave a talk in the area of Signal
Processing. He also gave a talk in Ranking
Selection in the 2010 Southern Statistics
Conference of Taiwan, which was held at NCKU
in early July. He has also discussed a joint
research work with T-J Wu on "The weighted
average information criterion for multivariate
regression model selection”. A paper on this
subject has been submitted. Professor Song X.
Chen of Peking University & Dept. Statistics,
Iowa State University will visit NCKU and NCTS
(South) on 12/17-12/18/2010 and give a talk.
Professor Guangming Pan of Di v i s i o n o f
Mathematical Sciences, School of Physical and
Mathematical Sciences, Nan yang Technological
University, Singapore will visit NCTS (South) and
NSYSU from 1/5/2011 to 1/19/2011.
2. Visitor
Prof. and Chief Yu Shyr石瑜of Division of
Cancer Biostatistics, Dept. of Biostatistics &
Director of Cancer Biostatistics Center, Vanderbilt
University, USA will visit NCTS (South) and
NCKU from 1/3/2011 to 1/16/2011. He will give
talks in Bioinformatics and discuss research
project with faculties at Statistics Department of
NCKU.
IV. Financial Statistics and Time Series
Coordinator: Mei-Hui Guo
The activities from mid-April, 2010 to the
present time are as follows:
3. Workshop
1. Seminar
The ”2010 Workshop on Statistical Methods”
was held on June 24, 2010 at NCKU. There were
a series of lectures: "Modeling Multivariate Time
Series via Independent Components” and
"Constrained Factor Models and Their
Applications”, given by Prof. Ruey S. Tsay 蔡瑞
胸 (Academician of Academia Sinica & Professor
of University of Chicago, USA). Totally, there
were about 90 participants.
Professor Ostap Okhrin of Institute of Statistics
and Econometrics, Humboldt-University zu
Berlin, Germany gave a lecture entitled: "On the
S t r u c t u r e a n d E s t i m a t i o n o f H i e ra r c h i c a l
Archimedean Copulas” on 6/25/2010 at NUK,
III. Biostatistics and Bioinformatics
Coordinator: Tiee-Jian Wu
The activities from mid-April, 2010 to to the
present time are as follows:
Highlights of the Regional Programs -›› 66
2. Visitor
Professor Ostap Okhrin of Institute of Statistics
and Econometrics, Humboldt-University zu
Berlin, Germany visited our center from 6/246/27, 2010. He has given lectures in NUK (see
above) and discussed research ideas in financial
mathematics and statistics. Also, Prof. Guangming
Pan潘光明 of Division of Mathematical Sciences,
School of Physical and Mathematical Sciences,
Nan yang Technological University, Singapore
will visit our center from 1/5/2011 to 1/19/2011.
He will give several talks at NSYSU, NUK and
NCKU, and discuss research topics in Statistical
analysis of high dimensional time series models
V. Industrial Statistics
Coordinator: S.-L. Jeng
The activities from mid-April, 2010 to the
present time are as follows:
1. Seminar
Professor Kin Hing Phoa潘建興 of Institute of
Statistical Science, Academia Sinica gave a
seminar talk entitled: "Nonregular Designs: A
Better Choice for Experiments” on 5/6/2010 at
NCKU.
2. Visitor
Professor Vangazhiyil Roshan Joseph of Dept.
of Industrial and Systems Engineering, Georgia
Institute of Technology, USA will visit our center
from 11/20/2010-12/05/2010, give a talk in
industrial statistics and discuss research ideas with
faculties at NCKU.
Research Results
From mid-April, 2010 until the present time,
our program has already invited or will invite
totally 8 visiting scholars (among them, Prof.
Ruey S. Tsay is an academician of Academia
Sinica); held 10 seminar talks; sponsored the
"2010 workshop on Statistical Methods” (about 90
participants). Furthermore, under the (partial)
support of our program, 14 papers in the form of
reprints or preprints have been generated and
acknowledged the support of NCTS (South).
Publications
[1] M
u-Fa Chen (2010). Speed of stability for
birth death processes . Front. Math. China 5:3
, 379-515.
[2] P. Chen, L. Osadciw and T.-J. Wu (2010).
Multiple targets characterization of
e l e c t r o m a g n e t i c v u l n e r a b i l i t y. S i g n a l
Processing, 90, 344-351.
[3] X
. Luo and W-Y Tsai. (2010). Conditional
Nelson-Aalen and Kaplan-Meier Estimators
with MÄuller-Wang Boundary Kernel. World
Scientific Review Volume XL.
[4] R -B Chen, C-H Chu, T-Y Lai and Y-N Wu
(2010). Stochastic matching pursuit for
Bayesian variable selection. Stat Comput,
DOI 10.1007/s11222-009-9165-4.
[5] M .-R. Chen (2010). Two-person red-andblack game with Lower Limit. Probability in
the Engineering and Informational Sciences
(accepted).
[6] W. Wang, R-B Chen and C-L Hsu (2010).
Using Adaptive Multi-Accurate Function
Evaluations in a Surrogate-Assisted Method
for Computer Experiments (submitted).
[7] S.-C. Chen, L-A Li, S. Li and J. He (2010).
Influence of choices of statistical models on
neural spike trend (submitted).
[8] S.-C. Chen, M S. Rosenberg and B Lindsay
( 2 0 1 0 ) . M i x t u r e Tr e e : a p r o g r a m f o r
constructing phylogeny (submitted).
[9] S-.C. Chen, D M Hayden, S. S Young, and
J-N Tzeng (2010). he wavelet transforms and
statistical models for near infrared spectra
analysis (submitted).
[10] E M Buzaianu, P Chen and T-J Wu (2010).
Subset Selection Procedures to Identify EM
Fields Following Log-normal Distributions
(submitted).
[11] T-J Wu, P. Chen and Y. Yan. (2010). The
weighted average information criterion for
multivariate regression model selection
(submitted).
[12] J Yan, T-J Wu and C Su (2010). Some Limit
Theory for Weighted Sums and Levy
Processes (manuscript in preparation).
[13] S -L Jeng, B-Y Huang and W.Q. Meeker
(2010). Accelerated Destructive Degradation
Tests Robust to Distribution Misspecification
(submitted).
[14] T-J Wu, H-Y Chen and H-C Yu (2010). Root
n estimates of integrated squared density
partial derivatives (submitted).
67 ‹‹- Highlights of the Regional Programs
Activities of Onsite Scientists
Title
Center Scientists
Honorary Fellowship
Young Theory Award
Name
Postdoctoral Fellow
Activities of Onsite Scientists -›› 68
Period
Chih-Wen Shih
Dynamical Systems
2009/08/01-2011/07/31
Kuo-Chang Chen
(Chern Fellow)
Dynamical Systems
2009/08/01-2011/07/31
Ching-Hsiao Cheng
PDE
2009/08/01-2010/07/31
Wen-Ching Winnie Li
Number Theory
2009/05/14-2011/07/31
Song-Sun Lin
Dynamical Systems
2009/08/01-2010/07/31
Duy-Minh Nhieu
Differential Geometry
2009/08/01-2011/07/31
Wen-Wei Lin
Scientific Computation
2008/08/01-2010/07/31
Nan Kuo Ho
(Young Theory Award)
Differential Geometry
2009/08/01-2010/07/31
Jyh-Haur Teh
Algebraic Topology
2009/08/01-2010/07/31
Pei Yuan Wu
Operator Theory,
Functional Analysis,
Matrix Analysis
2009/08/01-2010/07/31
Yi-Fan Yang
Number Theory
2009/01/01-2010/12/31
Jung Chao Ban
Dynamical System
2010/01/01-2011/12/31
Jiun-Cheng Chen
Algebraic Geometry
2009/01/01-2011/12/31
Ching-Lung Lin
PDE
2009/01/01-2011/12/31
Jeng-Daw Yu
Number Theory
2009/01/01-2011/12/31
Der-Chen Chang
Differential Geometry
Fourier Analysis and
Geometric Analysis
Several Complex
Variables
2010/05/05-2010/07/19
Ching-Shui Cheng
Statistics
2010/05/26-2010/06/24
So-Hsiang Chou
Scientific Computation
2010/01/01-2010/04/30
Xiaoqing Zhao
Mathematical Biology
2010/03/07-2010/06/06
Andreas Schweizer
Number Theory
2008/08/01-2010/07/31
Chieh-Yu Chang
Number Theory
2009/08/01-2010/07/31
Visiting Professor
Visiting Associate
Professor
Field
.1 Center Scientists
I. Chih-Wen Shih
National Chiao-Tung University
National Center for Theoretic Sciences,
Center Scientist
Conferences and Visiting
- 1 8 th Conference on Differential Equations,
Taipei
- Annual Meeting, Taiwan Mathematical Society
• MBI, Ohio State University, USA
• Department of Mathematics, UBC, Canada
NCTS Activities
- N
CTS Dynamics Day - a Workshop focusing on
non-hyperbolic systems, Nov, 2009 (organizer)
- 2 010 NCTS Workshop on Dynamical Systems,
May, 2010 (organizer)
Visitors
• P
rofessor Ying-Cheng Lai, Arizona State
University, USA (Jan. 10 - 14, 2010)
Research works
1. C
h i h - We n S h i h , J u i - P i n Ts e n g , G l o b a l
synchronization and asymptotic phases for a
ring of identical cells with delayed coupling,
submitted
2. K
ang-Ling Liao, Chih-Wen Shih, Snapback
repellers and homoclinic orbits for multidimensional maps, submitted.
3. A
vner Friedman, Chiu-Yen Kao, Chih-Wen
S h i h , Tr a n s c r i p t i o n a l c o n t r o l i n c e l l
differentiation: asymptotic limit, preprint.
4. K
ang-Ling Liao, Chih-Wen Shih, Jui-Pin
Ts e n g , S y n c h r o n i z e d o s c i l l a t i o n f o r
segmentation clock gene of zebrafish,
submitted
II. Kuo-Chang Chen
National Tsing Hua University, Professor
Conferences and Workshops
1. N
C T S Ta i w a n - F r a n c e Wo r k s h o p o n
Theoretical Sciences, National Tsing Hua
Univeristy, Hsinchu, Taiwan, October 26,
2009. (40 min talk)
2. F
ourth Trilateral Meeting on Analysis and
Applications "Australia-Italy-Taiwan",
Academia Sinica, Taipei, Taiwan, December
7-11, 2009. (Organizer, 1-hour talk)
3. L
ecture Series for Special Topics in Analysis,
POSTECH, Pohang, Korea, November 23 December 4, 2009. (Main speaker)
4. A
IMS International Conference on Dynamical
Systems, Differential Equations and
Applications, Dresden, Germany, May 25-28,
2010. (Plenary speaker)
Visits
1. I saac Newton Institute for Mathematical
Sciences (Cambridge, UK) and Swansea
University (Swansea, Wales, UK), August
1-22, 2009.
2. C
hinese Academy of Sciences, Peking
University, Capital Normal University, Beijing,
China, January 5-28, 2010.
NCTS Activities
1. N
CTS Workshop on Calculus of Variations and
Related Topics, National Tsing Hua Univeristy,
H s i n c h u , Ta i w a n , M a y 6 - 8 , 2 0 1 0 .
(co-organizer)
2. N
CTS Workshop on Dynamical Systems,
National Tsing Hua Univeristy, Hsinchu,
Taiwan, May 12-15, 2010. (co-organizer)
3. NCTS Dynamical systems seminar
4. N
CTS Summer Course on Dynamical Systems,
July–August, 2010. (co-organizer)
Recent Publications
1. O
n action-minimizing retrograde and prograde
orbits of the three-body problem (with Y.-C.
Lin). Comm. Math. Phys., 291, 403-441
(2009).
69 ‹‹- Activities of Onsite Scientists
2. V
ariational constructions for some satellite
orbits in periodic gravitational force fields.
Amer. J. Math., 132, 681-709 (2010).
3. O
n the barycenter of the tent map (with Xun
Dong). Proc. Amer. Math. Soc., 138, 40254035 (2010).
4. C
onvex central configurations of the n-body
problem which are not strictly convex (with
J.S. Hsiao), preprint.
III. Ching-hsiao Cheng
National Central University, Assistant
Professor
Conferences and Visiting
– United States of America –
Visiting Professor Steve Shkoller at University
of California, Davis. (Jan.20 - Mar. 8 and Jul. 5 Sep. 5 2010)
– The Republic of China, Taiwan –
• 2 009 Fourth Trilateral Meeting on Analysis and
Applications "Australia -Italia-Taiwan”, Taipei,
Taiwan. (Dec. 7 - Dec. 11, 2009)
• F
o u r t h Wo r k s h o p o n N o n l i n e a r P a r t i a l
Differential Equations: Analysis, Computation
and Applications, Taipei, Taiwan. (Jun. 11 - Jun.
14, 2010)
NCTS Activities
• 2 010 NCTS short course on free boundary
problems, lecturer (May 20~Jun. 17, 2010)
Publications
1. C
.H. Arthur Cheng, Steve Shkoller, "The
interaction of the 3D Navier-Stokes equations
with a moving nonlinear Koiter elastic shell",
to appear on SIAM J. Math. Anal., 42(3).
2. C.H. A. Cheng, D. Coutand, and S. Shkoller,
"On the limit as the density ratio tends to zero
for two perfect incompressible 3-D fluids
separated by a surface of discontinuity",
Comm, Partial Differential Equations, 35, 817-845, (2010).
Activities of Onsite Scientists -›› 70
IV. Wen-Ching Winnie Li
Professor of Mathematics, Pennsylvania State
University
Director, National center for Theoretical
Sciences (beginning June 1, 2009)
Activities Organized
1. I organized a weekly student seminar titled
"Introduction to p-adic Hodge theory", from
fall 2009 to spring 2010.
2. I hosted the visit by Prof. Ling Long, Iowa
State University, July 6-Aug 4, 2009. We
worked together on noncongruence modular
forms.
3. T
ogether with the Division Head Prof. ChungYu Mou of physics division, we organized
"Taiwan-France Workshop on Theoretical
Sciences", Oct. 26, 2009. This is part of the
international co-operation program with France
cosponsored by the NSC, Institut Francais de
Taipei, Institut des Hautes Études Scientifiques
(IHES), Centre National de la Recherche
Scientifique (CNRS), and NCTS. A group of
four French delegates visited various
institutions in Taiwan Oct 20 to 27, 2009 to
promote further scientific co-operative
activities. During the one day workshop four
French and four Taiwanese scientists gave
lectures. Among them, four were physicists and
four mathematicians. There was also a photo
picture exhibition titled "The Unravelers"
provided by the IHES to celebrate their 50th
anniversary.
4. W
ith JoungJu Choie we organized a special
session on "Modular forms and related topics"
in KMS-AMS meeting in Seoul, Korea, Dec.
16-17, 2009. Five mathematicians from Taiwan
were invited to speak. The same group of
people visited Postech University Dec. 19-20,
2009 to attend a number theory workshop
jointly organized by Choie and myself. This is
the first joint conference between the Pohang
Mathematics Institute and NCTS.
5. I offered a joint advanced graduate course with
Andreas Schweizer titled "Noncongruence
subgroups and noncongruence modular forms"
at NCTS in the spring semester of 2010.
6. J oint with Andrew Granville and Eyal Goran, I
co-organized a "Workshop on graphs and
arithmetic" at CRM, Montreal, Canada, March
8-12, 2010. Two of the speakers were from
Taiwan.
– Taiwan –
7. I hosted the visit by Prof. Keqin Feng of
Tsinghua University in Beijing, China, June
24-July 7, 2010. During this period, Prof. Feng
also visited NCTS subproject II at NCKU for 5
days.
• T
aiwanese Mathematics Society Annual
Meeting, Dec 4-6, 2009, Chiayi, Invited Plenary
Address: Unreasonable effectiveness of number
theory.
8. J oint with Young-Ju Choie, we organized the
"2010 Taiwan-Korea workshop on number
theory", July 5-6, 2010. This is the second joint
activity between NCTS and Postech. A group
of 11 Korean number theorists visited Taiwan.
Among the 11 speakers, 6 are from Korea and
5 from Taiwan.
• 2 010 Taiwan-Korea Workshop on Number
Theory, July 5-6, 2010, co-organizer.
9. T
ogether with Jing Yu, we organized the
"NCTS international conference on
automorphic forms and related topics", July
7-9, 2010. Nineteen number theorists from 6
different countries in the world spoke in this
conference. Among them seven were from
Taiwan.
10. During the week July 12-16, 2010, I invited
professors S. Friedberg, J. Hoffstein, D. Jiang,
and M. Tsfasman to give survey talks,
summarizing recent key developments of
certain important areas in number theory.
11. I actively organized and participated in the two
summer student programs in number theory in
July-August, 2010, led by Y. Yang. and W.
Yao.
Conferences / Workshops
– Canada –
• W
orkshop on Graphs and Arithmetics, March
8-12, 2010, CRM, Montreal, Canada,
co-organizer.
– Korea –
• I nternational Workshop on Theoretical Sciences,
a Taiwan-France bilateral conference in physics
and mathematics held at NCTS, Oct 26, 2009,
co-organizer.
• W
orkshop of Algebra and Geometry, Chiayi,
April 30-May 1, 2010, invited speaker, title: The
Riemann Hypothesis.
• N
CTS International Conference on
Automorphic Forms and Related Topics, July
7-9, 2010, co-organizer.
– Turkey –
• I nternational Conference on Sequences, Codes
and Curves, September 25-29, Antalya, Turkey,
invited speaker, title: Zeta functions of the
pseudocodewords of low-density-parity-check
codes.
– United States –
• N
umber theory and Representation Theory{
conference in honor of Benedict Gross's 60th
birthday, Harvard Univ., June 3-5, 2010.
• P
seudorandomness in Mathematical
StructuresWorkshop, Institute for Advanced
Study, Princeton, N.J., June 14-18, 2010.
Colloquium/Seminar Talks
1. Canada
McGill, Concordia, and Montreal Universities
joint colloquium, March 12, 2010, invited speaker,
title: Recent development on the arithmetic of
noncongruence modular forms.
2. Taiwan
• S
pecial session on Modular Forms and Related
Topics, AMS-KMS joint meeting in Seoul, Dec.
16-17, 2009, co-organizer.
• C
olloquium, National Chiao-Tung University,
D e c . 8 , 2 0 0 9 , i n v i t e d s p e a k e r, t i t l e :
Unreasonable effectiveness of number theory.
• P
ostech-TaiwanWorkshop in Number Theory,
Pohang, Dec. 19-20, 2009, invited speaker, title:
Recent developments in noncongruence
modular forms.
• C
olloquium, National Taiwan University, March
1, 2010, invited speaker, title: Unreasonable
effectiveness of number theory.
71 ‹‹- Activities of Onsite Scientists
• N
CTS Open Problems seminar, March 24,
2010, invited speaker, title: The Riemann
Hypothesis.
• C
olloquium, National Cheng-Kung University,
May 6, 2010, invited speaker, title: The
Riemann Hypothesis.
3. Turkey
Number Theory Seminar, October 5, 2009,
Middle East Technical University, Ankara, Turkey,
invited speaker, title: Modular curves and coding
theory.
4. United States
Workshop on Noncongruence Modular Forms
and Modularity, August 17-21, 2009, American
Institute of Mathematics, Palo Alto, CA, U.S.A.,
co-organizer.
Publications
A. NCTS affiliated
1. Modular curves and coding theory: a survey,
Proceedings of the Ninth International
Conference on Finite Fields and
Applications, Dublin, Contemporary Math.
vol 518, 301-313 (2010), Amer. Math. Soc.,
Providence.
3. (with Ming-Hsuan Kang) Zeta functions of
complexes arising from PGL(3), submitted.
V. Song-Sun Lin
National Chiao-Tung University,
Chair Professor of National Chiao-Tung
University
Publications
• N
onemptiness problems of plane square tiling
with two colors, Proceedings of American
Mathematical Society, (2010), to appear. (with
W.G. Hu)
• S
patial entropy and minimal cycles of edge
coloring, preprint. (with J.Y. Chen and W.G.
Hu)
• M
ixing property of two dimensional shifts of
finite type, preprint. (with J.C. Ban, W.G. Hu
and Y.H. Lin)
VI. Duy-Minh Nhieu
2. Zeta functions of group based graphs and
complexes. Fields Communications Volume
WIN - Women In Numbers, Proceedings of
the WIN Workshop, Banff International
Research Station, Banff, Canada, to appear.
National Central University, Professor
National Center for Theoretic Sciences,
Center Scientist
3. ( joint with Oliver Atkin, Ling Long and
Tong Liu) Galois representations with
quaternion multiplications associated to
noncongruence modular forms, submitted.
2009 Taiwan-Norway Joint Workshop on
Geometric Analysis and Mathematical Physics,
NCTS, Dec 15-16, 2009. Invited speaker.
B. Acknowledging NCTS
1. Zeta functions in combinatorics and number
theory, Proceedings of the 4th In- ternational
Congress of Chinese Mathematicians,
Hangzhou, China, 2007, AMS/IP Studies in
Advanced Mathematics, vol. 48 (2010), 351366.
2. ( with Ming-Hsuan Kang and Chian-Jen
Wang) Zeta functions of complexes from
PGL(3): a representation-theoretic approach,
Israel J. Math, vol. 177 (2010), 335-347.
Activities of Onsite Scientists -›› 72
Conferences
Workshop/Seminar/Minicourse
• N
CTS Course in Aspects of Analysis on Model
Domains in Cn+1, NCTS, May 17-June 28 2010,
Instructor (with Der-Chen Chang).
• W
orshop on Harmonic Analysis, July 05-July
16, NCU, Co-organizer with Chin-Cheng Lin
and Ming Yi Lee. Invited speakers: J. G. Bak,
Pohang University of Science and Technology,
Korea, Yongsheng Han, Auburn University,
USA, Marcin Bownik, University of Oregon,
USA, Kazo Yabuta, Kwansei Gakuin University,
Japan.
Referee
IEEE transaction on signal processing.
Reviews:
Reviewed papers for the AMS Math review
(three papers).
Publications
• j oint with D. Danielli, N. Garofalo, SubRiemannian Calculus and monotonicity of the
perimeter for graphical strips, Math Z., 265
(2010), no. 3, 617--637
• joint with D. Danielli, N. Garofalo and S. Pauls,
The Bernstein problem for embedded surfaces in
the Heisenberg group H^1,Indiana Journal of
Mathematics. (to appear)
VII. Wen-Wei Lin
National Chiao-Tung University,
National Chairship Professor
Chair Professor of Chiao Tung University
Conferences and Visitings
-Italy-
• 1 5th Conference of the International Linear
Algebra Society (ILAS2010), Pisa, Italy, June,
2010 (Invited Speaker).
• P
r o f e s s o r E r i c K i n g - Wa h C h u , M o n a s h
University, Australia (May. 24 - Jun. 16, 2010)
Publications
1. Q uadratic Model Updating with Symmetry,
Positive Definiteness and No Spill-Over, SIAM
Matrix Anal. Appl., Vol. 31, No. 2 (2009), 546564. (with D. Chu and M. Chu)
2. A
Minimal Energy Tracking Method for Nonradially Symmetric Solutions of Coupled
Nonlinear Schrödinger Equations, J. Comp.
Physics, Vol. 228, No. 21 (2009), 7941-7956.
(with Y. C. Kuo, S. F. Shieh and W. Wang)
3. C
haotic Synchronization in Lattices of TwoVariable Maps Coupled with One-Variable,
IMA J. Appl. Math., Vol. 74, No. 6 (2009),
827-850. (with C. C. Peng and Y. Q. Wang)
4. C
onvergence Rates of Some Iterative Methods
for Nonsymmetric Algebraic Riccati Equations
Arising in Transport Theory, Lin. Alg. Appl.,
Vol. 432, No. 1 (2010), 283-291. (with C. H.
Guo)
5. A
Structure-Preserving Doubling Algorithm for
Quadratic Eigenvalue Problems Arising from
Time-Delay Systems, J. Comp. Appl. Math.,
Vol. 223 (2010), 1799-1745. (with T. Li and E.
K. W. Chu)
-Germany-
6. S
tructured Backward Error for Palindromic
Polynomial Eigenvalue Problems, Numer.
Math., 2010, Vol. 116, No. 1 (2010), 95-122.
(with R. C. Li and C. S. Wang)
Visitors
VIII. Nan-Kuo Ho
• I nternational Workshop on Accurate Solutions
of Eigenvalue Problems (IWASEP), Berlin,
Germany, July, 2010 (Invited Speaker).
• P
r o f e s s o r E r i c K i n g - Wa h C h u , M o n a s h
University, Australia (Nov. 15 - Dec. 31, 2009)
• P
rofessor Yi-Qian Wang, Nanjing University,
China (Nov. 15 - Nov. 27, 2009)
• P
rofessor So-Hsiang Chou, Bowling Green
State University, USA (Jan. 1 - Jun. 60, 2010)
• P
rofessor Biswa Nath Datta, North Carolina
State University, USA, (Jan. 12 - Feb. 1, 2010)
• P
rofessor Moody T. Chu, North Carolina State
University, USA, (Mar. 29 - Apr. 9, 2010)
National Tsing Hua University, Professor
National Center for Theoretic Sciences,
Center Scientist
Conferences (invited speaker)
1. T he 2 nd TIMS-OCAMI Joint International
Workshop on Differential Geometry and
Geometric Analysis, Taipei, Taiwan, March
21-23, 2010.
Visits
1. G e o rg - A u g u s t - U n i v e r s i t a t G o t t i n g e n ,
73 ‹‹- Activities of Onsite Scientists
Germany. Visit Prof. Chenchang Zhu from 10
April 2010 to 20 April 2010.
•
ach week I invited experts to talk famous
E
open problems in their fields for undergraduate
and graduate students. We were able to manage
to have 12 lectures in the spring semester of
2010, and the problems were from algebraic
geometry, number theory, dynamical system,
mathematical physics and complex analysis.
2. C
hinese University of Hong Kong, Hong Kong.
Visit Prof. Xiaowei Wang from 14 March 2010
to 20 March 2010.
3. H
ong Kong University, Hong Kong. Visit Prof.
Siye Wu from 24 March 2010 to 2 April 2010.
4. U
niversity of Geneva, Geneva, Visit Prof.
Anton Alekseev from 20 April 2010 to 8 May
2010.
•
NCTS Activities
2. O
rganizing the NCTS(Taiwan)-CPT(France)
joint workshop which will be held on February
21-25, 2011.
Research Works
1. ( Joint with C.C. Melissa Liu) Anti-perfect
Morse Stratification, to appear in Selecta
Mathematica.
2. ( Joint with C.C. Melissa Liu and Daniel
Ramras) Orientability in Yang-Mills Theory
over Nonorientable Surfaces, Comm. Anal.
Geom. 17 (2009), no.5, 903-953.
3. ( Joint with C.C. Melissa Liu) Yang-Mills
connections on Orientable and Nonorientable
Surfaces, Memoirs of the AMS. 202 (2009),
no.948, 1-98.
IX. Jyh-Haur Teh
National Tsing-Hua University, Associate
Professor
Conferences and Visitings
-Taiwan-
Invited Speaker, Semi-topological algebraic
geometry, in Workshop of algebra and geometry,
April, 2010, National Chung Cheng University.
NCTS Activities
Activities of Onsite Scientists -›› 74
Student Seminar On Modern Geometry
I n the spring semester of 2010, four graduate
students under my supervision studying
different aspects of geometry. They presented
each week for half to one hour, focused on
topics about Clifford algebras, Dirac operators,
the proof of Hodge theorem, topological
K-theory and differential forms.
5. U
niversity of Toronto, Toronto, Visit Prof. Lisa
Jeffrey from 22 June 2010 to 23 August 2010.
1. N
CTS student seminar on Geometry and
Topology.
Open Problem Seminar
•
tudent Seminar On Algebraic Geometry And
S
Algebraic Topology
I n the summer vacation of 2010, 10 students
who were participants of NCTS summer
independent study program were under my
supervision to study different topics in
algebraic geometry and algebraic topology.
Topics included Galois theory, covering
s p a c e s , e l l i p t i c c u r v e s , c o d i n g t h e o r y,
Riemannian geometry, Feynman integrals and
complex manifolds.
Publications
• J .H. Teh, Semi-topological algebraic geometry,
arXiv:1001.2355, submitted.
• J . H . Te h , A l m o s t a l g e b r a i c g e o m e t r y,
arXiv:1001.2371, submitted.
• H . Y. Liao and J. H. Teh, Semi-topological
Galois theory and the inverse Galois problem,
arXiv:1006.1166, submitted.
• J . H. Teh, Stringy mirror symmetry, arXiv:
1007.4448, submitted.
X. Pei Yuan Wu
National Chiao Tung University, Professor
Conferences
1. P
articipation of the conference: Abstract
Harmonic Analysis 2009 (Kaohsiung, Taiwan,
December 18 – 22, 2009)
2. P
articipation and invited talk at the NCTS
Colloquium: Jordan Theory and Analysis
(Hsinchu, Taiwan, April 8 – 12, 2010, "A
journey through numerical ranges”)
3. P
articipation and invited talk at the conference:
The 5th Workshop on Matrices and Operators
(Taiyuan, Shanxi, China, July 11 – 15, 2010,
"Crawford numbers of powers of a matrix”)
4. P
articipation and invited talk at the conference:
The 9 th International Conference on Matrix
Theory and its Applications (Shanghai, China,
July 18 – 22, 2010, "A journey through
numerical ranges”)
Publications
1. P
. Y. Wu, H.-L. Gau and M. C. Tsai, Numerical
radius inequality for C0 contractions, Linear
Algebra Appl., 430 (2009), 1509 – 1516.
2. H .-L. Gau and P. Y. Wu, Inner functions of
numerical contractions, Linear Algebra Appl.,
430 (2009), 2182 – 2191.
3. K.-Z. Wang and P. Y. Wu, Numerical ranges of
radial Toeplitz operators on Bergman space,
Integral Equations Operator Theory, 65 (2009),
581 – 591.
4. H.-L. Gau, C. K. Li and P. Y. Wu, Higher-rank
numerical ranges and dilations, J. Operator
Theory, 63 (2010), 181 – 189.
5. H .-L. Gau and P. Y. Wu, Unitary part of a
contraction, J. Math. Anal. Appl., 366 (2010),
700 – 705.
6. H .-L. Gau and P. Y. Wu, Defect indices of
powers of a contraction, Linear Algebra Appl.,
432 (2010), 2824 – 2833.
7. K.-Z. Wang and P. Y. Wu, Crawford numbers
of powers of a matrix, Linear Algebra Appl.,
accepted.
Conference talks
1. C onstruction and applications of a class of
modular functions, Joint workshop on number
theory between Japan and Taiwan, Waseda
University, Japan, March 9-11, 2009.
2. C ongruences of the partition function, East
Asia number theory conference, Tsing Hua
University, China, August 19-22, 2009.
3. Congruences of the partition function, Nankai
number theory conference, Nankai University,
China, August 24-28, 2009.
4. Congruence of the partition function, KMSAMS joint meeting, Seoul, Korea, December
15-20, 2009.
5. M onodromy of Picard-Fuchs differential
equation, Postech-NCTS Workshop on number
theory, Pohang, Korea, December 19-20, 2009.
6. M odular forms of half-integral weights on
SL(2,Z), Automorphic forms and related topics,
NCTS, Hsinchu, Taiwan, July 7-9, 2010.
7. Apery limits and special values of L-functions,
Tokyo Metropolitan University workshop,
August 24, 2010.
8. Jacobsthal identity for Q(sqrt(-2)), Workshop
on number theory, geometry, and physics at the
crossroads, Tsuda College, Japan, August
30-31, 2010.
Visits
1. Waseda University, Japan, visit Ki-Ichiro
Hashimoto from July 25 to August 16, 2009.
2. Waseda University, Japan, visit Ki-Ichiro
Hashimoto from January 20 to February 10,
2010.
3. T
suda College, Japan, visit Shinji Fukuhara
from August 21 to September 4, 2010.
NCTS Activities
F.2 Honorary Fellowship
Yifan Yang
National Chiao Tung University, Professor
National Center for Theoretic Sciences,
Center Scientist
• NCTS number theory seminar.
Research Works
1. S
hinji Fukuhara and Yifan Yang, period
polynomials and explicit formulas for Hecke
operators on Gamma_0(2), Math. Proc.
Cambridge Philos. Soc., 146 (2009), 321-250.
75 ‹‹- Activities of Onsite Scientists
2. F
ang-Ting Tu and Yifan Yang, defining
equations of X_0(2^{2n}), Osaka J. Math, 46
(2009), 105-113.
– United States –
3. Y
ifan Yang, modular units and cuspidal divisor
class groups of X_1(N), J. Algebra, 322 (2009),
514-553.
• 1 2 th international workshop on Cellular
Nanoscale Networks and their Applications.
B e r k e l e y, U . S . A . F e b r u a r y 3 ~ 5 ( 2 0 1 0 ) ,
University of California, Berkeley - section
chair and invited speaker.
4. A
ristides Kontogeorgis and Yifan Yang,
automorphism groups of hyperelliptic modular
curves, LMS J. Comp. Math. 13 (2010), 144163.
– China –
• D
epartment of Mathematics, University of
Science and Technology of China, China,
September 1 (2010).
5. Y
ifan Yang and Jeng-Daw Yu, structure of the
cuspidal rational torsion subgroups of
J_1(p^n), J. London Math. Soc 82 (2010), 203228.
NCTS Activities
6. S
hinji Fukuhara and Yifan Yang, twisted Hecke
L-values and period polynomials, J. Number
Theory 130 (2010), 976-999.
Publications
7. H
eng Huat Chan, Ling Long, and Yifan Yang,
a cubic analogue of the Jacobsthal identity,
Amer. Math. Monthly, to appear.
8. Y
ifan Yang and Wadim Zudilin, an Sp_4
modularity of Picard-Fuchs differential
e q u a t i o n s f o r C a l a b i - Ya u t h re e f o l d s ,
Contemporary Math 517, 381-413.
9. Y
ifan Yang, congruences of the partition
function, Int. Math. Res. Not., in press.
10. H eng Huat Chan, Yoshio Tanigawa, Yifan
Yang, and Wadim Zudilin, new analogues of
Clausen’s identities arising from the theory of
modular forms, submitted.
11. Ki-Ichiro Hashimoto, Ling Long, and Yifan
Yang, Jacobsthal identity for Q(sqrt(-2)),
submitted.
12. S
hinji Fukuhara and Yifan Yang, a basis for
M_k(Gamma_0(4)) and representations of
integers as sums of squares, submitted.
F.3 Young Theory Award
I. Jung Chao Ban
National Dong Hwa University, Associate
Professor
Conferences and Visiting
Activities of Onsite Scientists -›› 76
• 2 010 CTS Workshop on Dynamical Systems invited speaker (May 12~15, 2010)
1. H
ausdorff dimension and variational principle
for repellers, Trans Amer. Math. Soc. vol. 362,
no.2, 727-751 (2010) (with Yong-Luo Cao &
Huyi Hu).
2. C
ellular neural networks and zeta functions
Proc. 12th international workshop on Cellular
Nanoscale Networks and their Applications
(2010) (with Wen-Guei Hu, Song-Sun Lin &
Yin-Heng Lin).
3. S
patial complexity in multi-layer cellular
neural networks, Proc. 12 th international
workshop on Cellular Nanoscale Networks
and their Applications (2010) (with ChihHung Chang, Song-Sun Lin & Yin-Heng Lin).
4. P
ullback and forward attractors for dissipative
cellular neural networks with additive noises,
Proc. 12 th international workshop on
Cellular Nanoscale Networks and their
Applications (2010) (with Cheng-Hsiung Hsu
& Tzi-Sheng Yang).
5. M
ultifractal analysis of matrix potential under
countable sofic shifts, submitted (2010).
6. M
ultifractal analysis for products of positive
matrices under countable symbol spaces,
submitted (2010) (with Yong-Luo Cao & Yun
Zhao).
7. F
ractral dimension of one-dimensional cellular
automata, submitted (2010) (with Chih-Hung
Chang).
8. F
actor, diamond and density of pressure,
submitted (2010) (with Chih-Hung Chang).
9. T
he complexity of permutive cellular
automata, submitted (2010) (with Chih-Hung
Chang, Ting-Ju Chen & Mei-Shao Lin).
10. Z
eta function for two-dimensional subshift of
finite type, submitted (2010) (with Wen-Guei
Hu, Song-Sun Lin & Yin-Heng Lin).
II. Jiun-Cheng Chen
National Tsing Hua University, Associate
Professor
Conferences and visiting
• N
TU MATH MONTH(July, 2009): Invited
Speaker.
• Visiting Ohio State (July-August, 2010)
NCTS Activities
• NCTS Algebraic Geometry Seminar
• NCTS Student Complex geometry Seminar
Visitings
• D
ept. of Math., Hokkaido Univ, August 17-31
2010.
NCTS Activities
• T
o p i c a l P r o g r a m i n P a r t i a l D i ff e r e n t i a l
Equations 2010 -01-19~ 2010-02-04
• T
he summer course in PDE at NCTS 2010 -0629~ 2010-08-10
Research Works
• C
hing-Lung Lin, Gunther Uhlmann and JennN a n Wa n g ( 2 0 1 0 ) , O p t i m a l t h r e e - b a l l
inequalities and quantitative uniqueness for the
Stokes system, DCDS-A, (28), No.3, 1273-1290.
A special issue. Dedicated to Louis Nirenberg
on the occasion of his 85th birthday edited by
Luis Caffarelli, Yanyan Li.
• C
hing-Lung Lin, Gen Nakamura and Jenn-Nan
Wang (2010), Optimal three-ball inequalities
and quantitative uniqueness for the Lame
system with Lipschitz coefficients, Duke
Mathematical Journal.(155), No.1, 189-204
Publications
• J iun-Cheng Chen, On Mukai Conjecture with
large Pseduo-index. To appear in Advance in
Pure Mathematics, 2010.
• J iun-Cheng Chen, Hsian-Hua Tseng, Cone
Theorem via Deligne-Mumford stacks,
Mathematische Annalen (363), 2009.
IV. Jeng-Daw Yu
National Taiwan University, Assistant
Professor
Conferences and Visiting
-Korea-
III. Ching-Lung Lin
Visiting: Korea Institute for Advanced Study,
Seoul, January 20 – 27, 2010.
National Cheng-Kung University,Associated
Professor
-Spain-
I do the qualitative and quantitative uniqueness
for some equations and elasticity systems.These
results are quite useful in studying the nodal sets
of eigenfunctions or localization in the AndersonBernoulli model. It is an important tool for
stability estimates in inverse boundary value
problems.It also connected with volume bounds of
unknown inclusions in terms of boundary
measurements.
Summer School: p-adic Cohomologies and
Arithmetic Applications. IMUS, University of
Sevilla, Seville, June 14 – 18, 2010.
-Taiwan-
Conference: Higher Dimensional Algebraic
Geometry. National Taiwan University, March 29
– April 2, 2010. [Invited speaker]
Conference: Workshop on Arithmetic Geometry
and Related Topics. TIMS, National Taiwan
University, July 12 – 16, 2010. [Organizer]
77 ‹‹- Activities of Onsite Scientists
-UK-
Conf er ence: Effe ctive Me thods in p - a d i c
cohomology. Oxford University, March 15 – 19,
2010. [Invited speaker]
Publications
• ( With Y. Yang) Structure of the cuspidal rational
torsion subgroup of J_1(p^n). J. Lond. Math.
Soc. (2) 82 (2010), no. 1, 203 – 228.
• S
pecial lifts of ordinary K3 surfaces and
applications. To appear in Pure Appl. Math. Q
F.4 Visiting Professor
Andrea Fraser from Dalhousie University at
Canada; Professor Mitsuru Sugimoto from
Nagoya University, Japan; Professor Der-Chen
Chang from Georgetown University, USA;
Professor Ming-Yi Lee from National Central
University and Professor Hwai-Chiuan Wang and
Dr. Jin-Wen Lan from National Tsing Hua
University. All speakers gave very nice talks on
different topics in Fourier analysis which
including compactness properties of partial
differential operators, applications of pseudodifferential operators to parabolic PDEs; Hardy
type inequalities; estimates for boundary value
problems for elliptic PDEs in Hardy spaces and
BMO; harmonic analysis on the Heisenberg
group.
I co-organized two Workshops with Professor
Chiung-Jue Sung from National Tsing Hua
University. The first was "2010 NCTS Workshop
on Fourier Analysis and Its Applications to
PDEs” which was held at NCTS on July 1, 2010.
The second workshop I organized with
Professor Chiung-Jue Sung from National Tsing
Hua University was the "2010 NCTS
International Conference on Several Complex
Variables and Complex Geometry” which was
held at NCTS and from July 9-11, 2010. The
invited speakers are Professor Shing-Tung Yau
and Professor Yum-Tong Siu from Harvard
University; Professor Peter Greiner from
University of Toronto; Professor John Erik
Fornaess from University of Michigan at Ann
Arbor; Professor Paul Yang from Princeton
University; Professor Nagi-Ming Mok from
University of Hong Kong; Professor Xiaojun
Huang from Rutgers University at New
Brunswick; Professor Mei-Chi Shaw from
University of Notre Dame; Professor Stephen S.T.
Yau from University of Illinois at Chicago;
Professor Song-Ying Li from University of
California at Irvine; Professor Xianghong Gong
from University of Wisconsin at Madison;
Professor Sai Kee Yeung from Purdue University
Professor, Profesor Der-Chen Chang from
Georgetown University, Professor Chiung-Jue
Sung and Professor Hung-Ling Chiu from
National Central University. The conference was
extremely successful and set up a very high
standard for mathematical activities in Taiwan.
Speakers introduced their update research projects
to audiences. Besides, Professor Yum-Tong Siu
also gave comments at the end of almost every
talk and pointed out possible new research
directions related to the talks.
The speakers were Professor Eric Grinberg
from New Hampshire University; Professor
Besides that, I was invited to give colloquium
talks at two universities which including National
I. Der-Chen Chang
Georgetown University and NCTS
Activities Participation
During my visit at NCTS, I gave a series of
lectures on "Geometric Analysis on Model
Domains in C n ” (with Professor Nhieu from
National Central University) at NCTS (Hsinchu).
There were more than 8 students from National
Tsing Hua University, National Chung-Cheng
University and National Central University plus
several research assistants from NCTS to attend
my lectures. Two of the students who attended this
short course received their Ph.D. degrees during
last summer. Dr. Ting-Huei Chang graduated from
National Tsing University and Dr. Liang-Chu
Chang received her Ph.D. degree from National
Chung-Cheng University. They attended my
lectures in the past few years while I visited
NCTS. We are now woring together on Li-Yau
estimates on sub-elliptic partial operators. After I
came back from Taiwan, we continue to discuss
this project through email messages. It is my great
pleasure to work with these two bright young
researchers in Taiwan.
Activities of Onsite Scientists -›› 78
Sun-Yat Sen University and Fu-Jen Catholic
University. These activities give me opportunities
to exchange ideas in mathematics with colleagues
in Taiwan.
CTS Preprints:
• G
eometric analysis on generalized Hermite
operators, (with Sheng-Ya Feng), NCST
preprint, (2010).
Current Projects
Two of the students who attended this short
course received their Ph.D. degrees during last
summer. Dr. Ting-Huei Chang graduated from
National Tsing University and Dr. Liang-Chu
Chang received her Ph.D. degree from National
Chung-Cheng University. They attended my
lectures in the past few years while I visited
NCTS. We are now woring together on Li-Yau
estimates on sub-elliptic partial operators. After I
came back from Taiwan, we continue to discuss
this project through email messages. It is my great
pleasure to work with these two bright young
researchers in Taiwan.
I am also working on a project with Professor
Ming-Yi Lee from National Central University.
We try to prove a div-curl lemma for weighted
Hardy spaces and weighted BMO. This will round
out the picture of the direction which was initiated
by Coifman, Lions, and Simmes. We have already
obtained some preliminary results on this project.
Activities Promotion
During June 28 to June 30, 2010, I
c o - o rg a n i z e d t h e 2 0 1 0 N C T S / T P E - T I M S
minicourse and Workshop on Geometric and
Complex Analysis with Professor Shu-Cheng
Chang and Professor Mao-Pei Tsui at the National
Taiwan University. The speakers were Professor
Mei-Chi Shaw from University of Notre Dame;
Professor Jih Hsin Cheng from the Amademia
Sinica; Professor Walter Wei from University of
O k l a h o m a ; P r o f e s s o r B e n We i k o v e f r o m
University of California at San Diego; Professor
Eric Grinberg from New Hampshire University;
Professor Andrea Fraser from Dalhousie
University at Canada and me.
I was invited to serve on committees for final
oral exams of two Ph.D. candidates: Dr. TingHuei Chang from National Tsing University and
Dr. Liang-Chu Chang from National ChungCheng University. I was also invited to serve on a
committee for final oral exams of master degree
candidate: Mr. Shi-Tsun Wu from Fu-Jen Catholic
University
II. Ching-Shui Cheng
University of California, Berkeley
During my visit in summer 2009, I gave a
series of four three-hour lectures on "MultiStratum Fractional Factorial Designs”, covering
the analysis, construction and optimality of
factorial designs in experiments with multipleerror terms resulting from complex structures of
the experimental units. I gave another series of
four three-hour lectures on "Minimum Aberration
and Some Related Criteria for Fractional Factorial
Designs” in summer 2010, discussing a popular
criterion for choosing fractional factorial designs
and its relation to other criteria that have been
proposed in the literature. In both series of
lectures, I gave extensive reviews of the state of
art, and pointed out directions for further research.
During my visits, I had frequent discussions
with Professor Sheng-Tsaing Tseng and Professor
Shao-Wei Cheng at the Institute of Statistics,
National Tsing Hua University, on research topics
and the role that the National Center for
Theoretical Sciences can play in promoting the
development of statistics research in Taiwan. I
also collaborated with Professor Pi-Wen Tsai at
National Taiwan Normal University on research.
We have completed a paper entitled "Multistratum
Fractional Factorial Designs”, which has been
accepted by Statistica Sinica. Another paper is
being written.
I gave a colloquium talk at the Institute of
Statistics, National Chiao-Tung University, on
June 4, 2010.
The visits also provided me with the
opportunity to write a book on the theory of
fractional factorial design. I have completed about
380 double-spaced pages.
Paper completed with the support of NCTS:
• C
heng, C.S. and Tsai, P. W. "Multistratum
Fractional Factorial Designs”, to appear in
Statistica Sinica.
79 ‹‹- Activities of Onsite Scientists
III. So-Hsiang Chou
Teaching
Bowling Green state University
During my visit at NCTS, I taught the NCTS
course "Infinite Dimensional Dynamical Systems
in Population Biology" (every Wednesday from
March 10 to May 26). Among the audience are the
research-related professors, postdoctoral fellows
and graduate students from National Tsing Hua
University, National Chiao Tung University,
National Central University, and Tamkang
University.This course is based on my book
"Dynamical Systems in Population Biology"
(2003, Springer) and recent works.
Teaching
2 nd S e m e s t e r , 2 0 1 0 , C o m p u t a t i o n a l
Electromagnetics, 16 lectures, 180 minutes each
lecture, 16 notes written, Participants include
math and nonmath majors from National Chiao
Tong University, and National Central University,
also some researchers and professors From ChiaoTo n g U n i v. a n d N a t i o n a l Ta i w a n N o r m a l
University.
Preprints from Joint Research
During this period Prof. D. Y. Kwak from
KAIST, Korea visited me for joint research on
some interface elliptic problems. I spent most of
time with Prof. W. W. Lin’s group in Chioa-Tong
University on fluid structure Interaction problems
and photonic crystal problems. Below are the
preprints:
1. ( with D. Y. Kwak and C. Attanayake) On the
optimal order convergence of immersed finite
element methods for elliptic problems,
submitted to Advances In Computational Math,
2010.
2. (with T. M. Huang, W. Q. Huang and W. W.
Lin) Efficient Arnoldi Algorithm for Rational
Eigenvalue Problems of a Fluid-Solid System,
3. A conservative immersed interface finite
element method for one-dimensional problems
Talks Given
1. " O p t i m a l C o n v e rg e n c e A n a l y s i s o f a n
Immersed Interface Finite Element Method” in
6 th workshop of numerical algebra a n d
applications, Pu-Hsin, Taiwan, May 1, 2010.
2. " Optimal Order Convergence Analysis of
Numerical Interface Problems" at National
Chengchi University, May 5, 2010.
IV. Xiaoqing Zhao
University Research Professor, Memorial
University of Newfoundland, Canada
Visiting Professor, March 7-June 6, 2010,
NCTS, Taiwan
Activities of Onsite Scientists -›› 80
Research
I finished two joint research articles in the
areas of Differential Equations and Mathematical
Biology with Prof. Sze-Bi Hsu (NTHU and
NCTS) and Dr. Feng-Bin Wang (NTHU), which
were included in the NCTS series of preprints:
a. P
r ep r in t s 2 0 1 0 - 4 - 0 0 5 , " D y n a mic s o f A
Periodically Pulsed Bio-reactor Model with A
Hydraulic Storage Zone", Sze-Bi Hsu, FengBin Wang and Xiao-Qiang Zhao
b. P
reprints 2010-6-001, "A Lotka-Voterra
Competition Model with Seasonal Succession",
Sze-Bi Hsu and Xiao-Qiang Zhao.
These two papers were submitted for
publication and are under review now.
We also discussed some potential research
projects on evolution dynamics of biological
systems for further collaborations.
Activities
1. I was invited to give a colloquium talk, titled
"Spatial Dynamics of Monotone Evolution
Systems With Applications", at National
Central University in April.
2. I was invited to give a colloquium talk, titled
"Spreading Speeds and Traveling Waves for
Monostable Evolution Systems", at Tamkang
University in April.
3. I also attended the 2010 NCTS Workshop on
Dynamical Systems (May 12-15), and gave an
invited talk, titled "Bistable Waves for
Monotone Semiflows with Applications".
These activities provided me good
opportunities to exchange ideas in mathematics
with colleagues in Taiwan.
F.5 Visiting Associate Professor
Andreas Schweizer
National Center for Theoretical Sciences
Teaching
February 2009: N CTS Winter School, Aspire
Park, Tao Yuan County 4 lectures
à 75 minutes on Drinfeld Modular
Curves
Spring 2010: NCTS & NTHU Graduate Course on
Noncongruence Subgroups and
Noncongruence Modular Forms,
(together with Prof. Wen-Ching
Winnie Li)
Papers published, accepted, submitted or
started in that period
1. ( with Matthias Schütt) On Davenport-Stothers
inequalities and elliptic surfaces in positive
characteristic, Quarterly Journal of
Mathematics (Oxford) 59 (2008),
499-522(published in December 2008)
2. ( with A.W. Mason) Nonrational genus zero
function fields and the Bruhat-Tits tree,
Communications in Algebra, 37 vol. 12 (2009),
4241-4258 (NCTS-preprint 2008-10-003)
3. V
alue-sharing of meromorphic functions on a
Riemann surface, Journal of Mathematical
Analysis and Applications 365 (2010), 220-228
(NCTS-preprint 2009-5-001)
4. ( with A.W. Mason) The cusp amplitudes and
quasi-level of a congruence subgroup of over
any Dedekind domain, submitted (NCTSpreprint 2009-8-002)
5. S
trong Weil curves over q (T) with small
conductor, Journal of Number Theory 131
(2011), 285-299 (NCTS-preprint 20010-2-003)
6. ( with A.W. Mason) The Bruhat-Tits tree and
elliptic points of the Drinfeld modular groups,
in preparation
Collaboration started in that period
with Prof. Yifan Yang (Chiao Tung University),
Project: O
n the torsion of elliptic curves over
suffciently general function fields.
Research Visit
4 - 14 August 2009 - Research visit to Glasgow
University (Scotland) for discussions with Prof.
A.W. Mason. The main subject was the material of
what is going to be our sixth joint paper (see item
[6] under Papers ...)
Conferences, Workshops, Talks
• 2 7 - 30 July 2009 - Conference on Value
Distribution Theory and Complex Geometry,
Hsinchu,
• I nvited talk "Value-sharing of meromorphic
functions on a Riemann surface”
• 1 2 August 2009 - Algebra Seminar, Glasgow
University (Scotland):
"On the class groups of quadratic function
fields”
• 1 4 October 2009 - NCTS Number Theory
Seminar: "The Bruhat-Tits tree”
• 2 1 October 2009 - NCTS Number Theory
Seminar:
"Elliptic points of the Drinfeld modular groups”
Other professional activities
• W
ritten 15 referee’s reports for different
mathematical journals.
2009 at NCTS: 9
2010 at NCTS: 4
• W
ritten 14 reviews for Zentralblatt MATH
2009 at NCTS: 8
2010 at NCTS: 4
F.6 Report of Post Doctors
Chieh-Yu Chang
National Center for Theoretical Sciences
Research
My main research work focuses on
transcendence theory over function fields in
positive characteristic. Recently, I have been
focusing on certain special values of arithmetic
Drinfeld modular forms. In the past year, I used
the recent development of t-motivic methods to
81 ‹‹- Activities of Onsite Scientists
show the algebraic independence of the nonzero
values of arithmetic Drinfeld modular forms of
positive weight at non-isogenous CM points. The
result is presented in the preprint [8]. In the near
future, I hope to establish the similar/expected
result for the forms at non-CM points.
In the past year, I spent much time on writing
and revising some preprints. Precisely, I have
finished the writing of [5], [8] ,[9] and [10], and
revised [7]. The most important task for me is to
finish the writing of [9], which is a joint work
with Papanikolas. The project is a continuation of
our previous work (cf. [6]) to higher rank Drinfeld
modules. In that paper, we give a complete answer
for the problem on algebraic independence of
Drinfeld logarithms at algebraic points. Besides, I
also write up a survey article on recent progress of
transcendence theory in positive characteristic (cf.
[10]).
Invited talks at Seminars/Workshops/
Conferences
1. A
lgebra Seminar, Univ. of Kyushu, Japan, Feb.
2010.
2. Number Theory Seminar, Texas A&M Univ.,
March 2010.
3. W o r k s h o p o n D r i n f e l d m o d u l e s a n d
L-functions, CRM, Spain, April 2010.
4. NCTS Number Theory Seminar, April 2010.
5. N umber Theory Seminar, Tsing Hua Univ.,
Beijing, June 2010.
6. Number Theory Seminar, Morningside Center
of Mathematics, Beijing, June 2010.
Visiting
•
•
•
•
niv. of Kyushu (Japan) (Feb. 15~ 23 2010)
U
Texas A&M Univ. (Feb. 28-March. 27 2010)
CRM (Spain) (April 8-22 2010)
Tsing Hua University (Beijing) (June 17-29
2010)
Activities of Onsite Scientists -›› 82
Publications and Preprints
[1] C
.-Y. Chang and J. Yu, Determination of
algebraic relations among special zeta values
in positive characteristic, Advances in
Mathematics 216 (2007), 321-345.
[2] C.-Y Chang, A note on a refined version of
Anderson-Brownawell-Papanikolas criterion,
Journal of Number Theory 129 (2009), 729738.
[3] C.-Y. Chang, M. A. Papanikolas, D. S. Thakur
a n d J . Yu , A l g e b r a i c i n d e p e n d e n c e o f
arithmetic gamma values and Carlitz zeta
values, Adv. Math. 223 (2010), 1137-1154.
[4] C.-Y. Chang, M. A. Papanikolas and J. Yu,
Geometric gamma values and zeta values in
positive characteristic, Int. Math. Res. Notices
(2010) vol. 8, 1432-1455.
[5] C.-Y. Chang, Transcendence of special values
of quasi-modular forms, to appear in Forum
Math.(DOI 10.1515/FORM. 2011. 072)
[6] C . - Y. C h a n g a n d M . A . P a p a n i k o l a s ,
Algebraic relations among periods and
logarithms of rank 2 Drinfeld modules, to
appear in Amer. J. Math.
[7] C.-Y. Chang, M. A. Papanikolas and J. Yu,
Frobenius difference equations and algebraic
independence of zeta values in positive equal
characteristic, to appear in Algebra & Number
Theory.
[8] C .-Y. Chang, Special values of Drinfeld
modular forms and algebraic independence,
submitted 2010.
[9] C . - Y. C h a n g a n d M . A . P a p a n i k o l a s ,
Algebraic independence of periods and
logarithms of Drinfeld modules, submitted
2010.
[10] C.-Y. Chang, Frobenius difference equations
and difference Galois groups, submitted
2010.
Preprints
Series I
Title and Author
2010-1-01
On Hyperbolic Dynamics of Multidimensional Systems with Homoclinic Tangencies
of Arbitrary Orders
Sergey Gonchenko and Ming-Chia Li
2010-1-02
Geodesics on -Type Quaternion Groups with Sub-Lorentzian Metric and Their
Physical Interpretation
Anna Korolko and Irina Markina
2010-1-03
An Intrinsic Formulation to the Rolling Manifolds Problem
Mauricio Godoy Molina, Erlend Grong, Irina Markina and Fatima Silva Leites
2010-1-04
On a Class of Nilpotent Distributions
Ovidiu Calin and Der-Chen Chang
2010-1-05
Condition Numbers of Spectral Projections and Matrix Sign Function
Wei-guo Wang, Chern-Shuh Wang and Yi-min Wei
2010-1-06
Stochastic Trigonometry and Stochastic Invariants
Ovidiu Calin and Der-Chen Chang
2010-1-07
The Rayleigh-Ritz Method, Re nement and Arnoldi Process for Periodic Matrix
Pairs
Eric King-wah Chu, Hung-Yuan Fan, Zhongxiao Jia, Tiexiang Li and Wen-Wei Lin
2010-1-08
Single Phytoplankton Species Growth with Light and Advection in a Water
Column
Sze-Bi Hsu and Yuan Lou
2010-1-09
Almost Algebraic Geometry
Jyh-Haur Teh
2010-1-10
Semi-Topological Algebraic Geometry and Riemann-Roch Theorem
Jyh-Haur Teh
2010-1-11
Special Values of Drinfeld Modular Forms and Algebraic Indepencence
Chieh-Yu Chang
83 ‹‹- Preprints
Series I
Title and Author
2010-1-12
Convex Central Configurations of the n-body Problem Which are not Strictly
Convex
Kuo-Chang Chen and Jun-Shian Hsiao
2010-1-13
Strong Weil Curves over
Andreas Schweizer
2010-1-14
Zero Distribution and Decay at Infinity of Drinfeld Modular Coefficient Forms
Ernst-Ulrich Gekeler
2010-1-15
Para-Eisenstein Series for the Modular Group GL( q[T])
Ernst-Ulrich Gekeler
2010-1-16
Transcendence of Special Values of Quasi-Modular Forms
Chieh-Yu Chang
2010-1-17
Singular Integral Operators on Triebel–Lizorkin Spaces of Para-Accretive Type
Chin-Cheng Lin and Kunchuan Wang
2010-1-18
Calderón–Zygmund Operators on Product Hardy Spaces
Yongsheng Han, Ming-Yi Lee, Chin-Cheng Lin and Ying-Chieh Lin
2010-1-19
Weighted Boundedness for Rough Marcinkiewicz Integrals with Different Weights
Yong Ding and Chin-Cheng Lin
2010-1-20
Local Hardy–Littlewood Maximal Operator
Chin-Cheng Lin and Krzysztof Stempak
2010-1-21
Dynamics of A Periodically Pulsed Bio-reactor Model with A Hydraulic Storage
Zone
Sze-Bi Hsu, Feng-Bin Wang and Xiao-Qiang Zhao
2010-1-22
Frobenius Difference Equations and Difference Galois Groups
Chieh-Yu Chang
2010-1-23
Algebraic Independence of Periods and Logarithms of Drinfeld Modules
Chieh-Yu Chang and Matthew A. Papanikolas
2010-1-24
A Lotka-Voterra Competition Model with Seasonal Succession
Sze-Bi Hsu and Xiao-Qiang Zhao
Preprints -›› 84
(T) with Small Conductor
q
Series I
Title and Author
2010-1-25
Geometric Analysis on Generalized Hermite Operators
Der-Chen Chang and Sheng-Ya Feng
2010-1-26
Solving a Structured Quadratic Eigenvalue Problem by a Structure-Preserving
Doubling Algorithm
Chun-Hua Guo and Wen-Wei Lin
2010-1-27
On a Curious Property of Bell Numbers
Zhi-Wei Sun and Don Zagier
2010-1-28
Efficient Importance Sampling Estimation for Joint Default Probability: the First
Passage Time Problem
Chuan-Hsiang Han
2010-1-29
An Improved Procedure for VaR/CVaR Estimation under Stochastic Volatility
Models
Chuan-Hsiang Han, Wei-Han Liu and Tzu-Ying Chen
2010-1-30
A p-adic Nevanlinna-Diophantine Correspondence
Ta Thi Hoai An, Aaron Levin and Julie Tzu-Yueh Wang
2010-1-31
On Theta Series from Quaternion Algebras over Function Fields
Fu-Tsun Wei and Jing Yu
2010-1-32
Nonemptiness Problems of Plane Square Tiling with Two Colors
Wen-Guei Hu and Song-Sun Lin
2010-1-33
Semi-topological Galois Theory and the Inverse Galois Problem
Hsuan-Yi Liao and Jyh-Haur Teh
2010-1-34
Stringy Mirror Symmetry
Jyh-Haur Teh
2010-1-35
Pressures for Asymptotically Sub-additive Potentials Under a Mistake Function
Wen-Chiao Cheng, Yun Zhao and Yongluo Cao
2010-1-36
Competition between Microorganisms for a Single Limiting Resource with Cell
Quota Structure and Spatial Variation
James P. Grover, Sze-Bi Hsu and Feng-Bin Wang
2010-1-37
On a Mathematical Model Arising from Competition of Phytoplankton Species for
a Single Nutrient with Internal Storage: Steady State Analysis
Sze-Bi Hsu and Feng-Bin Wang
85 ‹‹- Preprints
Series I
Title and Author
2010-1-38
Hierarchy of Relevant Couplings in Perturbative Renormalization Group
Transformations
Hong-Yan Shih, Wen-Ming Huang, Sze-Bi Hsu and Hsiu-Hau Lin
2010-1-39
On a System of Reaction-Diffusion Equations Arising from Competition with
Internal Storage in an Unstirred Chemostat
Sze-Bi Hsu, Jifa Jiang and Feng-Bin Wang
2010-1-40
Dimension Spectrum for Sofic Systems
Jung-Chao Ban, Chih-Hung Chang, Ting-Ju Chen and Mei-Shao Lin
2010-1-41
Multifractal Analysis for Countable Shift Space with Matrix Potentials
Yun Zhao, YongLuo Cao and JungChao Ban
2010-1-42
Factor Map, Diamond and Density of Pressure Functions
Jung-Chao Ban and Chih-Hung Chang
2010-1-43
Efficient Importance Sampling for Estimating Lower Tail Probabilities under
Gaussian and Student's t Distributions
Chuan-Hsiang Han and Ching-Tang Wu
2010-1-44
Efficient Arnoldi-Type Algorithms for Rational Eigenvalue Problems Arising in
Fluid-Solid Systems
So-Hsiang Chou, Tsung-Ming Huang, Wei-Qiang Huang and Wen-Wei Lin
2010-1-45
Visualization, Screening, and Classification of Cell Cycle-Regulated Genes in Yeast
Henry Horng-Shing Lu and Han-Ming Wu
2010-1-46
Smaller Population Size at the MRCA Time for Stationary Branching Processes
Yu-Ting Chen and Jean-Francqis Delmas
2010-1-47
Boolean Networks
Tung-Hung Chueh and Henry Horng-Shing Lu
2010-1-48
Two-Sided Exit for Phase-Type Lévy Models and Perpetual Callable Bond
Yu-Ting Chen, Yuan-Chung Sheu and Ming-Yao Tsai
2010-1-49
Geometric Pre-Ordering on C*-Algebras
Chi-Wai Leung, Chi-Keung Ng and Ngai-Ching Wong
2010-1-50
On the Distribution of Torsion Points Modulo Primes
Yen-Mei J. Chen and Yen-Liang Kuan
Preprints -›› 86
Series I
Title and Author
2010-1-51
The Complexity of Permutive Cellular Automata
Jung-Chao Ban, Chih-Hung Chang, Ting-Ju Chen and Mei-Shao Lin
2010-1-52
Hausdorff Dimension of Weakly Permutive Cellular Automata
Jung-Chao Ban and Chih-Hung Chang
2010-1-53
On Theta Series In Characteristic 2
Chih-Yun Chuang and Ting-Fang Lee
2010-1-54
On Definite Shimura Curves and Autormophic Forms over Function Fields
Fu-Tsun Wei and Jing Yu
2010-1-55
Hopf FibrationI:Geodesics and Distances
Der-Chen Chang, Irina Markina and Alexander Vasilev
2010-1-56
Traveling Plane Wave Solutions of Delayed Lattice Differental Systems in
Competitive Lotka-Volterra Type
Cheng-Hsiung Hsu and Ting-Hui Yang
2010-1-57
Traveling Wave Solutions for Time-Delayed Lattice Reaction-Diffusion Systems
Cheng-Hsiung Hsu, Jian-Jhong Lin and Ting-Hui Yang
2010-1-58
Existence of Traveling Wave Solutions for Diffusive Predator-Prey Type Systems
Cheng-Hsiung Hsu, Chi-Ru Yang, Ting-Hui Yang and Tzi-Sheng Yang
2010-1-59
Multistratum Fractional Factorial Designs
Ching-Shui Cheng and Pi-Wen Tsai
2010-1-60
Congruences of the Partition Function
Yifan Yang
2010-1-61
A Basis for Mk(Γ0(4)) and Representations of Integers Sums of Squares
Shinji Fukuhara and Yifan Yang
2010-1-62
Jacobsthal Identity for (√-2)
Ki-Ichiro Hashimoto, Ling Long and Yifan Yang
2010-1-63
Modular Curves and Coding Theory: A Survey
Wen-Ching W. Li
2010-1-64
Galois Representations with Quaternion Multiplications Associated to
Noncongruence Modular Forms
A.O.L. Atkin, Wen-Ching Winnie Li, Tong Liu and Ling Long
87 ‹‹- Preprints
Series I
Title and Author
2010-1-65
Zeta Functions of Group Based Graphs and Complexes
Wen-Ching W. Li
2010-1-66
Zeta Functions of Complexes Arising From PGL(3)
Ming-Hsuan Kang and Wen-Ching Li
Series II
Title and Author
2010-2-01
Blowup and Solitary Wave Solutions with Ring Profiles of Two-Component
Nonlinear Schrödinger Systems
Xianjin Chen, Tai-Chia Lin and Juncheng Wei
2010-2-02
Superspecial Abelian Varieties over Finite Prime Fields
Chia-Fu Yu
2010-2-03
On Hermitian Forms over Dyadic Non-Maximal Local Orders
Chia-Fu Yu
2010-2-04
On The Non-Vanishing of Hecke L-Valukes Modulo p
Ming-Lun Hsieh
2010-2-05
On The μ-Invariant of Anticyclotomic p-Adic L-Functions for CM
Ming-Lun Hsieh
2010-2-06
On The Existence of Maximal Orders
Chia-Fu Yu
Series III
Title and Author
2010-3-01
The Structure of Parafermion Vertex Operator Algebras
C. Dong, C. H. Lam, Q. Wang and H. Yamada
2010-3-02
The Cardinality of Some Symmetric Differences
Huang, Po-Yi; Ke, Wen-Fong; Pilz, Guenter F.
2010-3-03
Matrix Maps Over Planar Near-Rings
Ke, Wen-Fong; Meyer, Johan H.; Wendt, Gerhard
2010-3-04
Abstract Algebra in Statistics
Ke, Wen-Fong; Pilz, Guenter F.
Preprints -›› 88
Series III
Title and Author
2010-3-05
Quantum Codes from Hadamard Matrices
Ke, Wen-Fong; Lai, Kingfai; Zhang, Ruibin
2010-3-06
New Approach for the Nonlinear Programming with Transient Stability
Constraints Arising from Power Systems
X. J. Tong, S. Y. Wu and R. J. Zhou
2010-3-07
A New Exchange Method for Convex Semi-Infinite Programming
L. P. Zhang, S. Y. Wu and M. A. Lopez
2010-3-08
Optimal Three-Ball Inequalities and Quantitative Uniqueness for The Stokes
System
Ching-Lung Lin, Gunther Uhlmann, and Jenn-Nan Wang
2010-3-09
Reconstructing Potentials from Zeros of One Eigenfunction
Xinfu Chen, Y.H. Cheng and C.K. Law
2010-3-10
A Numerical Approach to Infinite-Dimensional Linear Programming in L1 Spaces
Satoshi Ito, Soon-Yi Wu, Ting-Jang Shiu and Kok Lay Teo
2010-3-11
A New Smoothing Newton-Type Algorithm for Semi-Infinite Programming
Chen Ling, Qin Ni, Liqun Qi and Soon-Yi Wu
2010-3-12
Convergence and Error Bound of A D-Gap Function Based Newton-Type
Algorithm for Equilibrium Problems
Liping Zhang, Soon-Yi Wu and Shu-Cherng Fang
2010-3-13
Choosability of Toroidal Graphs without Short Cycles
L. Cai and W. Wang and X. Zhu
2010-3-14
Decomposition of Sparse Graphs, with Application to Game Coloring Number
M. Montassier, A. Pecher, A. Raspaud, D. B. West and X. Zhu
2010-3-15
On-Line List Colouring of Graphs
X. Zhu
2010-3-16
Rainbow Domination on Trees
G. J. Chang, J. J. Wu and X. Zhu
2010-3-17
Rearrangeable Nonblocking Optical Interconnection Network Fabrics with
Crosstalk Constraints
Y.-P. Chen, Y.-M. Huang and L.-D. Tong
2010-3-18
Total Coloring of Planar Graphs of Maximum Degree Eight
N. Roussel and X. Zhu.
89 ‹‹- Preprints
Series III
Title and Author
2010-3-19
When Is The Direct Product of Generalized Mycielski Graphs A Cover Graph
Hsin-Hao Lai, K. W. Lih, C.-Y. Lin and L.-D. Tong
2010-3-20
Dade’s Invariant Conjecture for The Symplectic Group Sp4(2n) and The Special
Unitary Group Su4(22n) in Defining Characteristic
J. An, F. Himstedt and S. C. Huang
2010-3-21
Dade's Invariant Conjecture for The General Unitary Group ${\Rm GU}_4(Q^2)$
in Defining Characteristic
J. An and S. C. Huang
2010-3-22
Character Tables of The Maximal Parabolic Subgroups of The Ree Groups
$^2F_4(Q^2)$
F. Himstedt and S. C. Huang
2010-3-23
A New Iterative Method for Finding Common Solutions of a System of Equilibrium
Problems, Fixed-Point Problems, and Variational Inequalities
J. W. Peng, S. Y. Wu and J. C. Yao
2010-3-24
Rotating Spiral Waves in –Ω Systems on Circular Domains
Je-Chiang Tsai
2010-3-25
Multiplicity of Positive Solutions for A Semilinear Elliptic Equation in Rn+ with
Nonlinear Boundary Condition
Tsung-fang Wu
2010-3-26
Convexity Package for Momentum Maps on Contact Manifolds
Chiang, R.; Karshon Y
2010-3-27
Speed of Stability for Birth Death Processes
Mu-Fa Chen
2010-3-28
Multiple Targets Characterization of Electromagnetic Vulnerability
P. Chen, L. Osadciw and T.-J. Wu
2010-3-29
Conditional Nelson-Aalen and Kaplan-Meier Estimators with MÄuller-Wang
Boundary Kernel
X . Luo and W-Y Tsai
2010-3-30
Stochastic Matching Pursuit for Bayesian Variable Selection
R-B Chen, C-H Chu, T-Y Lai and Y-N Wu
2010-3-31
Two-Person Red-and-Black Game with Lower Limit
M.-R. Chen
Preprints -›› 90
Series III
Title and Author
2010-3-32
Using Adaptive Multi-Accurate Function Evaluations in a Surrogate-Assisted
Method for Computer Experiments
W. Wang, R-B Chen and C-L Hsuz
2010-3-33
Influence of Choices of Statistical Models on Neural Spike Trend
S.-C. Chen, L-A Li, S. Li and J. He
2010-3-34
Mixturetree: A Program for Constructing Phylogeny
S.-C. Chen, M S. Rosenberg and B Lindsay
2010-3-35
He Wavelet Transforms and Statistical Models for Near Infrared Spectra Analysis
S-.C. Chen, D M Hayden, S. S Young and J-N Tzeng
2010-3-36
Subset Selection Procedures to Identify EM Fields Following Log-normal
Distributions
E M Buzaianu, P Chen and T-J Wu
2010-3-37
The Weighted Average Information Criterion for Multivariate Regression Model
Selection
T-J Wu, P. Chen and Y. Yan
2010-3-38
Some Limit Theory for Weighted Sums and Levy Processes
J Yan, T-J Wu and C Su
2010-3-39
Accelerated Destructive Degradation Tests Robust to Distribution Misspecification
S-L Jeng, B-Y Huang and W.Q. Meeker
2010-3-40
Root N Estimates of Integrated Squared Density Partial Derivatives
T-J Wu, H-Y Chen and H-C Yu
91 ‹‹- Preprints
Appendix I. Visiting Mathematicians 2009
Name
Field of Interest
Period of Visit
Appendix I
Chong Li
(Zhejiang University)
Applied Mathematics
2009-11-18 ~ 2009-12-03
Chen-Yu Chi
(Harvard University)
Analytic and Algebraic
Geometry
2009-12-10 ~ 2010-01-29
Hitoshi Imai
(Tokushima University)
Applied Mathematics
2009-12-17 ~ 2009-12-20
Yoshio Sone
(Kyoto University)
Applied Mathematics
2009-12-18 ~ 2009-12-20
Shusen Yan
(The University of New England)
Geometry
2009-12-18 ~ 2009-12-20
Yung-Sze Choi
(University of Connecticut)
Applied Mathematics
2009-12-18 ~ 2009-12-21
Yasushi Hataya
(Yamaguchi University)
Applied Mathematics
2009-12-18 ~ 2009-12-21
Yuusuke Iso
(Kyoto University)
Applied Mathematics
2009-12-18 ~ 2009-12-21
Takayuki Kitamura
(Kyoto University)
Applied Mathematics
2009-12-18 ~ 2009-12-21
Kazumi Tanuma
(Gunma University)
Applied Mathematics
2009-12-18 ~ 2009-12-21
Kenji Nakanishi
(Kyoto University)
Applied Mathematics
2009-12-19 ~ 2009-12-21
Tohru Ozawa
(Waseda University)
Applied Mathematics
2009-12-19 ~ 2009-12-21
Gen Nakamura
(Hokkaido University)
Applied Mathematics
2009-12-20 ~ 2009-12-22
Lek-Heng Lim
(University of California, Berkeley)
Computational Sciences
2009-12-20 ~ 2010-01-03
Tian Ma
(Sichuan University, China)
Nonlinear Analysis
2009-12-22 ~ 2010-01-19
Weiqiang Wang
(University of Virginia, US (VA))
Algebraic Geometry
2009-12-26 ~ 2010-01-06
Jiu-Kang Yu
(Purdue University)
Geometry
2009-12-28 ~ 2010-01-03
Appendix I -›› 92
Name
Field of Interest
Period of Visit
Nonlinear Sciences
2009-12-28 ~ 2010-01-18
Shih-Hsien Yu
(National University of Singapore,
Singapore)
Boltzmann Equation
Conservation laws
Finite Difference Scheme
2009-12-28 ~ 2010-01-18
2010-04-05 ~ 2010-04-09
2010-05-30 ~ 2010-06-04
So-Hsiang Chou
(Bowling Green State University)
Scientific Computation
2010-01-01 ~ 2010-04-30
M. H. Kang
(Penn. State University)
Number Theory
2010-01-01 ~ 2010-08-05
Tzyy-Leng Horng
(Feng Chia University)
Differential Equation
2010-01-05 ~ 2010-01-07
Ming-Chih Lai
(National Chiao Tung University)
Differential Equation
2010-01-06 ~ 2010-01-07
Hsiang-Ning Luk
(Taichung Veterans General Hospital)
Medical
2010-01-06 ~ 2010-01-07
Jui-Chen Sung
(National Central University)
Heart electrophysiology
2010-01-06 ~ 2010-01-07
Chao-Nien Chen
(National Changhua University)
Differential Equation
2010-01-07--2010-01-10
Jeng-Tzong Chen
(National Taiwan Ocean University)
Differential Equation
2010-01-08 ~ 2010-01-09
Sze-Bi Hsu
(National Tsing Hua University)
Differential Equation
2010-01-08 ~ 2010-01-09
Ching-Lung Lin
(National Cheng Kung University)
Partial Differential Equation
2010-01-08 ~ 2010-01-09
Chih-Wen Shih
(National Chiao Tung University)
Differential Equation
2010-01-08 ~ 2010-01-09
Yoh Iwasa
(Kyushu University)
Theoretical Biology
2010-01-08 ~ 2010-01-10
Ying-Cheng Lai
(Arizona State University)
Dynamical System
2010-01-10 ~ 2010-01-17
Ruey S. Tsay
(University of Chicago)
Probability Theory and Statistics
2010-01-18 ~ 2010-01-31
Dong-Hui Li
(South China Normal University)
Algorithms for Optimization and
Nonlinear Equations
2010-01-21 ~ 2010-01-23
93 ‹‹- Appendix I
Appendix I
Shouhong Wang
(Indiana University, Bloomington)
Name
Field of Interest
Period of Visit
Appendix I
Sangyeol Lee
(Seoul national University)
Statistics
2010-01-22 ~ 2010-02-06
Yiqiang Zhou
(Memorial University)
Module and Ring Theory
2010-01-22 ~ 2010-02-19
Biswa Nath Datta
(Northern Illinois University)
Applied Mathematics
Scientific Computation
2010-01-27 ~ 2010-02-01
Joongul Lee
(Hongik University, Korea)
Algebraic Number Theory
2010-02-03 ~ 2010-02-06
Mile Reid
(University of Warwick)
Algebraic Geometry
2010-02-04 ~ 2010-02-16
Patrick Solé
(CNRS/LTCI)
Number Theory
2010-02-11 ~ 2010-02-17
Chong Li
(Zhejiang University)
Applied Mathematics
2010-02-14 ~ 2010-02-28
Wu-Yen Chuang
(NHETC, Rutgers University)
String Theory
2010-02-21 ~ 2010-02-22
Patrice Ossona de Me
(École des hautes études en sciences
sociales)
Discrete Mathematics
2010-02-21 ~ 2010-02-26
Manabu Akaho
(Tokyo Metropolitan University)
Geometry
2010-02-22 ~ 2010-02-26
Wolfgang Haerdle
(Humboldt-Universität zu Berlin)
Statistics
2010-02-22 ~ 2010-02-26
Urs Frauenfelder
(Seoul National University)
Geometry
2010-02-23 ~ 2010-02-28
Otto van Koert
(Seoul National University)
Geometry
2010-02-23 ~ 2010-02-28
Shinya Fujita
(Gunma National College of Technology)
Discrete Mathematics
2010-02-24 ~ 2010-03-09
Weng Kee Wong
(UCLA)
Statistics
2010-03-01 ~ 2010-03-14
Tsung-Min Hwang
(NTNU)
Scientific Computation
2010-03-01 ~ 2010-08-31
Zdenek Dvorak
(Charles University)
Discrete Mathematics
2010-03-06 ~ 2010-03-21
Appendix I -›› 94
Name
Field of Interest
Period of Visit
Mathematical Biology
Dynamical Systems
2010-03-07 ~ 2010-06-06
Paul Dorbec
(Université Bordeaux 1)
Discrete Mathematics
2010-03-08 ~ 2010-03-25
Wataru Takashi
(National Sun Yat-Sen University)
Nonlinear Analysis and
Optimization
2010-03-11 ~ 2010-03-12
William Q. Meeker
(Iowa State University)
Statistics
2010-03-12 ~ 2010-03-24
Hüseyin Kocak
(University of Miami)
Differential Equation
2010-03-14 ~ 2010-03-29
Houg-Kun Xu
(National Sun Yat-Sen University)
Probability
2010-03-15 ~ 2010-03-15
Mickael Montassier
(Université Bordeaux 1)
Discrete Mathematics
2010-03-15 ~ 2010-03-18
André Raspaud
(Université Bordeaux 1)
Probability
2010-03-15 ~ 2010-03-18
Wu-Yi Hsiang
(University of California, Berkeley)
Discrete Mathematics
2010-03-15 ~ 2010-04-02
Reyer Sjamaar
(Cornell university)
Geometry
2010-03-15 ~ 2010-04-03
Akio Arimoto
(Tokyo City University)
Probability Differential Equations
2010-03-23 ~ 2010-03-26
Basic Analysis, Global Analysis
Shuya Kanagawa
(Tokyo City University)
Probability
2010-03-23 ~ 2010-03-26
Ben T. Nohara
(Tokyo City University)
Algebraic Geometry
2010-03-23 ~ 2010-03-26
Hiroshi Takahashi
(Tokyo City University)
Probability
2010-03-23 ~ 2010-03-26
Stefan Kebekus
(Universität Freiburg)
Algebraic Geometry
2010-03-24 ~ 2010-04-01
Yoshitsugu Kabeya
(Osaka Prefecture University)
Algebraic Geometry
2010-03-24 ~ 2010-04-06
Hironori Shiga
(Waseda University)
Number Theory
2010-03-26 ~ 2010-04-07
95 ‹‹- Appendix I
Appendix I
Xiaoqiang Zhao
(Memorial University of
Newfoundland)
Name
Field of Interest
Period of Visit
Appendix I
Valery Alexeev
(University of Georgia)
Algebraic Geometry
2010-03-27 ~ 2010-04-05
Juan Cervino
(Universität Duisburg-Essen)
Algebraic Geometry
2010-03-28 ~ 2010-04-03
Andre Chatzistamatiou
(Universität Duisburg-Essen)
Algebraic Geometry
2010-03-28 ~ 2010-04-03
Georg Hein
(Universität Duisburg-Essen)
Algebraic Geometry
2010-03-28 ~ 2010-04-03
Hsian-Hua Tseng
(Ohio State University)
Algebraic Geometry
2010-03-28 ~ 2010-04-03
Yu-jong Tzeng
(Stanford University)
Algebraic Geometry
2010-03-28 ~ 2010-04-03
Takehiko Yasuda
(Kagoshima University)
Algebraic Geometry
2010-03-29 ~ 2010-04-03
Moody Ten-Chao Chu
(North Carolina State University)
Applied Mathematics
Scientific Computation
2010-03-29 ~ 2010-04-09
Jiun-Cheng Chen
(National Tsing Hua University)
Algebraic Geometry
2010-03-30 ~ 2010-04-02
Cho-Ho Chu 朱礎豪
(University of London)
Differential Geometry and
Geometric Analysis
2010-04-06 ~ 2010-04-13
Wilhem Kaup
(Universität Tübingen)
Differential Geometry and
Geometric Analysis
2010-04-06 ~ 2010-04-13
Edmund Y. M. Chiang
(Hong Kong University of Science and
Technology)
Differential Geometry and
Geometric Analysis
2010-04-07 ~ 2010-04-11
Chi-Keung Ng
(Nankai University)
Differential Geometry and
Geometric Analysis
2010-04-07 ~ 2010-04-12
Guy Joseph Roos
(Universite de Poitiers)
Differential Geometry and
Geometric Analysis
2010-04-07 ~ 2010-04-12
Matthew Neal
(Denison University)
Differential Geometry and
Geometric Analysis
2010-04-07 ~ 2010-04-13
Ivan P. Shestakov
(University de Sao Paulo)
Differential Geometry and
Geometric Analysis
2010-04-07 ~ 2010-04-13
Viktor Ginzburg
(UC Santa Cruz)
Geometry
2010-04-09 ~ 2010-04-19
Appendix I -›› 96
Name
Field of Interest
Period of Visit
Inverse Problems
2010-04-11 ~ 2010-04-22
Zhong Yi
(Guangxi Teachers Education
University)
Ring Theory
2010-04-12 ~ 2010-05-02
Ivan Cheltsov
(University of Edinburgh)
Algebraic Geometry
2010-04-14 ~ 2010-04-23
Choe Hi Jun
(Yonsei University, Korea)
PDE
2010-04-16 ~ 2010-04-26
Lei Li
(National Sun Yat-sen University)
Optimization
2010-04-22 ~ 2010-04-23
Wataru Takahashi
(Tokyo Institute of Technology)
Fixed Point Theory
Nonlinear Operator Theory
Set-valued Analysis
2010-04-22 ~ 2010-04-24
Ajda Fosner
(University of Primorska)
Algebra
2010-04-25 ~ 2010-04-29
Masami Okada
(Tokyo Metropolitan University)
General Mathematics
2010-05-04 ~ 2010-05-09
S. Jimbo
(Hokkaido University)
Dynamical System
Nonlinear PDE
2010-05-04 ~ 2010-05-12
Marc Chaperon
(Universite Paris VII)
Dynamical System
2010-05-04 ~ 2010-05-16
Alain Chenciner
(Universite Paris VII and IMCCE)
Dynamical System
2010-05-04 ~ 2010-05-16
Zhao Lei
(Shandong University)
Dynamical System
2010-05-04 ~ 2010-05-16
QiaoLing Wei
(Universite Paris VII)
Dynamical System
2010-05-04 ~ 2010-05-16
Eric Séré
(Universite Paris-Dauphine)
Dynamical System
Nonlinear PDE
2010-05-05 ~ 2010-05-09
Yiming Long
(Nankai University)
Dynamical System
Nonlinear PDE
2010-05-05 ~ 2010-05-10
Vittorio Coti Zelati
(University of Napoli)
Dynamical System
2010-05-05 ~ 2010-05-14
Der-Chen Chang
(Georgetown University)
Differential Geometry and
Geometric Analysis
2010-05-05 ~ 2010-07-19
2010-09-17 ~ 2010-09-21
97 ‹‹- Appendix I
Appendix I
Ting Zhou
(University of Washington)
Name
Field of Interest
Period of Visit
Appendix I
Xijun Hu
(Shandong University)
Dynamical System
2010-05-07 ~ 2010-05-15
Hao Min Chow
(Georgia Institute of Technology)
Dynamical System
2010-05-10 ~ 2010-05-15
Jerry Bona
(The University of Illinois at Chicago)
Partial Differential Equations
2010-05-10 ~ 2010-05-26
2010-06-09 ~ 2010-06-18
Hongqiu Chen
(The University of Memphis)
Partial Differential Equations
2010-05-10 ~ 2010-05-26
2010-06-09 ~ 2010-06-18
Shui-Nee Chow
(Georgia Institute of Technology)
Dynamical System
2010-05-11 ~ 2010-05-15
Qiu-dong Wang
(University of Arizona)
Dynamical System
2010-05-11 ~ 2010-05-16
YuXi Ren
(Tsinghua University, China)
Computational Sciences
2010-05-14 ~ 2010-05-16
Feng Xiao
(Tokyo Institute of Technology, Japan)
Computational Sciences
2010-05-14 ~ 2010-05-16
Vasily Volkov
(University of California, Berkeley)
Computer Science with a
Designated Emphasis in
Computational Science and
Engineering
2010-05-19 ~ 2010-05-21
Fadil Santosa
(School of Mathematics, University of
Minnesota)
Applied Mathematics and
Modelling, Optimization,
Imaging.
2010-05-20 ~ 2010-05-23
William W. Symes
(Rice University)
Imaging, Image Processing and
Inverse Problems
2010-05-20 ~ 2010-05-23
King-Fai Lai
(National Sun Yat-sen University)
Automorphic Form
2010-05-21 ~ 2010-05-22
2010-09-09 ~ 2010-09-11
Ming-Deh Huang
(University of Southern California)
Number Theory
2010-05-23 ~ 2010-05-27
Ching-Shui Cheng
(University of California, Berkeley)
Statistics
2010-05-26 ~ 2010-06-24
Jingjing Huang
(Penn. State University)
Number Theory
2010-05-26 ~ 2010-08-24
Dimitri Bertsekas
(Massachusetts Institute of
Technology)
Optimization
2010-06-01 ~ 2010-06-01
Appendix I -›› 98
Name
Field of Interest
Period of Visit
p-adic Hodge Theory
2010-06-04 ~ 2010-06-04
Chih-Chieh Chen
(University of Utah)
Numerical Analysis
2010-06-07 ~ 2010-07-16
Jin-Chuan Duan
(National University of Singapore)
Probability
2010-06-08 ~ 2010-06-09
WaiSun Don
(Hong Kong Baptist University)
Partial Differential Equations
2010-06-08 ~ 2010-06-14
Yasunori MAEKAWA
(Kobe University)
Nonlinear PDE
2010-06-10 ~ 2010-06-13
Zhouping Xin
(The Chinese University of Hong
Kong)
Partial Differential Equations
2010-06-10 ~ 2010-06-13
Li Chen
(Tsinghua University)
Nonlinear PDE in Differential
Geometry, Nonlinear PDE
in Applied Mathematics and
Mathematical Physics
2010-06-10 ~ 2010-06-14
Jie LIU
(National University of Singapore)
Computational Fluid Mechanics
Speech Processing
2010-06-10 ~ 2010-06-14
Athanasios Tzavaras
(University of Crete)
Applied Analysis
2010-06-10 ~ 2010-06-14
Hyeong-Ohk Bae
(Ajou University)
Nonlinear PDE
2010-06-10 ~ 2010-06-15
Tong Keun Chang
(Korea Institute for Advanced Study)
Nonlinear PDE
2010-06-10 ~ 2010-06-15
Yu-Hin Pang
(National University of Singapore)
Differential Geometry
2010-06-10 ~ 2010-06-15
ChuanJu Xu
(Xiamen University)
Computational Fluid Dynamics
2010-06-10 ~ 2010-06-15
Yung-Fu Fang
(National Cheng Kung University)
Nonlinear Partial Differential
Equations
2010-06-11 ~ 2010-06-13
Jose Antonio Carrill
(Universitat Autònoma de Barcelona)
Kinetic Equations
2010-06-11 ~ 2010-06-14
Ching-Hsiao Cheng
(National Central University)
Nonlinear PDE
2010-06-11 ~ 2010-06-14
99 ‹‹- Appendix I
Appendix I
Meng-Kai Hong
(National Chiao Tung University)
Name
Field of Interest
Period of Visit
Appendix I
BumJa Jin
(Mokpo National University)
Nonlinear PDE
2010-06-11 ~ 2010-06-14
Chi-Kun Lin
(National Chiao Tung University)
Partial Differential Equation,
Fluid Mechanics Nonlinear
Analysis
2010-06-11 ~ 2010-06-14
Yu-lin Lin
(Academia Sinica)
Nonlinear PDE
2010-06-11 ~ 2010-06-14
Tai-Ping Liu
(Academia Sinica)
Nonlinear PDE
2010-06-11 ~ 2010-06-14
Takayoshi Ogawa
(Tohoku University)
Nonlinear Partial Differential
Equations, Real Analysis,
Functional Analysis, Applied
Analysis
2010-06-11 ~ 2010-06-14
Yoshio Sone
(Kyoto University and Sinica)
Nonlinear PDE
2010-06-11 ~ 2010-06-14
Wei-Cheng Wang
(National Tsing Hua University)
Preprints, Slides and Ongoing
Projects
2010-06-11 ~ 2010-06-14
Xiaoping Wang
(Hong Kong University of Science and
Technology)
Numerical Methods for
Micromagnetics Simulations
2010-06-11 ~ 2010-06-14
Hyeonbae Kang
(Inha University)
Partial Differential Equations
2010-06-11 ~ 2010-06-15
Shuichi Kawashima
(Kyoto University)
Mathematical Fluid Mechanics
2010-06-12 ~ 2010-06-14
Tien-Yien Li
(Michigan State University)
Applied Mathematics
Dynamical System
2010-06-19 ~ 2010-06-27
Marica Pelanti
(INRIA Paris-Rocqencourt)
Numerical Approximation of
Hyperbolic Systems
2010-06-20 ~ 2010-06-25
Miura Hideyuki
(Osaka University)
Partial Differential Equations
2010-06-20 ~ 2010-06-28
Otto Van Koert
(Seoul National University)
Contact Topology
2010-06-20 ~ 2010-07-02
Mei-Chi Shaw
(University of Notre Dame)
Partial Differential Equations
and Complex Geometry
2010-06-20 ~ 2010-07-02
Appendix I -›› 100
Name
Field of Interest
Period of Visit
Geometry of Strongly PseudoConvex Manifold
2010-06-20 ~ 2010-07-03
Sebastian Noelle
(IGPM, RWTH Aachen)
Analysis and Numerical Analysis
of PDEs
2010-06-21 ~ 2010-06-26
David L. George
(Cascades Volcano Observatory, U.S.
Geological Survey)
Computational Mathematics
2010-06-21 ~ 2010-06-27
Kyung-Keun Kang
(Sungkyunkwan University)
Applied Numerical Mathematics
2010-06-21 ~ 2010-06-29
Jui-Tang Chen
(National Taiwan Normal University)
Partial Differential Equations
2010-06-21 ~ 2010-07-02
Mao-Pei Tsui
(The University of Toledo)
Geometric Analysis
2010-06-21 ~ 2010-07-02
Chin-Tung Wu
(National Pingtung University of
Education)
Geometric Analysis,
Partial Differential Equations
2010-06-21 ~ 2010-07-02
Chien-Min Kao
(University of Chicago)
High Performance Computing
2010-06-23 ~ 2010-07-20
Ruey S. Tsay
(University of Chicago)
Statistics
2010-06-24 ~ 2010-06-24
Ostap Okhrin
(Humboldt-University zu Berlin)
Statistics
2010-06-24 ~ 2010-06-27
KeQin Feng
(Tsinghua University Beijing)
Number Theory
2010-06-24 ~ 2010-07-07
Eric Grinberg
(University of New Hampshire)
Geometric Analysis
2010-06-25 ~ 2010-06-30
Oktay K. Pashaev
(Izmir Institute of Technology, Izmir,
Turkey)
Integrable Systems and Solutions
2010-06-25 ~ 2010-07-15
Horng-Tzer Yau
(Harvard University)
Probability Theory
Statistical Mechanics
2010-06-25 ~ 2010-08-08
Ben Weinkove
(UCSD)
Geometric Analysis
2010-06-26 ~ 2010-06-30
Ke-qin Feng
(Tsinghua University, Beijing)
Algebra
2010-06-26 ~ 2010-07-04
101 ‹‹- Appendix I
Appendix I
Saotome Takanari
(OCAMI)
Name
Field of Interest
Period of Visit
Appendix I
Andrea Fraser
(Dalhousie University)
Analysis
2010-06-26 ~ 2010-07-08
Jih-Hsin Cheng
(Academia Sinica)
Geometric Analysis, LowDimensional Topology
2010-06-28 ~ 2010-06-29
Walter Wei
(University of Oklahoma)
Minimality, Stability, Plateau
Problem
2010-06-28 ~ 2010-06-29
Mitsuru Sugimoto
(Nagoya University)
Differential Geometry and
Geometric Analysis
2010-06-28 ~ 2010-07-03
Eric L. Grinberg
(Temple University)
Differential Geometry and
Geometric Analysis
2010-07-01 ~ 2010-07-02
K. Feng
(Tsinghua University)
Arithmetic Geometry
2010-07-01 ~ 2010-07-04
Andrea Fraser
(Dalhousie University)
Differential Geometry and
Geometric Analysis
2010-07-01 ~ 2010-07-09
Changyuan Cheng
(National Pingtung University of
Education)
Dynamical Systems
2010-07-01 ~ 2010-08-30
Solomon Friedberg
(Boston College)
Number Theory
2010-07-02 ~ 2010-07-13
Michael A. Tsfasman
(Independent University of Moscow)
Number Theory
2010-07-02 ~ 2010-07-15
Jeffery Hoffstein
(Brown University)
Number Theory
2010-07-02 ~ 2010-07-18
Winfred Kohnen
(Ruprecht-Karls-Universitat
Heidelberg)
Number Theory
2010-07-03 ~ 2010-07-11
Bo-Hae Im
(Chung-Ang University)
Number Theory
2010-07-04 ~ 2010-07-07
Yoonjin Lee
(Ewha Womans University)
Number Theory
2010-07-04 ~ 2010-07-07
YoungJu Choie
(POSTECH)
Number Theory
2010-07-04 ~ 2010-07-10
Dong Uk Lee
(KIAS)
Number Theory
2010-07-04 ~ 2010-07-10
Yoonbok Lee
(POSTECH)
Number Theory
2010-07-04 ~ 2010-07-10
Appendix I -›› 102
Name
Field of Interest
Period of Visit
Number Theory
2010-07-04 ~ 2010-07-10
Pinyuen Chen
(Syracuse University)
Statistics
2010-07-04 ~ 2010-07-11
Bumkyu Cho
(POSTECH)
Number Theory
2010-07-04 ~ 2010-07-12
Lin HAN
(Inha University)
Number Theory
2010-07-04 ~ 2010-07-12
Ken Ihara
(POSTECH)
Number Theory
2010-07-04 ~ 2010-07-12
Subong Lim
(POSTECH)
Number Theory
2010-07-04 ~ 2010-07-12
Shing-Tung Yau
(Harvard University)
Differential Geometry,
Differential Equations and
Mathematics Physics
2010-07-04 ~ 2010-07-13
2010-08-10 ~ 2010-08-11
Wenzhi Luo
(Ohio State University)
Number Theory
2010-07-05 ~ 2010-07-11
Jiu-Kang Yu
(Purdue University)
Number Theory
2010-07-05 ~ 2010-07-13
Stepen Shing-Toung Yau
(University of Illinois at Chicago)
Algebra
2010-07-06 ~ 2010-07-18
Li Wen-Wei
(Université Paris Diderot 7)
Representation Theory
2010-07-07 ~ 2010-08-18
Paul C. Yang
(Princeton University)
Nonlinear PDE
Harmonic Analysis
2010-07-08 ~ 2010-07-09
Takao Yamazaki
(Tohoku University)
Algebra
2010-07-08 ~ 2010-07-10
Song-Ying Li
(University of California irvine)
Differential Geometry and
Geometric Analysis
2010-07-08 ~ 2010-07-11
Mei-Chi Shaw
(University of Notre Dame)
Differential Geometry and
Geometric Analysis
2010-07-08 ~ 2010-07-11
Sai Kee Yeung
(Purdue University)
Differential Geometry and
Geometric Analysis
2010-07-08 ~ 2010-07-12
Dihua Jiang
(University of Minnesota)
Number Theory
2010-07-08 ~ 2010-07-13
2010-07-22 ~ 2010-07-26
103 ‹‹- Appendix I
Appendix I
Yoon Kyung Park
(POSTECH)
Name
Field of Interest
Period of Visit
Appendix I
John Erik Fornaess
(University of Michigan)
Differential Geometry and
Geometric Analysis
2010-07-09 ~ 2010-07-11
Xianghong Gong
(University of Wisconsin Madison)
Differential Geometry and
Geometric Analysis
2010-07-09 ~ 2010-07-11
Xiaojun Huang
(Rutgers University)
Differential Geometry and
Geometric Analysis
2010-07-09 ~ 2010-07-11
Ngaiming Mok
(University of Hong Kong)
Differential Geometry and
Geometric Analysis
2010-07-09 ~ 2010-07-11
Yum-Tong Siu
(Harvard University)
Algebraic Geometry,
Differential Geometry and
Geometric Analysis
2010-07-09 ~ 2010-07-11
Xing Liang
(University of Science and Technology
of China)
PDE, Dynamical System
2010-07-09 ~ 2010-07-18
Nathann Cohen
(Chinese Academy of Sciences)
Discrete Mathematics
2010-07-11 ~ 2010-07-28
Leonardo Sampaio Rocha
(Chinese Academy of Sciences)
Discrete Mathematics
2010-07-11 ~ 2010-07-28
Tian Zheng
(Columbia University)
Probability Theory and Statistics
2010-07-12 ~ 2010-07-19
Ting-Hui Yang
(Tamkang University)
Dynamical Systems
2010-07-15 ~ 2010-09-15
Chin-Tu Chen
(The University of Chicago Medical
Center)
Functional and Physiological
Imaging, Molecular Imaging
2010-07-17 ~ 2010-07-28
Nikos Kavallaris
(University of Aegean)
PDE
2010-07-19 ~ 2010-07-26
Yuri G. Prokhorov
(Moscow state University)
Algebric Geometry
2010-07-27 ~ 2010-08-04
Nathann COHEN
(INRIA Spphia Antipolis)
Graph Theory
2010-07-30 ~ 2010-08-14
Leonardo Sampaio Roc
(INRIA Spphia Antipolis)
Graph Theory
2010-07-30 ~ 2010-08-14
Zhi Wei Sun
(Nanjing University)
Number Theory
2010-08-01 ~ 2010-08-08
Appendix I -›› 104
Name
Field of Interest
Period of Visit
Number Theory
2010-08-01 ~ 2010-08-11
Silke Wimmer Zagier
(Max Planck Institute for Mathematics)
Algebraic Logic, History of
Japanese Mathematics
2010-08-01 ~ 2010-08-11
Yun Zhao
(SooChow University)
Dynamical System
2010-08-01 ~ 2010-08-28
Chiu-Yen Kao
(Ohio State University)
Computational and Applied Math
2010-08-03 ~ 2010-08-19
Jonas Kibelbek
(Penn. State University)
Number Theory
2010-08-04 ~ 2011-12-15
Robert Griss
(University of Michigan)
Vertex Operator Algebras
2010-08-08 ~ 2010-08-22
Maria Pia Gualdani
(The University of Texas at Austin)
Applied Mathematics
2010-08-09 ~ 2010-08-12
Yen-Hsi Richard Tsai
(The University of Texas at Austin)
Multiscale Modeling and
Computations
2010-08-09 ~ 2010-08-12
Shunsuke Hayashi
(Kyoto University)
Applied Mathematics
2010-08-12 ~ 2010-09-11
Cristian Virdol
(Columbia University)
Arithmetic Geometry
2010-08-14 ~ 2011-07-31
Jigao Yan
(Suzhou University)
Statistics
2010-08-16 ~ 2010-08-29
Quo-Shin Chi
(Washington University)
Differential Geometry
2010-08-18 ~ 2011-08-12
Chin-Yu Hsiao
(Chalmers University of Technology
(Sweden))
Geomeryic Analysis in Several
Complex Variables
2010-08-19 ~ 2010-09-13
Yang Fang
(Penn. State University)
Number Theory
2010-08-19 ~ 2011-01-18
Xue-Wen Bao
(Fuzhou University)
Discrete Math
2010-08-25 ~ 2010-08-29
An Chang
(Fuzou University)
Discrete Math
2010-08-25 ~ 2010-08-29
Genghua Fan
(Fuzhou University)
Discrete Math
2010-08-25 ~ 2010-08-29
105 ‹‹- Appendix I
Appendix I
Don Zagier
(Max Planck Institute for Mathematics)
Name
Field of Interest
Period of Visit
Appendix I
Minhua He
(Fuzhou University)
Discrete Math
2010-08-25 ~ 2010-08-29
JianFeng Hou
(Fuzhou University)
Discrete Math
2010-08-25 ~ 2010-08-29
Ruofan Liu
(Fuzhou University)
Discrete Math
2010-08-25 ~ 2010-08-29
Albert Jeu-Liang Sheu
(University of Kansas)
Rings and Related Algebras
2010-08-25 ~ 2010-08-29
Daqing Yang
(Fuzou University)
Discrete Math
2010-08-25 ~ 2010-08-29
Chuixiang Zhou
(Fuzhou University)
Discrete Math
2010-08-25 ~ 2010-08-29
WenXing Zhu
(Fuzhou University)
Discrete Math
2010-08-25 ~ 2010-08-29
Tomoyuki Arakawa
(Nara Women University)
Algebra
2010-08-30 ~ 2010-09-05
Hiroki Shimakura
(Aichi University of Education)
Algebra
2010-08-30 ~ 2010-09-05
Hiromichi Yamada
(Hitotsubashi University)
Algebra
2010-08-30 ~ 2010-09-05
Hiroshi Yamauchi
(Tokyo Woman Christian’s University)
Algebra
2010-08-30 ~ 2010-09-05
Dominic David Joyce
(University of Oxford)
Differential Geometry
2010-09-01~2010-09-09
Wen-Ling Huang
(University of Hamburg)
Discrete Mathematics
2010-09-01 ~ 2010-09-30
Edmund Puczylowski
(University of Warsaw)
Ring Theory
2010-09-03 ~ 2010-10-01
Fabien Trihan
(University of Nottingham)
Number Theory
2010-09-05 ~ 2010-09-12
Gebhard Bockle
(University of Duisburg-Essen)
Number Theory
2010-09-06 ~ 2010-09-26
Bin Shu
(East China Normal University)
Algebra
2010-09-11 ~ 2010-11-09
Appendix I -›› 106
Name
Field of Interest
Period of Visit
Turbulent Transport and
Homogenization
2010-09-12 ~ 2010-09-25
Hubert Kiechle
(University of Hamburg)
Algebra
2010-09-12 ~ 2010-09-26
Edmund Puczylowski
(University of Warsaw)
Algebra
2010-09-17 ~ 2010-09-24
Ser Peow Tan
(National University of Singapore)
Geometry
2010-09-18 ~ 2010-09-26
W. Dale Brownawell
(Penn. State University)
Number Theory
2010-10-01 ~ 2010-10-31
2011-04-01 ~ 2011-04-30
Weizhu Bao
(National University of Singapore)
Applied Mathematics
Scientific Computation
2010-10-19 ~ 2010-10-29
Ercai Chen
(Nanjing Normal University)
Dynamical System
2010-10-27 ~ 2010-11-08
Fanping Zhen
(Liuzhou Teachers College)
Dynamical System
2010-10-27 ~ 2010-11-08
Jianya Liu
(Shandong University)
Number Theory
2010-10-30 ~ 2010-11-05
Johannes Meyer
(University of the Free State)
Algebra
2010-11-01 ~ 2010-11-14
Tomoki Kawahira
(Nagoya University)
Dynamical System
2010-11-07 ~ 2010-11-11
Akira Sakai
(Hokkaido University)
Mathematical Physics
(Probability and Statistical
Mechanics)
2010-11-18 ~ 2010-11-29
Mitsuru Shibayama
(Kyoto University)
Dynamical System
2010-11-18 ~ 2010-12-03
Roshan Joseph Vangazhiyil
(Georgia Institute of Technology)
Statistics
2010-11-20 ~ 2010-12-05
Masakazu Kojima
(Tokyo Institute of Technology)
Applied Mathematics
2010-11-21 ~ 2010-11-27
Guanglu Zhou
(Curtin University)
Applied Mathematics
2010-11-29 ~ 2011-01-01
Zhilin Li
(North Carolina State University)
Scientific Computation
2010-12-01 ~ 2010-12-21
107 ‹‹- Appendix I
Appendix I
Albert Fannjiang
(University of California, Davis)
Name
Field of Interest
Period of Visit
Appendix I
Yihong Du
(University of New England)
Dynamical System
Mathematical Biology
Nonlinear PDE
2010-12-04 ~ 2010-12-18
Lin Feng Mei
(University of New England)
Mathematical Bilolgy
2010-12-04 ~ 2010-12-18
Eamonn O'Brien
(University of Auckland)
Algebra
2010-12-05 ~ 2010-12-16
Giovanni Cerulli Irelli
(University of Padua)
Algebra
2010-12-05 ~ 2010-12-23
Yuan Lou
(Ohio State University)
Mathematical Biology
Nonlinear PDE
2010-12-06 ~ 2010-12-18
Junping Shi
(College of William and Mary)
Mathematical Biology
Nonlinear PDE
2010-12-08 ~ 2010-12-23
Avner Friedman
(Ohio State University)
Mathematical Biology
Nonlinear PDE
2010-12-09 ~ 2010-12-18
Bo Li
(University of California San Diego)
Applied Mathematics
2010-12-10 ~ 2010-12-16
Jame Grover
(University of Texas at Arlington)
Dynamical System
Mathematical Biology
2010-12-11 ~ 2010-12-18
James Keener
(University of Utah)
Mathematical Biology
2010-12-11 ~ 2010-12-18
Peter Kim
(University of Utah)
Mathematical Biology
2010-12-11 ~ 2010-12-18
Yangjim Kim
(University of Michigan)
Mathematical Biology
2010-12-11 ~ 2010-12-18
Andrew Nevai
(University of Central Folrida)
Mathematical Biology
2010-12-11 ~ 2010-12-20
Peter Hinow
(University of Wisconsin - Milwaukee)
PDE Mathematical Biology
2010-12-11 ~ 2010-12-21
Bei Hu
(University of Notre Dame)
PDE Mathematical Biology
2010-12-12 ~ 2010-12-17
Yu-Yu Liu
(UC Irvine)
Mathematical Biology
2010-12-12 ~ 2010-12-17
Rebecca Batorsky
(Tufts University)
Mathematical Biology
2010-12-12 ~ 2010-12-18
Appendix I -›› 108
Name
Field of Interest
Period of Visit
Mathematical Biology
2010-12-12 ~ 2010-12-18
Xinfu Chen
(University of Pittsburgh)
Dynamical System
Nonlinear PDE
2010-12-12 ~ 2010-12-18
Harsh Jain
(MBI)
Mathematical Biology
2010-12-12 ~ 2010-12-18
Christopher Klausmeimer
(Michigan State University)
Mathematical Biology
2010-12-12 ~ 2010-12-18
Alicia Prieto Langarica
(University of Texas)
Mathematical Biology
2010-12-12 ~ 2010-12-18
Chun Liu
(University Park)
Mathematical Biology
PDE
2010-12-12 ~ 2010-12-18
Masayasu Mimura
(Hiroshima University)
Dynamical System
2010-12-12 ~ 2010-12-18
Kuni Sakamoto
(Hiroshima University)
Dynamical System
Nonlinear PDE
2010-12-12 ~ 2010-12-18
Jonathan Adam Sherratt
(Heriot-Watt University)
Mathematical Biology
2010-12-12 ~ 2010-12-18
Angela Stevens
(University of Heidelberg)
Mathematical Biology
2010-12-12 ~ 2010-12-18
Zhian Wang
(Hong Kong Polytechnic University)
Mathematical Biology, PDE
2010-12-12 ~ 2010-12-18
Shari Wiley
(Howard University)
Mathematical Biology
2010-12-12 ~ 2010-12-18
Yoshio Yamada
(Waseda University)
Nonlinear PDE
2010-12-12 ~ 2010-12-18
Hong Qian
(University of Washington)
Mathematical Biology
2010-12-12 ~ 2010-12-22
Jan Haskovec
(Johann Radon Institute for
Computational and Applied)
Mathematical Biology
2010-12-13 ~ 2010-12-18
Jin Kui Wan
(Beijing Insititute of Technology)
Algebra
2010-12-15 ~ 2010-12-31
109 ‹‹- Appendix I
Appendix I
Joaquin Rivera-Cruz
(Colgate University)
Name
Field of Interest
Period of Visit
Appendix I
Song X. Chen
(Peking University & Iowa State
University)
Statistics
2010-12-17 ~ 2010-12-18
R. A. Bailey
(University of London)
Statistics
2010-12-20 ~ 2011-01-07
P. J. Cameron
(University of London)
Statistics
2010-12-20 ~ 2011-01-07
Joe Chuang
(City University London)
Algebra
2010-12-23 ~ 2010-12-25
Changliang Zou
(Nankai University)
Statistics
2010-12-27 ~ 2011-01-27
Yu Shyr
(Vanderbilt University School of
Medicine)
Statistics
2011-01-03 ~ 2011-01-16
Guangming Pan
(Nanyang Technological University,
Singapore)
Statistics
2011-01-05 ~ 2011-01-09
Kenji Nakanishi
(Kyoto University)
Applied Mathematics
2011-01-14 ~ 2011-01-14
Do Young Kwak
(Korea Advanced Institute of Science
and Technology)
Applied Mathematics
2011-01-14 ~ 2011-01-17
Sanghyuk Lee
(Seoul National University)
Applied Mathematics
2011-01-14 ~ 2011-01-17
Tetsu Mizumachi
(Kyushu University)
Applied Mathematics
2011-01-14 ~ 2011-01-17
Tsorng-Whay Pan
(University of Houston)
Applied Mathematics
2011-01-14 ~ 2011-01-17
Kotaro Tsugawa
(Nagoya University)
Applied Mathematics
2011-01-14 ~ 2011-01-17
Patrick Iglesias-Zemmou
(CNRS)
Geometry
2011-02-25 ~ 2011-03-04
Horst R. Thieme
(Arizona State University)
Analysis and Applied Analysis
2011-05-23 ~ 2011-06-07
Xiaojun Chen
(University of Michigan)
Algebraic Geometry
2011-06-01 ~ 2011-07-31
Appendix I -›› 110
NCTS 2008.9-2009.12 Conference, Workshop, School & Special Lecture
Time
Conference & Workshop
Place
Room 308 and
Room 101, New
Mathematics
Building, National
Taiwan Univ.
January 12, 2010
NCTS/CMMSC Dynamics Day: A Workshop on
Dynamics for Coupled Systems
Organizers:
Jonq Juang (Nat’l Chiao Tung University)
Ming-Chia Li ((Nat’l Chiao Tung University)
Wen-Wei Lin (Nat’l Chiao Tung University)
Chih-Wen Shih (Nat’l Chiao Tung University)
Lecture Room of
NCTS, National
Tsing Hua Univ.
January 19-22, 2010
Mini-workshop of Algebra
Speakers:
Jung-Kai Alfred Chen (NTU)
Shou-Jen Hu (TKU)
Kayo Masuda (KGU, Sanda)
Masayoshi Miyanishi (KGU, Sanda)
Yuri Prokhorov (MSU, Moscow)
Quan-Shui Wu (FU, Shanghai)
Jiping Zhang (PU, Beijing)
Department of
Mathematics,
National Taiwan
Univ.
February 22- June
14, 2010
NCTS& NCTU Joint Course on Stochastic Processes:
Markov Chains and Mixing
Instructor: Guan-Yu Chen (Nat’l Chiao Tung University)
National Chiao
Tung Univ.
February 24-27,
2010
Symplectic & Contact Winter School
Speakers:
Manabu Akaho (Tokyo Metropolitan University)
Urs Frauenfelder (Seoul National University)
Otto van Koert (Seoul National University)
Shu-Cheng Chang (National Taiwan University)
Eugene Z. Xia (National Cheng Kung University)
R204, 2F, NCTS,
National Cheng
Kung Univ.
February 24-June 16,
2010
NCTS& NTHU Joint Course: Noncongruence
Subgroups and Noncongruence Modular Forms
Instructors:
Wen-Ching W. Li (NCTS & NTHU)
Andreas Schweizer (NCTS)
Lecture Room of
NCTS, National
Tsing Hua Univ.
111 ‹‹- Appendix II
Appendix II
January 1-8, 2010
2010 Conference in Differential Equations
Organizers:
Tai-Chia Lin (NTU)
Weichung Wang (NTU)
Jyh-Hao Lee (Academia Sinica)
I-Liang Chern (NTU) Jenn-Nan Wang (NTU)
Chiun-Chuan Chen (NTU)
Appendix II
Time
Conference & Workshop
February 25-June 17,
2010
Numerical Methods for PDEs
Instructor: So-Hsiang Chou (Bowling Green State University)
National Chiao
Tung Univ.
February 25-June 17,
2010
NCTS & NCTU Joint Course Topics in Number
Theory Modular Forms -Theory and Applications
Instructor: Yifan Yang (Nat’l Chiao Tung University)
National Chiao
Tung Univ.
March 10-May 26,
2010
Infinite Dimensional Dynamical Systems in Population
Biology
Instructor: Xiaoqiang Zhao
(Memorial University of Newfoundland, Canada)
Lecture Room of
NCTS, National
Tsing Hua Univ.
March 19-21, 2010
2010 圖論研討會 Seminar on Graph Theory
Organizers:
Xuding Zhu (National Sun Yat-sen University)
Tsai-Lien Wong (National Sun Yat-sen University)
Li-Da Tong (National Sun Yat-sen University)
International
Conference Hall,
College of Science,
National Sun Yatsen Univ.
March 19-21, 2010
Minicourse on Inverse Problems
Speakers:
Hyeonbae Kang (Seoul National University)
Gen Nakamura (Hokkaido University)
Gunther Uhlmann (University of Washington)
Room 308, New
Mathematics
Building, National
Taiwan Univ.
March 29-April 2,
2010
Workshop on Higher Dimensional Algebraic Geometry,
2010
Organizers:
Jungkai Alfred Chen (National Taiwan University)
Hélène Esnault (Universität Duisburg-Essen)
Eckart Viehweg (Universität Duisburg-Essen)
Chin-Lung Wang (National Taiwan University)
Room 101, New
Mathematics
Building, National
Taiwan Univ.
April 8-12, 2010
NCTS Colloquium Jordan Theory and Analysis
Organizers:
Cho-Ho Chu (University of London)
Ngai-Ching Wong (Nat’l Sun Yat-sen University)
Lecture Room of
NCTS, National
Tsing Hua Univ.
April 22, 2010
2010 Optimization Meeting (1)
Speakers:
Wataru Takahashi (National Sun Yat-Sen University)
Lei Li (Nankai University, National Sun Yat-Sen Univ.)
Juhe Sun (National Taiwan Normal University)
Zheng Hai Hwang (Tianjin University)
Yan An Hwang (National Dong Hwa University)
Shue Chin Huang (National Dong Hwa University)
Organizer: Jein-Shan Chen (Nat'l Taiwan Normal University)
Appendix II -›› 112
Place
M210, Department
of Mathematics,
National Taiwan
Normal Univ.
Time
Conference & Workshop
Place
NCTS and NTHU-CMS Minicourse on Compensated
Compactness Method
Instructor: Tianhong Li (Chinese Academy of Sciences)
Lecture Room of
NCTS, National
Tsing Hua Univ.
May 6-8, 2010
2010 NCTS Workshop on Calculus of Variations and
Related Topics
Organizers:
Chao-Nien Chen (Nat’l Changhua Univ. of Education)
Kuo-Chang Chen (Nat’l Tsing Hua University)
Lecture Room of
NCTS, National
Tsing Hua Univ.
May 12-15, 2010
2010 NCTS Workshop on Dynamical Systems
Organizers:
Kuo-Chang Chen (Nat’l Tsing-Hua University)
Cheng-Hsiung Hsu (Nat’l Central University)
Chih-Wen Shih (Nat’l Chiao-Tung University)
Lecture Room of
NCTS, National
Tsing Hua Univ.
May 17-June 28,
2010
NCTS Course in Aspects of Analysis on Model Domains
n+1
in C
Instructors:
Der-Chen Chang (Georgetown Univ. & NCTS)
Duy-Minh Nhieu (National Central Univ.)
Chiung-Jue Sung (National Tsing Hua Univ.)
Lecture Room of
NCTS, National
Tsing Hua Univ.
May 20-June 17,
2010
2010 NCTS Minicourse on PDE
Instructor: Ching-Hsiao Cheng (Nat’l Central University)
Lecture Room of
NCTS, National
Tsing Hua Univ.
May 21, 2010
One-day Workshop on Algebra
Organizer: Ming-Chang Kang (NTU)
Room 308, New
Mathematics
Building, National
Taiwan Univ.
May 27-June17,
2010
2010 NCTS & NTHU Special Course Minimum
Aberration and Some Related Criteria for Fractional
Factorial Designs
Instructor: Ching-Shui Cheng (UC Berkeley)
Lecture Room of
NCTS, National
Tsing Hua Univ.
June 11-14, 2010
Fourth Workshop on Nonlinear Partial Differential
Equations: Analysis, Computation and Applications
Organizers:
Weizhu Bao (NUS)
I-Liang Chern (NTU)
Seung-Yeal Ha (SNU)
Jian-Guo Liu (Duke)
Hisashi Okamoto (Kyoto)
Wei-Cheng Wang (NTHU)
Zhou Ping Xin (CUHK)
Room 101, New
Mathematics
Building, National
Taiwan Univ.
113 ‹‹- Appendix II
Appendix II
April 22-June 3,
2010
Appendix II
Time
Conference & Workshop
Place
June 21-July 2, 2010
2010 NCTS/TPE-TIMS Mini-Course and Workshop on
Geometric and Complex Analysis
Organizers :
Der-Chen Chang (Georgetown University, USA)
Shu-Cheng Chang (NTU, Taiwan)
Mao-Pei Tsui (University of Toledo, USA)
Room 101, New
Mathematics
Building, National
Taiwan Univ.
June 22, 2010
Symposium on Mathematical Models and Numerical
Methods for Hazardous Geophysical Mass Flows
Organizer: Keh-Ming Shyue (National Taiwan University)
Room 308, New
Mathematics
Building, National
Taiwan Univ.
June 24, 2010
2010 Workshop on Statistical Methods
Speaker: Ruey S. Tsay (Academician of Academia Sinica,
Taiwan / University of Chicago, USA)
Audio-visual Room
62331, 3F, Dept. of
Statistics, National
Cheng Kung Univ.
June 29-August 26,
2010
NCTS Summer Course in Number Theory
Instructors:
Wei-Chen Yao (Taipei Municipal University of Education)
Ming-Hsuan Kang (NCTS)
Lecture Room of
NCTS, National
Tsing Hua Univ.
June 30-August 26,
2010
NCTS 2010 Summer Program in Geometry
Organizers:
Shu-Jung Kao (National Tsing Hua University)
Jyh-Haur Teh (National Tsing Hua University)
Lecture Room of
NCTS, National
Tsing Hua Univ.
July 1, 2010
2010 NCTS Workshop on Fourier Analysis and Its
Applications to PDEs
Organizers:
Der-Chen Chang (Georgetown University & NCTS)
Chiung-Jue Sung (National Tsing Hua University)
Lecture Room of
NCTS, National
Tsing Hua Univ.
July 2- September 7,
2010
NCTS 2010 Summer Research Program in Number
Theory
Organizer: Yifang Yang (Nat’l Chiao Tung University)
Lecture Room of
NCTS, National
Tsing Hua Univ.
July 5-6, 2010
2010 Taiwan-Korea Workshop on Number Theory
Organizers:
YoungJu Choie (POSTECH)
Wen-Ching W. Li (NCTS)
Lecture Room of
NCTS, National
Tsing Hua Univ.
July 5-August 20,
2010
Summer course on image Science in 2010
Organizer : I-Liang Chern (National Taiwan University)
Room 638, AstroMath. Building,
National Taiwan
Univ.
Appendix II -›› 114
Time
Conference & Workshop
Place
Lecture Room of
NCTS, National
Tsing Hua Univ.
July 7-9, 2010
2010 NCTS International Conference on Automorphic
Forms and Related Topics
Organizers:
Wen-Ching W. Li (NCTS)
Jing Yu (National Taiwan University)
Lecture Room of
NCTS, National
Tsing Hua Univ.
July 8-August 19,
2010
2010 Summer Course on Lévy Processes with
Applications in Finance
Instructor: Yuan-Chung Sheu (Nat’l Chiao Tung Univ.)
National Chiao
Tung Univ.
July 9-11, 2010
2010 NCTS International Conference on Several
Complex Variables and Complex Geometry
Organizers:
Der-Chen Chang (Georgetwon University & NCTS)
Xiaojun Huang (Rutgers Univ., New Brunswick)
Ngaiming Mok (University of Hong Kong)
Chiung-Jue Sung (National Tsing Hua University)
Lecture Room of
NCTS, National
Tsing Hua Univ.
July 12-August 6,
2010
High performance computing
Organizer: Weichung Wang (National Taiwan University)
Speakers:
Chin-Tu Chen (University of Chicago, USA)
Chien-Min Kao (University of Chicago, USA)
Weichung Wang (National Taiwan University)
Room 307, New
Mathematics
Building, National
Taiwan Univ.
July 12-August 9,
2010
2010 NCTS Summer Course in Math. Modeling and
Analysis in Biological Science
Instructors:
Sze-Bi Hsu (Nat'l Tsing-Hua Univ.)
Ying-Hen Hsieh (China Medical University)
Yun-Huei Tzeng (Biodiversity Research Center, Academia
Sinica)
Lecture Room of
NCTS, National
Tsing Hua Univ.
115 ‹‹- Appendix II
Appendix II
July 6-August 26,
2010
NCTS Summer Course on Dynamical Systems
(Summer 2010): Measures and Computations for
Dynamical Systems
Instructors:
Jung Chao Ban (Nat’l Dong Hwa Univ.)
Shu-Ming Chang (Nat’l Chiao Tung Univ.)
Yun Zhao (Soochow Univ.)
Wen-Chiao Cheng (Chinese Culture Univ.)
Time
Conference & Workshop
Place
Appendix II
July 14-16 , 2010
NCTS International Conference on Probability and
Statistics with Applications in Biology
Organizers:
Nan-Jung Hsu (Nat’l Tsing Hua Univ.),
Henry Horng-Shing Lu (Nat’l Chiao Tung Univ.)
Yuan-Chung Sheu (Nat’l Chiao Tung Univ.)
Hsiuying Wang (Nat’l Chiao Tung Univ.)
Lecture Room of
NCTS, National
Tsing Hua Univ.
July 19-August 27,
2010
Introduction to Number Theory
Organizer: Chia-Fu Yu (Academia Sinica)
6F. Astro-Math.
Building, National
Taiwan Univ.
August 2, 4, 6, 9,
2010
2010 NCTS Distinguished Lecture Series
Instructor:
Don Zagier (Director of MaxPlanck Mathematics
Institute,Bonn and College de France, Paris)
Lecture Room of
NCTS, National
Tsing Hua Univ.
August 16- 27, 2010
Infinite-dimensional Lie Algebras
Organizer: Shun-Jen Cheng (Academia Sinica)
6F. Astro-Math.
Building, National
Taiwan Univ.
August 30September 1, 2010
2010 NCTS Summer Course on Scientific Computation
Introduction to Fluid Mechanics, Models and
Computations
Instructor: Ming-Chih Lai (Nat’l Chiao Tung University)
September 3, 2010
Mini-Workshop on infinite dimensional Lie algebras
and related topics
Speakers:
Tomoyuki Arakawa (Nara Women University, Japan
Hiroshi Yamauchi (Tokyo Woman Christian’s University)
Hiroki Shimakura (Aichi University of Education, Japan)
Hiromichi Yamada (Hitotsubashi University, Japan)
R204, 2F, NCTS,
National Cheng
Kung Univ.
September 8-24,
2010
2010 NCTS Lecture Series on Number Theory
Instructor: Gebhard Böckle (University Heidelberg)
Lecture Room of
NCTS, National
Tsing Hua Univ.
September 13, 2010January 10, 2011
2010 NCTS Topical Program in Mathematical Biology : Lecture Room of
Topics in PDE with Application to Mathematical
NCTS, National
Biology
Tsing Hua Univ.
Instructor: Sze-Bi Hsu (Nat’l Tshing Hua Univ.)
September 14, 2010January 31, 2011
2010 NCTS & NCTU Joint Course on Stochastic
Portfolio Theory
Instructor: Yuan-Chung Sheu (Nat’l Chiao-Tung Univ.)
Lecture Room of
NCTS, National
Tsing Hua Univ.
September 20October 18, 2010
NCTS Lecture Series in Number Theory & Arithmetic
Geometry
Instructor: Cristian Virdol (NCTS Taipei)
Lecture Room of
NCTS, National
Tsing Hua Univ.
Appendix II -›› 116
Lecture Room of
NCTS, National
Tsing Hua Univ.
Time
Conference & Workshop
Place
2010 NCTS Course on Dynamical Systems -Countable
Markov Systems and Phase Transition Dynamics
Instructor: Jung-Chao Ban (Nat’l Dong Hwa Univ.)
October 1-15, 2010
2010 NCTS Lecture Series on Number Theory
Instructor: W. Dale Brownawell (Penn. State University)
Lecture Room of
NCTS, National
Tsing Hua Univ.
October 4December 6, 2010
NCTS Fall Course on Fontaine's Theory in Equal
Characteristic
Instructor: Chieh-Yu Chang ((NCTS & NCU)
Lecture Room of
NCTS, National
Tsing Hua Univ.
October 6December 13, 2010
NCTS Seminar on Frobenius Modules
Instructors:
Jeng-Daw Yu (NTU)
Chieh-Yu Chang (NCTS & NCU)
Lecture Room of
NCTS, National
Tsing Hua Univ.
October 11, 2010
Algebraic Geometry Day at NCTS(South)
Speakers:
Wan Keng Cheong (NCKU)
Kungho Chan (NCKU)
Eugene Z. Xia (NCKU)
R204, 2F, NCTS,
National Cheng
Kung Univ.
November 20, 2010
The First Taiwan Geometry Symposium
Speakers:
Kuo-Wei Lee (TIMS, National Taiwan University)
Yng-Ing Lee (National Taiwan University)
Duy-Minh Nhieu (National Central University)
Organizers:
Yng-Ing Lee (National Taiwan University)
River Chiang (National Cheng Kung University)
Nan-Kuo Ho (National Tsing Hua University)
December 13- 17,
2010
Workshop on PDE Models of Biological Process
Organizers:
Sze-Bi Hsu (Nat’l Tsing-Hua Univ.), Chair
Avner Friedman (Mathematical Bioscience Institute, Ohio
State Univ.)
Yuan Lou (Mathematical Bioscience Institute, Ohio State
Univ.)
Jong Shenq Guo (Nat’l Taiwan Normal Univ.)
Chuin-Chuan Chen (Nat’l Taiwan Univ.)
Chih-Wen Shih (Nat’l Chiao-Tung Univ.)
R204, 2F, NCTS,
National Cheng
Kung Univ.
Lecture Room of
NCTS, National
Tsing Hua Univ.
117 ‹‹- Appendix II
Appendix II
Lecture Room of
NCTS, National
Tsing Hua Univ.
September 24December 3, 2010
Time
Appendix II
January 14-17, 2011
Appendix II -›› 118
Conference & Workshop
19th Workshop on Differential Equations and Its
Application
Plenary Speakers:
Rainer Kress (University Goettingen)
Chang-Shou Lin (National Taiwan University)
Tai-ping Liu (Academia Sinica)
Gen Nakamura (Hokkaido Univerity)
Yoshio Tsutsumi (Kyoto University)
Place
International
Conference Room,
National Cheng
Kung Univ.
Physics Division
Report of the Division Head
General Remarks
e are now in the second year of 3rd phase
of NCTS operation. This phase will last 6
years and will allow some flexibility in planning
Center programs. In this phase, the Center
continues the format established in the 2nd phase
with main project located in National Tsing Hua
University (NTHU), co-hosted by National Tsing
Hua University, National Chiao Tung University
(NCTU) and National Central University (NCU).
In addition, the subproject I located at National
Taiwan University (NTU) with Prof. Wei-Shu Hou
(侯維恕) from NTU as Principal Investigator
while the subproject II located at National Cheng
Kung University (NCKU) with Prof. Yan-Tien Lu
(盧炎田) as Principal Investigator. In November
of 2010, the Principal Investigator of subproject I
is replaced by Prof. Pei-Ming Ho (賀培銘) from
NTU. In 2010, about 1/3 of the budget is
distributed to Subproject I while 1/6 is channeled
through Subproject II. The rest of the annual
NCTS budget is allocated to the main project.
In terms of research, the Division continues the
organization of theorists in Taiwan into focus
groups to facilitate interaction and nurture
collaboration. In addition, the Center maintains a
good size of research staffs to carry out research
of current interest and support the activities of
focus groups. The Center also has very active
visitor programs for international researchers.
Their visits with varied length of stay will include
seminars and series of lectures. This will bring up
to date for the researchers in Taiwan the most
recent development in various areas of physics
and increases the visibility of research work in
Taiwan.
Organizational Structure
The operation of Physics Division is conducted
Report of the Division Head -›› 120
by its director with the help of the Executive
Committee. Division director and Principal
Investigators of Subprojects (Professors Wei-Shu
Hou/Pei-Ming Ho and Yan-Tien Lu) are ex officio
members of this committee. In 2010, the other
members of the committee are Profs. Chon-Saar
Chu (朱仲夏, NCTU), Kin-Wang Ng (吳建宏,
Academia Sinica (AS)), Chung-Yu Mou (牟中瑜,
NTHU), Min-Hsiung Tsai (蔡民雄, National Sun
Yat Sen University), Hsien-Chung Kao (高賢忠,
National Taiwan Normal University). Members of
the Executive Committee represent different areas
of physics and different regions in Taiwan,
providing opinions and suggestions based on their
expertise. They also serve as second group of
reviewers for personnel appointments at Center.
Review of 2009
An extensive review of the Center operation
was conducted at NSC from Dec 26 to Dec 27,
2009. The members of physics review committee
are Prof. Tu-Nan Chang (張圖南, University of
Southern California), Prof. Fu Chun Zhang (張富
春, Hong Kong University), Prof. Ting-Kuo Lee
(李定國, AS), Prof. Hsiang- Nan Li (李湘楠, AS).
Most programs have received good review. But
changes are suggested for the following areas and
have been implemented subsequently:
1. The initiative for build-up of Theory Support
for LHC physics has received poor mark due to
its very narrow physics objective and lack of
clear strategy. The budget is thereby reduced
by 50% as suggested by the review committee.
2. T h e i n i t i a t i v e t o e s t a b l i s h G P U-b a s e d
supercomputing platform which has a very
large cost in equipment was judged as a facility
which is used only by National Taiwan
University and does not serve the community
as a whole. The support for this initiative is
then discontinued.
3. The focus group on Plasma Science was
deemed ineffective. It is subsequently merged
with topical program on laser/maser plasmas.
Scientific Activities
Most of the scientific activities are planned and
carried out by various focus groups in the form of
workshops. The size of these workshops varies
from 40 people to more than 100 participants.
These activities provide many opportunities for
physicists in Taiwan to exchange ideas and to
learn from each other. In addition, there are
international conferences organized by focus
groups in collaboration with research
organizations in other countries. These will
broaden the perspectives of our worker, nurture
future collaboration and enhance our visibilities
on the international scene. In 2010 a special large
scale workshop on LHC (Large Hadron Collider)
physics has been organized by C. P. Yuan (袁簡
鵬, Michigan State University) and T. C. Yuan (阮
自強, AS) of LHC focus group. This 2-month long
workshop will have 9 physicists from US, 7 from
Japan, 3 from Korea, 2 from India, and 8 from
China. This workshop is quite timely in view of
the start-up of the new accelerator LHC in
Geneva.
This year NCTS has put some emphasis in the
training of young researchers in theoretical
physics by offering advanced courses for graduate
students. Ling-Fong Li (李靈峰) has been
teaching a 2-semester course on "Quantum Field
Theory" at Tsinghua University to provide the
very basic skill for students going into high energy
physics. Professor Harry C. S. Lam (藍志成,
McGill University in Canada) was brought in to
teach a 6-week course on "Group Theory and Its
Application to Physics". This course covers topics
which are very useful for many different areas of
physics. Professor Edward York Peng Yao (姚若
鵬, University of Michigan) has given a 4-week
mini course on "Gluon and Graviton Scattering
Amplitudes". In addition, there were numerous
schools organized by various focus groups on
many special topics of interest to help students to
get into research fields more easily.
The physics division has many formal
exchange agreements with Asian organizations in
Korea and Japan. These agreements enable young
researchers in Taiwan to participate in conferences
and workshops abroad to get more exposure and
nurture any future collaboration. The exchange
with China is informal but the activity is on the
rise.
Highlights of Researches
During past few years, the data from ATIC,
Pamela, and FERMI-LAT seems to yield some
results which the usual astrophysics might not be
able to account for. This raises the possibility that
they might due to the dark matter. Members of
Focus Group on LHC and Focus Group on
Cosmology and Astrophysics have been actively
pursuing research in this area by suggesting new
models trying to explain these anomalies. Cao
Qiang Geng (耿朝強), member of Focus Group
on LHC, has also been very active in trying to
explain the dark energy of the universe by the
mechanism of modifying Einstein's General
Relativity.
In the Focus Group on Atomic-MolecularO p t i c a l, D a w-We i Wa n g (王道維) a n d h i s
collaborators have developed a powerful
numerical method to study the quantum dynamics
of a Bose Einstein Condensation (BEC) including
quantum fluctuations. They find a significant
depletion effect due to quantum fluctuations.
Recruitment and Scientific Staff
In 2010, many of our post doctors are doing
quite well. Dr. Chia-Hsien Lin (林佳賢) has
obtained a tenure-track assistant professor
position, at National Central University in
Chungli. Dr. Pei-Jen Lin (林佩真) took a post
doctor job at National High Magnetic Field
Laboratory at Florida State University. Dr.
Takayuki Hirayama has joined Masukawa
Institute at Kyoto Sanyo University as post-doctor.
Dr. Hiroaki Kohyama has moved on to Chung
Yuan University as post doctor.
Four new people have joined the physics
division: Dr. Ling-Fong Li (division head), Dr.
Ming-Chiang Chung (張明強, assistant staff
scientist, condensed matter physics), Dr. Shulin
Sun (孫樹林, post doctor, condensed matter
physics), Dr. Chian-Shu Chen (陳 旭, post
doctor, particle physics) and Dr. Hunn-Da Chen
(陳鴻大, post doctor, biophysics). The other
research staffs at the Center are, Dr. Johan Alwall
(assistant research scholar, particle physics), Dr.
121 ‹‹- Report of the Division Head
Kazuyuki Furuuchi (assistant staff scientist,
string), Dr. Jae-Sik Lee (assistant research scholar,
particle physics), Dr. Dan Tomino (assistant
research scholar, particle physics), Dr, ChunChung Chen (陳俊仲, assistant research scholar,
soft condensed matter), Dr. Eibun Senaha (post
doctor, particle physics).
In 2010, there were several senior theorists
visiting NCTS from abroad for some length of
time, Prof. Vidar Gumundsson (3 months from
Iceland University), Xiaoyuan Li (李小源, 2.5
months from Institute for Theoretical Physics in
Beijing), Harry Lam (藍志成, 1.5 months from
McGill University in Canada), and Edward Y. P.
Yao (I month from University of Michigan) Beilok Hu (胡比樂, 6 weeks from University of
Maryland) and Tu-Nan Chang (6 weeks from
University of Southern California).
The Center Scientists program has renewed the
appointment of Chung-Hsien Chou (周忠憲,
NCKU) and new Center Scientists appointments
are Prof. Cheng-Wei Chiang (蔣正偉, NCU),
Report of the Division Head -›› 122
Prof, Hsuan-Yi Chen (陳宣毅, NCU), Prof. DawWei Wang (王道維, NTHU), on the junior level
and Prof. Baruch Rosenstein (儒森斯坦, NCTU)
on the senior level. The other Center Scientists are
Prof. David Lin (林及仁, NCTU) on the junior
level and Prof. Kingman Cheung (張敬民,
NTHU) on the senior level.
Young Theorist Award
Young Theorist Award was established in 2006
to promote excellent research work by young
theorists. This year many excellent candidates
from various institutions in Taiwan have applied.
The Executive Committee has selected Prof. YingJer Kao (高英哲) of National Taiwan University,
and Prof. Ray- Kuang Lee (李瑞光) of National
Tsinghua University.
Ling-Fong Li (李靈峰)
November 2010
Public Presentation of Review 2009
nd
2 floor, National Science Council (NSC)
Dec 26 (Sat)
09:00
09:30
09:40
10:00
10:20
11:00
Preparation meeting of the review committee
Host: Director Wen-Feng Liaw (Department Sciences & Mathematics, NSC)
Opening
Host: Director Wen-Feng Liaw (Department Sciences & Mathematics, NSC)
Overview of NCTS (Director Wen-Ching Li)
Report on Physics Division-main Project (Professor Chung-Yu Mou)
Report on Physics Division-subproject I (Professor Wei-Shu Hou)
Report on Physics Division-subproject II (Professor Yan-Tien Lu)
Break
Initiatives (subproject I)
11:15
11:30
11:45
12:00
12:15
Build-up of Theory Support for LHC Physics
Coordinator: Wei-Shu Hou (侯維恕, NTU)
Establish GPU-based Supercomputing Platform
Coordinator: Ting-Wai Chiu (趙挺偉, NTU)
Theory and Simulation of Plasmonic Metamaterials
Coordinator: Guang-Yu Guo (郭光宇, NTU)
Q&A
Lunch
Interdisciplinary Fields
13:30
13:45
14:00
14:15
14:30
Focus Group on Atomic-Molecular-Optical Physics
Coordinator: Daw-Wei Wang (王道維, NTHU)
Focus Group on Plasma Science
Coordinator: Frank Cheng (陳秋榮, NCKU)
Focus Group on Quantum Information Science
Coordinators: His-Sheng Goan (管希聖, NTU), Yueh-Nan Chen (陳岳男, NCKU)
Topic Program on Laser/Maser Plasma Sciences
Coordinator: Shih-Hung Chen (陳仕宏, NCU)
Q&A
Complex System
14:45
15:00
15:15
15:30
Focus Group on Critical phenomena and Complex System
Coordinator: Chin-Kun Hu (胡進錕, AS)
Focus Group on Soft Matter Physics
Coordinators: Hsuan-Yi Chen (陳宣毅, NCU), Hoong-Chien Lee (李弘謙, NCU), Ming-Chih Shih (施明智, NCHU)
Q&A
Break
Particles and Fields
15:45
16:00
16:15
16:30
16:45
17:00
Focus Group on Cosmology and Particle Astrophysics
Coordinator: Pisin Chen (陳丕燊, NTU)
Focus Group on Gravitation
Coordinator: Hoi-Lai Yu (余海禮, AS)
Focus Group on Lattice QCD and Hadron Physics
Coordinator: Ting-Wai Chiu (趙挺偉, NTU)
Focus Group on LHC Physics
Coordinator: Xiao-Gang He (何小剛, NTU)
Focus Group on String
Coordinator: Chiang-Mei Chen (陳江梅, NCU)
Q&A
Condensed Matter Physics
17:50
Focus Group on Computational Materials Research
Coordinator: Ching Cheng (鄭靜, NCKU)
Working Group on Quantum Phenomena in Condensed Matter Physics
Focus Group on Mesoscopic Physics and Strongly Correlated Systems
Coordinators: Hsiu-Hau Lin (林秀豪, NTHU), Chung-Hou Chung (仲崇厚, NCTU)
Focus Group on Numerical Methods for Strongly Correlated Physics
Coordinator: Ying-Jer Kao (高英哲, NTU)
Q&A
09:30
Review committee meeting
17:15
17:30
Dec 27 (Sun))
2005
2006
2007
2008
National Center for Theoretical Sciences. Physics Division
2009
2010
2011
Highlights of Programs
Complex System
Focus Group on Complexity and Life
Coordinator: H
suan-Yi Chen (National Central University; email: [email protected])
I. Brief Description
his focus group has ~40 PIs from various
institutes in north and central Taiwan.
The coordinator is Hsuan-Yi Chen (NCU Physics)
The committee members of our focus group are:
Chi-Keung Chan (Academia Sinica Physics),
Peilong Chen (NCU Physics), Kai-Jung
Chi(NCHU Physics), Pik-Yin Lai (NCU Physics),
Hoong-Chien Lee (NCU SysBiol), Sy-Sang
Liaw(NCHU Physics), Jiunn-Ren Roan(NCHU
Physics), Ming-Chih Shih(NCHU Physics), SunChong Wang (NCU SysBiol)
Current research projects include:
1. Econophysics: Fractal dimension analysis of
time sequences
2. Nonlinear Dynamics: Evolutionary dynamics,
biofilms, neural networks
3. B iophysics: Lipid rafts, interactions of lipid
bilayers with proteins, the mechanical
responses of spider webs, molecular motors,
cell adhesion and cell movement
4. B iomechanics: Insect locomotion, fluid
dynamics of biological sniffers
5. Granular Physics: The mechanism of vibrating
granular system
6. S ystems Biology: Evolution of genomes,
s y s t e m s b i o l o g y o f C h i n e s e p h a r m a c y,
synchronization in biological networks, etc.
Highlights of Programs -›› 124
Because of the interdisciplinary nature of our
topics, our FG members include several
mathematicians, biologists and information
scientists.
II. Activities
Regular meetings: 5 regular meetings at NCU,
NCTS, NCHU are funded by our FG
Bio-soft matter seminar at NCU Physics:
Thursday 12:00-13:00
here will be about 30 talks in this seminar
T
series this year. Most of the speakers are
graduate students and postdocs. About 25
people regularly attend this seminar series, the
main topics are nonequilibrium statistical
physics, biomenbranes, molecular motors,
biological networks, and fluid dynamics.
Systems Biology Colloquium at NCU Inst of Sys
Biol: Thursday 11:00-12:00
his weekly colloquium series strongly focus
T
on the application of systems biological
methods in studying real biological systems.
In this year there will be about 25 talks and
most invited speakers are from institutes
around Taiwan and from abroad. Usually the
size of the audience is about 50.
Biophysical Journal Club at NCHU Physics:
Thursday 12:00-13:00
iophysical Journal Club has attracted broad
B
attendance from various disciplines. There will
be more than 25 scheduled talks in this year
and on average around 30 people attend the
Club meeting at each gathering. Details of the
activity subjects can be found at HYPERLINK
"http://nchu-bjc.blogspot.com/"http://nchu-bjc.
blogspot.com/
Nonlinear phenomena seminar at NCHU Physics:
Friday 15:30-18:00
onlinear phenomena seminar was organized
N
by Prof. Liaw. The scope of the seminar
includes granular physics, pattern formation,
and fractal analysis of complex systems. About
10 to 15 people attend the seminar series.
Seminar series at NCTS HsinChu: Friday 12:0013:00
siu-Hau Lin (NTHU) organized a seminar
H
series on evolutionary dynamics in the spring.
It is followed by another series on all topics
related to "complexity and life" in the fall. ~15
people from NCTS, NTHU, NCTU, etc, attend
these seminars. This series will be regular
events at NCTU HsinChu.
Workshops, conferences, and schools
1. M
ini-workshops: we have organized two 1-day
mini-workshops.
a. M ini-workshop on hydrodynamics of
interacting fluids/particles, 2010/03/05
Department of Physics, National Central
University,
b. Nonlinear biophysics in exitable systems,
2010/04/12 Institute of Physics, Academia
Sinica, Taipei
I n each mini-workshop, about 8 domestic and
international scholars were invited to present
their recent works. The total number of
participants in each workshop was ~50.
During these small-scale activities the
participants found plenty of opportunities to
exchange ideas and had a lot of discussions.
2. I nternational School for Micro- and NanoScience for Biological Surfaces,
2010/4/16~2010/4/22, National Chung Hsing
University (Taichung) and Huisun Forest
Station (Nantou).
2 German scholars were invited to introduce
general background on biological functional
surfaces, the surface science techniques for
insect biomechanics, and bio-inspired design
from diverse animal attachments. They also
demonstrated simple experimental techniques
and supervised the participants to measure
adhesion and friction force on insects and
plants in a 4-day field work. ~80 participants
from physics, chemistry, engineering, biology,
and agriculture departments attended this
school.
3. C
omplex systems symposium,
2010/05/21~5/23, Sun Moon Lake (Nantou)
bout 35 student speakers from different
A
graduate institutes around Taiwan presented in
this student symposium. Talks were in the
general field of complex systems including
nonlinear dynamics, statistical physics,
biological physics, systems biology, and
biomechanics. We have attracted about 80
attendees , ~20 were PIs and ~60 students. To
provide more chances for the participants to
discuss their research works, there was a
discussion session during which the
participants could discuss with the speakers
about their talks in details.
4. 2 010 Taipei International Workshop for Soft
Matter and Biophysics, 2010/05/24~05/28,
Department of Chemistry, NTU, Taipei
his 1-week workshop attracted about 100
T
participants. Talks from international scholars
were mixed with talks from local speakers.
Student posters were arranged so that more
discussions between speakers and participants
were possible. The focus of this workshop was
rheology. This is the 4 th of a series of
successful workshop starting from 2002. In
the future, we will organize this workshop
every other year.
5. T
he 7 th Cross-Strait Workshop on Biology
Inspired Theoretical Sciences,
2010/06/25~06/30, National Cheng Kung
University, Tainan
his is the 7th of a successful series of meetings
T
on biology inspired theoretical sciences. About
90 people attended this workshop, ~40 talks
were given in the workshop with half of the
speakers from mainland the other half were
local speakers.
6. Workshop on stem cells (後基因體時代分子
醫學研究發展之展望學術研討會II),
125 ‹‹- Highlights of Programs
2010/10/31, 國泰醫院
bout 40 participant will attend this 1-day
A
workshop focusing on the stem cell research
and its applications in medical sciences.
7. B
iophysics Workshop IV: Vision beyond
Visibility, 2010/11/5~11/7, Huisun Forest
Station (Nantou).
his upcoming workshop focuses on the
T
biophysics of vision. This workshop will cover
the whole visual pathway (from eye to brain)
and explore different aspects of vision in
diverse animals living in different
environments; a variety of methodologies will
also be introduced. We expect our members
and other people from physics, biology, and
other related fields to attend this workshop.
8. B
io-Soft matter days 2011: 2011/01/23 ~ 01/25
Taipei
e will combine this workshop with the
W
annual meeting of PSROC. All FG members
will be encouraged to present their research
results in PSROC soft matter/biophysics
sessions, and a few topics will be chosen to be
discussed in details in bio-soft matter days
2011 . We expect this type of workshops will
help FG members to know each other’s work
in more details and the discussions will
encourage future collaborations within the FG.
Supporting young scientists
A. International conferences
Under the support of our FG, we have sent one
young PI, 1 postdoc, and 4 graduate students to
attend international conferences and research
visits.
B. Student Awards
• S
ymposium on Animal Behavior and Ecology-The Biological Society of China 2010 Joint
Annual Conference
1. C .-T. Chang won the Oral Presentation
Award.
2. Y. Chen also won the Oral Presentation
Award.
3. H. B. Tseng won the Student’s Poster Award
4. W.T. Teng also won the Student’s Poster
Award
Highlights of Programs -›› 126
• 2 010 Annual Meeting for Physical Society of
Taiwan
1. C.-T. Chang won the Best Student’s Poster
Award in Biophysics/ Soft matter
III. Visitors and International
Collaborations
Kai-Jung Chi (NCHU) has established
collaboration with Prof. Stanislav Gorb from the
Zoology Institute of Kiel University, Germany.
Two graduate students of Chi are now working on
projects related to insect adhesion. Prof. Kai-Jung
Chi is invited by Prof. Gorb to give talks at Kiel
University in Dec 2010. She will establish
collaborative research plans during this trip. Dr.
Ming-Huang Wu (NCHU) will join this research
trip funded by NCTS.
As a part of the long-term collaboration
between Hsuan-Yi Chen (NCU) and Prof.
Mikhailov (FHI-MPI, Berlin, Germany) on
nonequilibrium soft matters. Mr. M-J Huang,
currently a PhD student will visit Frirz-Harber
Institute of the Max-Planck Society (FHI) at
Berlin from early Oct to late Dec 2010 through a
grant from FHI. Prof. Mikhailov also visited
Taiwan for about a week in May 2010 as a part of
this collaboration, part of his visit was funded by
NCTS.
Pik-Yin Lai (NCU) sent his PhD student, Miss
W-I Jiang for a research visit to Prof. Osipov
(Nizhny Novgorod State Medical Academy,
Russia) to study the nonlinear dynamics of cardiac
tissues.
IV. Highlights of Research Results
Prof. Liaw and his colleagues have developed
a fast method in calculating fractal dimensions of
time series. The method would be very useful for
analyzing data in various fields including finance,
biomedicine, and environment studies.
In a recent paper published in the Journal of
the Royal Society Interface, Prof. Kai-Jung Chi
and collaborator Prof. Louise Roth (Duke
University) combined analyses of allometry and
scaling with the application of mechanical
principles to uncover the principles of footpad
design in mammals of wide range of sizes. This
work was reported by Scientific American
(podcasted in "60-Second Science"), Science
Daily, PhysOrg, Wired Science, etc.
In a recent experiment, Yea-Wei Hseuh (NCU)
found an unusual dependence of lipid order on
ergosterol concentration in POPE-ergosterol
model membrane. This result was commented by
an anonymous referee as "it challenges some
expectations regarding the effect of a sterol on a
phospholipids bilayer".
Prof. Pik-Yin Lai (NCU) and his colleagues
developed a novel method that make use of
evolution adaptation and robustness as guiding
principles to identify the system-level modularity
organizations as conserved cores from highly
robust evolved modularity realizations and applied
successfully to yeast protein-protein interaction
network and neuronal network in C. elegans.
By analyzing the distribution of the k-mer
frequencies in many chromosomes, Prof. H-C Lee
(NCU) and his colleagues found that genome
growth and evolution is best described by a model
characterized by random segmental duplication
and random point mutation, but not of any model
whose dominant growth mechanism is not
segmental duplication.
V. Selected Publications
[1] H
ong-Da Chen, Wen-Lang Fan, Sing-Guan
Kong, HC Lee, Universal Global Imprints of
Genome Growth and Evolution - Equivalenth
Length and Cumulative Mutation Density,
PLoS ONE 5(4): e9844 (2010)
[2] F
ei Fang Chung, Sy-Sang Liaw, and Ming
Chung Ho, Energy and phase transition in a
vibrating granular system, Granular Matter
12, 369 (2010)
[3] H
-J Lin, H-Y Chen, Y-J Sheng, and H-K Tsao,
Free energy and critical force for adhesion
clusters, Phys. Rev. E 81, 061908 (2010)
[4] H
s u a n - Yi C h e n a n d A . S . M i k h a i l o v,
Dynamics of biomembranes with active
multiple-state inclusions, Phys. Rev. E 81,
031901 (2010)
[5] Y
. S. Chou, Pik-Yin Lai, and C. K. Chan,
Bursting of Neurons induced by inhibitory
mechanism, Chin. J. Phys. 48, p.143-155
(2010)
[6] S
y-Sang Liaw, Feng-Yuan Chiu, Cheng-Yen
Wang, and You-Hsien Shiau Fractal analysis
of stock index and electrocardiograph, to be
published in Chinese Journal of Physics
(2010)
[7] C
hi, K.-J. and Roth, V.L., Scaling and
mechanics of carnivoran footpads reveal the
principles of footpad design, J. Royal Socc
I n t . 7 , 11 4 5 ( 2 0 1 0 ) ( w i t h o u t N C T S
acknowledgement)
127 ‹‹- Highlights of Programs
Focus Group on Critical Phenomena and Complex Systems
Coordinator: Chin-Kun Hu (Academia Sinica, email: [email protected])
I. Brief Description
he purpose of this FG is to develop ideas
and methods in statistical and nonlinear
physics, then apply such ideas and methods to
complex physical, biological, and social problems.
The focus research topics include (1) Theoretical
models of critical phenomena, chaos, and pattern
formation, (2) Structures, folding, aggregation,
and evolution of biological macromolecules, (3)
Modeling and analysis of complex network and
signals. The activities of this FG can be found at
"Activity" of LSCP website: http://proj1.sinica.
edu.tw/~statphys/.
The key researchers of this FG include (1)
Shu-Chiuan Chang (張書銓) at Physics Dept. of
National Cheng-Kung University, Chi-Ning Chen
(陳企寧) at Physics Department of National
Dong-Hwa University, Dr. Yi-Chiuan Chen (陳怡
全), Institute of Mathematics of Academia Sinica,
Wen-Jong Ma (馬文忠) at Graduate Institute of
Applied Physics, National Chengchi University,
Chung-I Chou (鄒忠毅) at Department of Physics
of Chinese Culture University, Ming-Chung Ho
(何明宗) at Department of Physics of National
Kaohsiung Normal University, Ming-Chang
Huang (黃敏章) at Department of Physics of
Chung-Yuan Christian University, Tai-huang
Huang (黃太煌) at Institute of Biomedical
Sciences of Academia Sinica, Po-han Lee (李柏
翰) at The Affiliated Senior High School of
National Taiwan Normal University, Chai-Yu Lin
(林財鈺) at Physics Department of National
Chung Cheng University, Jung-Hsin Lin (林榮信)
at Research Center for Applied Sciences &
Institute of Biomedical Sciences of Academia
Sinica, Yu-Pin Luo (羅煜聘), Department of
Electronic Engineering of National Formosa
University, Chi-Tin Shih (施奇廷), Department of
Physics of Tunghai University, Wen-Jer Tzeng (曾
文哲) at Department of Physics of Tamkang
University, Dr. Ming-Chya Wu (吳明佳) at
Research Center for Adaptive Data Analysis of
Highlights of Programs -›› 128
National Central University, Jui-Ling Yu (余瑞琳)
at Department of Applied Mathematics of
Providence Univ., Zicong Zhou (周子聰) at
Department of Physics of Tamkang Univ. (2)
Long term visitors: D. Y. Lando from Belarus
National Academy of Sciences, BELARUS; N.
Sh. Izmailian from Yerevan State University in
Armenia; David B. Saakian from Yerevan Physics
Institute in Armenia, (3) Postdoctoral fellow:
S h u r a H a y r y a n, Ya o-C h e n H u n g, K a r e n
Petrosyanand Chia-Hei Yang at Inst of Phys. of
AS; Chung-ke Chang at Institute of Biomedical
Sciences, Academia Sinica, (4) Ph.D. students:
Chun-Ling Chang at Natl Central Univ., HsinLing Jiang at Natl-Hsing Hua Univ., Chien-Zhong
Wang at Natl Chung Hsin Univ., Shi-Jie Wang at
Natl Chung Hsin Univ.
II. Activities
Academic Activities (see "Activities" at http://
proj1.sinica.edu.tw/~statphys/).
[1] W
e organized a series of four 2010 NCTS
Workshops on Critical Phenomena and
Complex Systems on 28 & 29 January, 19 &
20 March, 5 July, and 10 & 11 September
2010. Another workshop will be organized in
Nov. or Dec. 2010.
[2] W
e have organized Taiwan-StatPhys 2010:
The 10th Taiwan International Symposium on
Statistical Physics at AS on 27-31 July 2010. Train young-generation physicists
[1] S
hu-Chiuan Chang, Chi-Ning Chen, Chai-Yu
Lin, and Jui-Ling Yu, Wen-Jer Tzeng visited
NCTS (North) in the summer break of 2010.
[2] P
h.D. student Mr. Shi-Jie Wang visited
University of Tokyo for one week in MarchApril 2010 to collaborate with Prof. Nobuyasu
Ito"s group at Department of Applied Physics
on analysis of complex human network.
[3] P
h. D student Hsin-Ling Chiang attended The
F i r s t I n t e r n a t i o n a l Wo r k s h o p o n
Computational Biological Physics, Ho Chi
Minh City on 1-6 February 2010 and
discussed with Prof. Main Suan Li on
collaborative research problems.
III. V isitors and International
Collaborations
Short term visitors can be found from speakers
of StatPhys-Taiwan 2010 and Workshops listed in
II.A. We are collaborating with visitors on
following problems.
[1] A
. E. Allahverdyan (Yerevan Physics Inst) and
C.-K. Hu collaborate to study polymorphism
and sympatric speciation; a manscript on this
topic is in preparation.
[2] S
hura Hayryan, Ming-Chya Wu and ChinKun Hu in collaboration with Prof. Nikolay V.
Dokholyan"s group at North Carolina are
establishing database and website for threedimensional structures of microRNA. More
than 2000 3D structures of microRNA have
been calculated.
[3] M
ing-Chya Wu, Yao-Chen Hung, Shi-Jie
Wang, Chin-Kun Hu, in collaboration with Z.
R. Struzik and Y. Yamamoto at University of
Tokyo are analyzing physiological signals to
identify health problems in human subjects.
[4] H
sin-Ling Chiang, Wen-Jong Ma, Yun-Ru
Chen (Genomics Res Center of AS), Rita
Chen (Inst. Bio. Chem., AS), and Chin-Kun
Hu in collaboration with Mai-Suan Li (Polish
Academy of Sciences) and Hisashi Okumura
(Institute for Molecular Science at Okazaki,)
to work on protein folding and aggregation
problems.
[5] J ui-Ling Yu and Prof. Olga. S. Rozanova of
Department of Math. at Moscow State
University are establishing a mathematical
model for predicting the trajectory of typhoon
on curved space.
[6] C
hi-Ning Chen and Prof. Jonathan Dushoff
(Dept. of biology, McMaster University,
Canada, 26 July-21 August in Taiwan) are
working on the SIRS model of epidemics
using stochastic partial differential equations
[T. Reichenbach et al, Nature 448, 1046
(2007); PRL 99, 238105 (2007)].
[7] M
ing-Chang Huang and Prof. N. Sh.
Izmailian (Yerevan Inst. Phys) published a
collaborative paper on finite-size corrections
for the Ising model.
IV. Highlights of Research Results
[1] W
en-Jong Ma and Chin-Kun Hu published a
series of papers on novel velocity distributions
for polymer chains and aggregation behavior
of polymer chains [J. Phys. Soc. Japan 79,
024005, 024006, 054001, and Oct issue
(2010)] . The later is useful for understanding
protein aggregation related to
neurodegenerative diseases, e.g. Alzheimer"s
disease, Huntington"s disease, Parkinson"s
disease, etc.
[2] M
ing-Chang Huang, Jinn-Wen Wu, Yu-Pin
Luo and Karen G. Petrosyan studied the
influence of Gaussian color noise on .gene
regulatory network and found that finite
correlation time of noise reduces the
fluctuations and enhances the correlation
between the fluctuations of the molecular
components [J. Chem. Phys. 132, 155101
(2010)].
[3] Y
ao-Chen Hung and Chin-Kun Hu found that
noise can play a constructive role in the P53 (a
protein related to cancer control) regulatory
network [Comp. Phys. Commu. doi:10.1016/
j.cpc.2010.07.002 (2010)]
[4] J . Bush, Shura Hayryan, Chin-Kun Hu, J.
Skrivanek and Ming-Chya Wu published a
computer package for detecting cavities in
macromolecules and calculating volume and
surface area of such cavities [Comp. Phys.
Commu., in press (2010)].
[5] C
hai-Yu Lin proposed a renormalization
group method to calculate critical exponent of
the sandpile model [Phys. Rev. E 81, 021112
(2010)].
Invited Presentations
[1] C
hin-Kun Hu gave (1) an invited talk on
"Simple models for relaxation and
aggregation of biopolymers" at The First
International Workshop on Computational
Biological Physics, Ho Chi Minh City, 4-6
F ebruary 2010; (2) an invited talk on
"Empirical mode decomposition and
synchrogram approach to cardiorespiratory
Synchronization" at International Symposium
129 ‹‹- Highlights of Programs
for Dynamic Electrocardiography, Nagoya
Lucent Tower, 27 March 2010; (3) an invited
talk "Relaxation and aggregation of
biopolymers, and q-statistics" at 2010 Annual
Meeting of Taiwan Biophysical Society,
Taipei, on 19-21 May 2010; (4) "Simple
models for protein aggregation" at The 7 th
Biology Inspired Theoretical Sciences
(BITS7), National Cheng Kung University,
Tainan, 25-28 June 2010; (5) a plenary talk on
"Geometrical origin of q-statistics in systems
of polymer chains and L-J molecules" at The
6th Dynamic Days Asia Pacific (DDAP6) at
New South Wales University, Sydney on
12-14 July 2010; (6) an invited talk "Effects
of noises in some complex nonlinear and
biological systems" at the 4 th EU-China
Summer School on Complex Sciences on
11-14 August 2010; (7) an invited talk
"Simple model for protein aggregation" at the
conference "The physics of cell functionality"
on 16-20 August 2010 and an invited talk
"Models of biological Evolution" at the
workshop "Emergent behavior of
biomolecular ensemble and Networks" on 24
August 2010; (8) an invited talk
"Neurodegenerative diseases and aggregation
of proteins" at 2nd Symposium on Systems
and Synthetic Biology (TriSys) in Tokyo on
4-6 October 2010.
[2] M
ing-Chya Wu gave invited talk "Phase
statistics approach to human ventricular
fibrillation" at International Symposium for
Dynamic Electrocardiography, Nagoya Lucent
Tower, 27 March 2010.
V. Publications
Only list 2010 papers, selected ones are good
enough.
A. Papers with NCTS as the affiliation
1. O .S. Rozanova, J.-L. Yu, and C.-K. Hu,
Ty p h o o n e y e t r a j e c t o r y b a s e d o n a
mathematical model: comparing with
observational data, Nonlinear Anal. Real World
Appl. 11, 1847 (2010)
2. C.-Y. Lin, A Renormalization-group Approach
to the Manna Sandpile, Phys. Rev. E 81, 021112
(2010)
3. S h u - C h i u a n C h a n g a n d R o b e r t S h r o c k .
Highlights of Programs -›› 130
Weighted graph colorings, Journal of Statistical
Physics, 138, 496-542 (2010)
4. D. B. Saakian, A. S. Martirosyan, and C.-K. Hu,
Different fitnesses for in vivo and in vitro
evolutions due to the finite generation-time
effect, Phys. Rev. E 81, 061913 (2010)
5. D . B. Saakian and C.-K. Hu, Selection via
flatness as a dynamical effect in evolution
models with finite population, Phys. Rev. E 82,
011902 (2010)
6. C hia-Hei Yang, Ching-Ling Hsu, Nan-Yow
Chen, and Chi-Tin Shih. Temporal Dynamics of
Site Percolation in Nanoparticle Assemblies,
Computer Physics Communication, in press
(2010).
B. Papers acknowledged NCTS supports
1. W.-J. Ma and C.-K. Hu, Generalized statistical
mechanics and scaling behavior for systems of
non-equilibrium polymer chains I: monomers
connected by regid bonds, J. Phys. Soc. Japan
79, 024005 (2010)
2. W.-J. Ma and C.-K. Hu, Generalized statistical
mechanics and scaling behavior for systems of
non-equilibrium polymer chains II: monomers
connected by springs, J. Phys. Soc. Japan 79,
024006 (2010)
3. W.-J. Ma and C.-K. Hu, Molecular dynamic
approach to aggregation of polymer chains with
monomers connected by rigid bonds, J. Phys.
Soc. Japan 79, 054001 (2010)
4. W.-J. Ma and C.-K. Hu, Molecular dynamic
approach to aggregation of polymer chains with
monomers connected by rigid bonds, J. Phys.
Soc. Japan 79, in press (2010)
5. J. Busa, S. Hayryan, C.-K. Hu, J. Skrivanek,
and M.-C. Wu, CAVE: A Package for Detection
and Quantitative Analysis of Internal Cavities
in a System of Overlapping Balls: Application
to Proteins, Comp. Phys. Commu., doi:10.1016/
j.cpc.2010.08.032 (2010)
6. M.-C. Huang, J.-W. Wu, Y.-P. Luo and K. G.
Petrosyan, Fluctuations in Gene Regulatory
Networks as Gaussian Colored Noise, J. Chem.
Phys. 132, 155101 (2010)
7. Y. C. Hung and C.-K. Hu, Constructive role of
noise in p53 regulatory network, Comp. Phys.
Commu., in press (2010)
Highlights of Programs
Condensed Matter Physics
Working Group on Quantum Phenomena in Condensed Matter Physics
A. Focus Group on Mesoscopic Physics and Strongly Correlated Systems
Coordinators: C
hung-Hou Chung (National Chiao Tung University; email: [email protected]),
Ming-Chiang Chung (NCTS; email: [email protected])
I. Brief Description
The focus group is formed to promote
research topics on mesoscopic physics
and strongly correlated systems and provide
opportunities for condensed matter theoreticians
interested in different materials and methods to
increase the interaction and cooperation. In recent
two years this focus group serves as a platform
between NCTS in Taiwan and junior research
groups in APCTP (Asian Pacific Center for
Theoretical Physics) to facilitate the international
collaborations, especially with young talented
researchers from the asian pacific region (China,
Korea, Japan and Taiwan). In addition we
financially support students and young researchers
to participate international conferences.
We have over 70 sing-up members in this focus
group and around 1/3 of the members have been
actively participating the group activities. The
research topics are addressed on spintronics,
topological insulators, graphenes, multiferroic
materials, quantum transport, entanglement in
condensed matters and nanostructures.
II. Activities
In the past one year (Sep. 2009 - Sep 2010),
our focus group has organized the following
activities:
1. M
iniworkshop on Mesosopic and Spin, NCTS/
NCTU, May 15, 2010
e had a one-day mini-workshop on two new
W
topics in condensed matter physics--graphene
and topological insulators. This mini-workshop
attracted a lot of attention in Taiwan. The
participants include experts from Academia
Sinica, NTHU, NCTU, and other major
universities in Taiwan. Prof. Shun-Qing Shen
from Hong-Kong University gave an excellent
introduction to quantum spin Hall effect in
graphene and topological insulators in
semiconductor materials. Prof. T.K. Ng from
Hong-Kong University of Science and
Technology also presented a new theoretical
proposal to detect the exotic Majorana state in
topological insulator-superconductor junction.
Prof. Chung-Yu Mou from NTHU reported
new results on magnetism in graphene. There
were many discussions/exchange of ideas
between local participants and international
speakers both in the talks and during the coffe
breaks. We think this is a very successful miniworkshop in NCTS. After the event, many
participants still continued exchanging
interesting ideas with the speakers of the
workshop. Example: Prof. Chung-Hou Chung
and Prof. T.K. Ng are collaborating on the
nonequilibrium transport through quantum dot
coupled to topological insulators.
2. Q
uantum Condensation 2010 (QC10), Aug
09-19 2010 (Hsinchu)
131 ‹‹- Highlights of Programs
he idea of QC workshop was initiated by
T
Prof. Peter Fulde (Director of APCTP) . The
goal of this workshop is to intensively increase
the collaboration among the condensed matter
physicists working in the asian pacific
countries. In this 2-week’s workshop we want
to create a laid-back atmosphere for
participants for building trust and long-term
collaborations. In 2009 our focus group helped
Prof. Xin Wan (APCTP) organize QC09 in
APCTP, Pohang Korea. In 2010 QC10 was
held in NCTS, Hsinchu as we planned at the
beginning.
ith the participation of Prof. Fulde we invited
W
19 researchers from Korea, China, Hongkong
and Japan, and 10 more local researchers to
participate the workshop (see visitors and
international collaborations). This year the
workshop had two essential topics: advanced
topics in superconductivies and entanglement
in condensed matter. In the first week the
workshop was held in the campus of Tsinghua
university. The second part of the workshop
was held in Sitou.
I n this year, QC10 achieved two essential aims:
firstly in addition to old participants of QC09,
new participants from Japan and Hongkong
contributed a lot in this workshop. As a
consequence, QC11 will be organized by Prof.
Ng Ta i-Kai at Hongkong univ e r s i t y o f
technology and science. Secondly after QC10
workshop we also organized a summer school.
Some of the QC10 participants became
lecturers and the students could benefit from
their wide knowledge. Please visit website
HYPERLINK "http://sites.google.com/site/
quantcond/qc10" http://sites.google.com/site/
quantcond/qc10 to have more information.
3. QC10 summer school, Aug 19-21, 2010
s mentioned in the last paragraph, QC10
A
summer school was organized together with
QC10 workshop. The topics on the summer
school are superfluid, superconductivities and
entanglement in condensed matter. In order
that the students and junior researchers can
profit from QC10 workshop, 8 lecturers were
selected from QC10 participants and
everybody gave a 2-hour’s lecture from the
general common knowledge to advanced
Highlights of Programs -›› 132
research topics like topological insulators,
unconventional superconductivities, FFLO
states, dynamical mean field theory, geometry
measurement of entanglement, entanglement
spectra of the Moor-Read states and
entanglement area laws. Details see http://sites.
google.com/site/quantcond/qc10-summerschool .
4. W
ith limited travel supports, we manage to
support 10 graduate students and postdocs to
attend international conferences. This channel
of supports is precious for the talented young
bloods and their exposure to the international
community has given them a glimpse about the
outside world. In addition, we hope to attract
young talents into condensed matter physics
via summer school, workshops/miniprograms
and journal clubs.
III. Visitors and International
Collaborations
International visitors
For miniworkshop on mesoscopic and Spins
1. P rof. Ng Tai-Kai (Hongkong university of
technology and science, Hongkong)
2. Prof Shen Shun-Qing (Hongkong university,
Hongkong)
For QC10 we invited 19 international researchers
and postdocs as follows:
1. Prof. Peter Fulde (APCTP, Korea and MPIPKS
Germany)
2. Prof. Chen Qijin (Zhejian university, China)
3. Prof. Chen Yan (Fudan university, China)
4. Prof. Kim Ki-Seok (APCTP, Korea)
5. P rof. Kontani Hiroshi (Nagoya University,
Japan)
6. P rof. Ng Tai-Kai (Hongkong university of
technology and science, Hongkong)
7. Prof. Sato Masatoshi (ISSP, the university of
Tokyo, Japan)
8. Prof Shen Shun-Qing (Hongkong university,
Hongkong)
9. Prof. Takimoto Tetsuya (APCTP, Korea)
10. Prof. Tong Ninghua (Remin university, China)
2. P
r o f . R o l a n d Wi n k l e r ( U n i v e r s i t y o f
Regensburg)
at Karlsruhe and Vojta at Yale on the quantum
phase transitions in nano-systems out of
equilibrium which has become a new subject
recently due to advance in nano-technologies. At
the quantum critical point, physical observables
often show universal power-law scaling behaviors.
I n t e r e s t i n g l y, t h e s e c r i t i c a l p r o p e r t i e s i n
equilibrium at finite temperatures are quite
different from those in nonequilibrium.They
pioneerly investigate the non-equilibrium
transport near a quantum phase transition in a
generic and relatively simple case model, the
dissipative resonant level model, that has many
ramifications in nanosystems. They formulate a
rigorous mapping and apply a controlled
frequency-dependent renormalization group
approach to compute the non-equilibrium current
in the presence of a finite bias voltage V [ Phys.
Rev. Lett. 102, 216803 (2009)]. They furthermore
generalized the setup to a real spinful quantum dot
coupled to interacting Luttinger liquid leads with a
bias voltage.
International collaborators
Graphene
1. C hung-Hou Chung (NCTU) + K. Le Hur
(Yale), Peter Woelfle (Karlsruhe, Germany),
Matthias Vojta (Koeln, Germany), Gergely
Zarand (University Budapest, Hungary), Pascal
Simon (CNRS, Grenoble, France) on quantum
transport problems.
Chung-Yu Mou collaborates with Ming-Che
Chang (NTNTU) and Bor-Luen Huang (NTNU)
to investigate the density of state due to strong
point defects in graphene. A similar problem was
previously analyzed in the context of d-wave and
the issue of what is the density of state in strong
point defects is considered to be unsolved.
Instead of focusing on density of states directly,
we analyze eigenfunctions of inverse T-matrix in
the unitary limit. It turns out that the density of
state can be found via this analysis and is
characterized by the well-known Thomas-Porter
type distribution. This finding solves the longtime unsolved issue in d-wave superconductors
and also provides an interpretation of the origin of
ferromagnetism in strongly disordered graphene.
11. P rof. Wan Xin (APCTP, Korea and Zhejian
university China)
12. Prof. Watanabe Gentaro (APCTP, Korea)
13. D r. Wei Tzu-Chieh (University British
Colombia, Canada)
14. Dr. Hu Zi-Xiang (APCTP, Korea)
15. Dr. Frank Pollman (MPIPKS, Germany)
16. Dr. Lee Hyun-Jung (APCTP, Korea)
17. Dr. Tran Minh-Tien (APCTP, Korea)
18. D r. Soomya Prasad Mukherjee (APCTP,
Korea)
19. Dr. Li Ki-Hoon(APCTP, Korea)
Other visitors
1. Prof. Kenji Harada, (Kyoto University)
2. Ming-Chiang Chung (NCTS), Pochung Chen
(NTHU) + Sungkit Yip and Ian
McCulloch(University of Queensland,
Australian) on spin-2 Bose gases.
3. C hon-Saar Chu(NCTU) + A.G. Malshulkov
(Russia) on spintronics
4. H siu-Hau Lin (NCHU) + Toshiya Hikihara
(Hokkaido University) and Jian-Ming Tang
(University of New Hamshire) on Graphenes.
5. Hsiu-Hau Lin (NCHU) + Sung-Ik Lee (Korea
Atomic Energy Research Institute) and
Sungmog Yeo (Korea Atomic Energy Research
Institute) on Spintronics.
IV. Research Highlights
Nonequilibrium quantum phase transition
Chung-Hou Chung collaborates with Woelfle
Hsui-Hau and his coworkers work on powerlaw singularity in the local density of states due to
the point defect in graphene. Defects in graphene
give rise to zero modes that are often related to the
sharp peak in the local density of states near the
defect site. Here we solved all zero modes induced
by a single defect in the finite-size graphene and
show that their contributions to the local density
of states vanish in the thermodynamic limit.
Instead, lots of resonant states emerge at low
133 ‹‹- Highlights of Programs
energies and eventually lead to a power-law
singularity in the local density of states. Our
findings show that the impurity problem in
graphene should be treated as a collective
phenomenon rather than a single impurity state
[Phys. Rev. B 80, 121404(R) (2009)].
Spintronic
Chon-Saar Chu continues his long-term
collaboration with Malshukov. They have shown
that the Rashba spin-orbit contribution to spin
accumulation can be restored in a driving field
that is nonuniform spatially. The spin diffusion
equation appropriate for the nonunifom case is
derived. Our finding shows that the physical
mechanism for this spin accumulation is different
from the conventional one. While the
conventional one has the polarization direction the
same for both the spin accumulation and the spin
current, it differs for the spin accumulation and
the spin current. A simple scheme for the
generation of the nonuniform driving field is
discussed [Physical Review B 81, 115312 (2010)].
RG Transformation
Hsiu-Hau Lin and his coworkers work on the
hierarchy of relevant couplings in perturbative
renormalization group transformations.The phase
diagram for the interacting fermions in weak
coupling is described by the perturbative
renormalization group equations. Due to the lack
of analytic solutions for these coupled non-linear
differential equations, it is rather subtle to tell
which couplings are relevant or irrelevant. They
propose a powerful classification scheme to build
up the hierarchy of the relevant couplings by a
scaling Ansatz found numerically. To demonstrate
its superiority over the conventional classification
for the relevant couplings, we apply this scheme
to a controversial phase transition in the two-leg
ladder and show that it should be a non-trivial
crossover instead. The scaling Ansatz we propose
here can classify the relevant couplings in
hierarchical order without any ambiguity and can
improve significantly how we interpret the
numerical outcomes in general renormalization
group methods. [Phys. Rev. B 81, 121107(R)
(2010)]
Quantum Information in Condensed Matter
Ming-Chiang Chung collaborates with
Highlights of Programs -›› 134
Pochung Chen and Sungkit Yip on edge state,
entanglement entropy spectra and critical hopping
constants in anisotropic honeycomb lattice.For a
bipartite honeycomb lattice, they show that the
Berry phase depends not only on the shape of the
system but also on the hopping couplings. Using
the entanglement entropy spectra obtained by
diagonalizing the block Green’s function matrices,
the maximal entangled state with the eigenvalue
1/2 of the reduced density matrix is shown to have
one-to-one correspondence to the zero energy
states of the lattice with open boundaries, which
depends on the Berry phase. For the systems with
finite bearded edges along x-direction we find
critical hopping couplings: the maximal entangled
states (zero-energy states) appear pair by pair if
one increases the hopping coupling over the
critical couplings.
Pochung Chen and his coworkers have applied
the tensor network method, in particular the
combined TEBD/TRG algorithm, to study the
frustrated spin-1/2 spin-dimer models and the
attractive two-species bosons in a square lattice.
For spin-dimer model, we identify the regime of
supersolid and critical fields at various fieldinduced transitions are determined accurately. For
two-species Bose-Hubbard model, we identify the
regime of exotic pair-superfluid and Various
quantum phase transitions across the phase
boundaries are characterized. Our works not only
provide guides to the experimental search of these
exotic phases but also demonstrate the potential in
applying the current formalism to 2D spin and
boson systems.
The authors of these highlighted works have
been invited to various workshops and
international conferences. Especially Chung-Hou
Chung was invited by the Brown university,
Havard university, MIT and IBM in 2009.
V. Selected Publications
[1] C .H. Chung, K.V.P. Latha, K. Le Hur, M.
Vojta, P. Woelfle,"Tunable Kondo-Luttinger
systems far from equilibrium",
arXiv:1002.1757, (Phys. Rev. B, 2010,
accepted and in press)
[2] Chung-Hou Chung, Tsung-Han Lee, "Tunable
Fano-Kondo resonance in side-coupled double
quantum dot system", Phys. Rev. B 82, 085325
(2010), selected for publication in Virtual
Journal of Nanoscience and Technology
[3] C hung-Hou Chung and K. V. P. Latha,
"Nonequilibrium occupation number and
charge susceptibility of a resonance level close
to a dissipative quantum phase transition",
Phys. Rev. B 82,085120 (2010)
[4] Yi-Ling Tsai, Chung-Hou Chung*, "Kondo
effect in a side-coupled double-quantum-dot
system embedded in a mesoscopic ring", Phys.
Rev. B 81, 195305 (2010), selected for
publication in Virtual Journal of Nanoscience
and Technology
[5] H ong-Yan Shih, Wen-Min Huang*, Sze-Bi
Hsu and Hsiu-Hau Lin "Hierarchy of relevant
couplings in perturbative renormalization
group Transformations" Phys. Rev. B 81,
121107(R) (2010)
[6] Wen-Min Huang and Hsiu-Hau Lin, "Andreev
bound states in iron pnictide superconductors"
Phys. Rev. B 81, 052504 (2010)
[7] D i m a B o l m a t o v a n d C h u n g - Yu M o u ,
"Tunneling Conductance of the Graphene SNS
Junction with a Single Localized Defect",
Journal of Experimental and Theoretical
Physics 110, 613 (2010)
[8] D ima Bolmatov and Chung-Yu Mou, "
Josephson effect in graphene SNS junction
with a single localized defect", Physica B 405,
2896 (2010)
[9] 9.S. -J. Tang, Tay- Rong Chang, Chien-Chung
Huang, Chang-Yeh Lee, Cheng-Maw Cheng,
Ku-Ding Tsuei, H. -T. Jeng, Chung-Yu Mou,"
Dispersive resonance bands within the space
c h a rg e l a y e r o f m e t a l - s e m i c o n d u c t o r
junction", Phys. Rev. B 81, 245406 (2010)
[10] 1 0 Wen-Ming Huang,Chung-Yu Mou and
Cheng-Hung Chang , "scattering phase
correction for semiclassical quantization rules
in multi-dimensional quantum systems" ,
Communications in Theoretical Physics 53,
250 (2010)
[11] Huang DJ, Okamoto J, Huang SW, and C. Y.
Mou, "Magnetic Transitions of Multiferroic
Frustrated Magnets Revealed by Resonant
Soft X-ray Magnetic Scattering", J. of Phys.
Soc. Jap. 79, 011009 (2010)
[12] 1 2 . L . Y. Wa n g , C . S . C h u , a n d A . G .
Malshukov, Spin generation in a Rashba-type
diffusive electron system by nonuniform
driving field, Physical Review B 81, 115312
(2010)
[13] Pochung Chen, Chen-Yen Lai, and Min-Fong
Yang, "Field-induced spin supersolidity in
frustrated S=1/2 spin-dimer models", Phys.
Rev. B 81, 020409(R), (2010)
[14] Wei-Chih Ting, Dian-Jiun Han, and Shin-Tza
Wu, Manipulation of coherent atom waves
using accelerated two-dimensional optical
lattices, New J. Phys. 12, 083059 (2010)
[15] Chung-Hou Chung, Karyn Le Hur*, Matthias
Vojta, and Peter Woeffle, "Non-equilibrium
transport at a dissipative quantum phase
transition", Phys. Rev. Lett. 102, 216803
(2009)
[16] S. V. Isakov, H.C. Chien, J.J. Wu, Y.C. Chen,
C.H. Chung, K. Sengupta*, Y.B. Kim*,
"Commensurate lock-in and incommensurate
supersolid phases of hardcore bosons on
anisotropic triangular lattices", Europhys.
Lett. 87, 36002 (2009)
[17] S. Yeo, J. E. Bunder, Hsiu-Hau Lin, MyungHwa Jung* and Sung-Ik Lee "Concurrent
magnetic and metal-insulator transitions in
Eu1-xSmxB6 single crystals", Appl. Phys.
Lett. 94, 042509 (2009)
[18] Hong-Yan Shih*, Wen-Min Huang, Sze-Bi
Hsu and Hsiu-Hau Lin "A new classification
scheme for relevant couplings in
renormalization group transformations"
Physica C (2009) doi:10.1016/j.
physc.2009.12.019
[19] We n - M i n H u a n g * a n d H s i u - H a u L i n ,
"Andreev bound states in sodium cobalt
oxide", Physica C (2009) doi:10.1016/j.
physc.2009.11.098
[20] Po-Yao Chang*, Wen-Min Huang and HsiuHau Lin "Impurity-induced conductance
anomaly in zigzag carbon nanotubes"J. Phys.:
Conf. Ser. 150, 022007 (2009)
[21] Yen-Chen Lee* and Hsiu-Hau Lin, "Flatband ferromagnetism in armchair graphene
nanoribbons", J. Phys.: Conf. Ser. 150,
042110 (2009)
135 ‹‹- Highlights of Programs
Working Group on Quantum Phenomena in Condensed Matter Physics
B. Focus Group on Numerical Methods for Strongly Correlated Physics
Coordinators: Y
ing-Jer Kao (National Taiwan University; email: [email protected]),
Po-Chung Chen (National Tsing Hua University; email: [email protected])
I. Brief Introduction
he "Numerical Methods on Strongly
Correlated Physics" (NMSCP) is a focus
group under the Quantum Phenomena in the
Condensed Matter Physics Working Group. It was
formed to provide a platform for condensed matter
theorists who are specializing and/or interested in
numerical simulations to facilitate interaction and
collaboration. In addition, activities and visitor
programs are designed to provide opportunities
f o r r es ear ch er s to es tab lis h in te r n a t i o n a l
collaborations. In addition, travel funds are
available to provide financial support to students
and junior researches to attend international
conferences. An executive committee of ten
members from major institutes is formed to
coordinate these activities and oversee the usage
of the fund.
In addition to the executive committee, there
are twenty-four active faculty members and thirtytwo junior members (postdocs and graduate
students). The focus research topics are (1)
numerical methods based on tensor network
states, (2) ab inito studies of organic and strongly
correlated materials, (3) quantum transport in
nanodevices and spintronics and (4) Bose-Einstein
condensation in cold atoms.
II. Activities
Our focus group organized or sponsored
following activities last year:
Miniworkshop on Tensor Network Based
Numerical Methods
May 28, 2010, Hsin-Chu
Highlights of Programs -›› 136
This is a one-day workshop on tensor network
based numerical simulations in strongly correlated
systems, where international visitor Prof. Kenji
Harada from Osaka University and local
researchers exchange ideas and establish future
collaborations.
Summer school on Computational Statistical
Physics
August 4-11, 2010, Taipei
This school was co-organized with the
Graduate Institute of Applied Physics, NCCU. The
school was aimed at giving pedagogical
introductions to a variety of numerical approaches
to students and scientists who are interested
computational physics. The topics include
optimization, classical and quantum Monte Carlo
methods, exact diagonalization and density matrix
renormalization group. We invited three worldleading experts Heiko Rieger, Anders Sandvik,
and Ian McCulloch to give lectures as well as run
tutorial sessions that help students to have handson experience; some senior students from our FG
also worked as tutors to assist the tutorial sessions.
About 70 students, postdocs and professors
registered for the school and we have received
very positive comments from them.
2 0 1 0 Wo r k s h o p a n d Su m m e r S c h o o l o n
Quantum Condensation (QC10)
August 9-21, 2010, Hsin-Chu
Q C 1 0 i s j o i n t l y o rg a n i z e d w i t h F G o n
Mesoscopic Physics and Strongly Correlated
Systems, and Asia-Pacific Center for Theoretical
Physics. We invited leading physicists from East
Asia, including Korea, China, Japan, and Taiwan,
to discuss interesting topics on quantum
condensation in different aspects of condensed
matter systems. Talks are scheduled in a way to
maximize interaction among participants and
panel discussion sessions are included to forge
collaborations. This is the second QC workshop,
continuation from the successful first QC meeting
in Pohang. It is expected that long-term
collaborations will be formed as a result of this
workshop.
Bi-weekly Meeting of NMSCP Focus Group
Taipei & Hsin-Chu
This meeting series focuses on two special
topics of quantum Monte Carlo and numerical
methods based on tensor networks. Seminars are
h e l d b i w e e k l y i n Ta i p e i a n d H s i n - C h u
alternatively with participants from institutes in
both areas. In addition, live webcast is provided
for remote participants. This informal seminar is
intended to motivate junior researchers to identify
and discuss on research topics. More information
about this meeting series can be found at http://
sites.google.com/sites/nmscp.
In addition to the above activities, the FG also
provided travel support for two Ph. D students
Ching-Yu Huang (NTNU) to attend 10th Canadian
Summer School on Quantum Information at
University of British Columbia, Canada, and
Chung-Ping Hsiao (NTHU) for a research visit at
School of Mathematics & Physics, University of
Queensland, Australia.
III. V isitors and International
Collaborations
Internatonal Visitors (Dec 09-Nov 10)
•
•
•
•
enji Harada (Osaka University, Japan),
K
Anders W. Sandvik (Boston University, USA),
Heiko Rieger (Saarland University, Germany),
I an McCulloch (University of Queensland,
Australia),
• Sheng Ju (Shouchow University, China).
International Collaborations
• Y
ing-Jer Kao (NTU) + A. W. Sandvik (USA),
R. G. Melko (Canada) on numerical methods
based on tensor networks.
• F e n g - L i L i n ( N T N U ) + T z u - C h i e h We i
(Canada) on entanglement entropy in quantum
systems.
• C
hao-Cheng Kaun (AS) + Hong Guo (McGill)
to study the spin transport in nanostructures.; +
Peeters (Belgium) on the spatially non-uniform
pairing induced by quantum confinement in
metallic nanograins; + T. Seideman (USA), and
M. C. Hersam (USA) on the current-driven
desorption at the organic molecule–
semiconductor interface; + D. A. Luzhbin
(Ukraine) on charge transport in molecular
junctions.
• Yu - C h e n g L i n ( N C C U ) + H e i k o R i e g e r
(Germany) on entanglement in quenched
disordered systems; + A. W. Sandvik (USA) on
entanglement entropy of spin systems.
• P o-Chung Chen (NTHU) + I. McCulloch
(Australia) on simulation based on matrix
product states; + G. Vidal (Australia) on
multiscale entanglement renormalization ansatz
(MERA).
• Hung-Chung Hsueh (TKU) + Wei Ku (USA) on
the new methodology (TDLDA+U) for strongly
correlated system; + Peihong Zhang (USA) on
LDA+U+GW method.
IV. Research Highlights
Numerical Methods Based on Tensor Network
States
Feng-Li Lin (NTNU) and his student Ching-Yu
Huang compute the multipartite entanglement
measures such as the global entanglement of
various one- and two-dimensional quantum
systems to probe the quantum criticality based on
the matrix and tensor product states (MPSs and
TPSs). They use the infinite time-evolving block
decimation (iTEBD) method to find the ground
states numerically in the form of MPSs and TPSs,
and then evaluate their entanglement measures by
the method of tensor renormalization group
(TRG). They find that these entanglement
measures can characterize the quantum phase
transitions by their derivative discontinuity right
at the critical points in all models considered [1].
Ying-Jer Kao (NTU) and his coworkers study
variationally optimized matrix-product states for
the transverse-field Ising chain using D×D
matrices with small D [2–10]. For finite system
size N there are energy minimums for symmetric
as well as symmetry-broken states, which cross
137 ‹‹- Highlights of Programs
each other at a field value h c (N,D); thus the
transition is first order. A continuous transition
develops as N→∞ . The asymptotic critical
behavior is then always of mean-field type (the
magnetization exponent ® =1/2) but a window of
field strengths where true Ising scaling holds
(® =1/8) emerges with increasing D. They also
demonstrate asymptotic mean-field behavior for
infinite-size two-dimensional tensor-product
(iPEPS) states with small tensors. The behaviors
should be generic at symmetry-breaking
transitions[2].
Po-Chung Chen (NTHU), Min-Fong Yang
(THU) and their student Chen-Yen Lai, based on a
recently developed algorithm based on the tensor
product states, investigate the magnetization
process of frustrated spin-1/2 spin-dimer models
on a square lattice. Clear evidence of a supersolid
phase over a finite regime of magnetic field is
observed. Besides, critical fields at various fieldinduced transitions are determined accurately.
The work also demonstrates clearly the potential
in applying the current tensor product state
formalism even to frustrated spin systems [3].
Ab inito studies of organic and strongly
correlated materials
Horng-Tay Jeng (AS) and his coworkers study
recently observed clear evidences in C60/Cu(111)
system that the charge transfer from Cu substrate
to the C60 monolayer is close to 3e/C60, which is
much larger than those in other systems. More
importantly the large charge transfer achieves
half-filling in the LUMO state of C60. This optimal
doping could affect the superconductivity in C60.
This large charge transfer is closely related to the
interface reconstruction that each C60 molecule
digs out 7 Cu atoms of the first Cu layer and then
sinks into the substrate by one Cu layer. To fit the
shape of C60 molecule, the reconstructed Cu cover
layer forms a "kagome-like" lattice [4].
Hung-Chung Hsueh (TKU) and collaborators,
within the framework of time-dependent densityfunctional theory (TDDFT), derive the dynamical
linear response of local-density approximation
plus U functional and benchmark it on NiO, a
prototypical Mott insulator. Formulated using
real-space Wannier functions, the computationally
inexpensive framework gives detailed insights
into the formation of tightly bound Frenkel
Highlights of Programs -›› 138
excitons with reasonable accuracy. Specifically, a
strong hybridization of multiple excitons is found
to significantly modify the exciton properties.
Furthermore, their study exposes a significant
generic limitation of adiabatic approximation in
TDDFT with hybrid functionals and in existing
Bethe-Salpeter-equation approaches, advocating
the necessity of strongly energy-dependent kernels
in future development [5].
Quantum transport in nanodevices and
spintronics
Chao-Cheng Kaun (AS) and coworkers study
the zero-bias t r a n s p o r t p r o p e r t i e s o f
alkanediisothiocyanate [-SCN-(CH2)n-NCS- , n=
4, 6, 8] molecules anchored to various quasi-onedimensional Au(111) electrodes by an ab initio
method within a standard two-probe methodology
based on the density-functional theory and the
nonequilibrium Green’s functions formalism.
They have shown that the high-/low-conductance
traces observed in STM break-junction
experiments on this molecular species can be
clearly related to the difference in the electronic
structures between the molecular contacts with
different geometric configurations of the nearinterface planes of the electrodes [6].
Guang-Yu Guo (NTU) and his collaborators,
by quantum Monte Carlo simulation of a realistic
multiorbital Anderson impurity model, study the
spin-orbit interaction (SOI) of an Fe impurity in
Au host metal. They show, for the first time, that
the SOI is strongly renormalized by the quantum
spin fluctuation. Based on this mechanism, they
can explain why the gigantic spin Hall effect in
Au with Fe impurities was observed in recent
experiments, while it is not visible in the
anomalous Hall effect. In addition, they show that
the SOI is strongly renormalized by the Coulomb
correlation U [7].
Bose-Einstein condensation in cold atoms
Wen-Chin Wu (NTNU) and his students,
Chou-Chun Huang and Chih-Hau Liu, have
recently investigated the behaviors of a rapidly
rotating Bose-Einstein condensate under extreme
elongation in a two-dimensional anisotropic
harmonic plus quartic trap are investigated. Due to
the quartic trap, the system remains stable at high
rotating velocity, and vortex lattices form even in
the absence of the repulsive s-wave interaction.
The interplay between the repulsive interaction
and the quartic trap potential can lead to rich
vortex lattice transition states.[8]
Several focus group members received
invitation for presentation at international
conferences. Ying-Jer Kao and Po-Chung Chen
were invited to International Workshop on DRMG
and other advances in NRG, Beijing, August 23 –
September 3, 2010, and QC10, Hsin-Chu, August
9-21, 2010. Guang-Yu Guo was invited to 2010
Topical Meeting on Advanced First-Principles
C a l c u l a t i o n s a n d M a n y - B o d y E ff e c t s i n
Correlated Electrons, Wako-Shi, Japan, August
3 1 - S e p t e m b e r 2 , 2 0 1 0 , 2 nd I n t e r n a t i o n a l
Symposium on Advanced Magnetic Materials and
Applications, Sendai, July 12-17, 2010, KITPC
Program on "Progress in Spintronics and
Graphene Research", Beijing, April 26-July 02,
2010, and Shanghai Workshop on Spintronics and
Low Dimensional Magnetism, Shanghai, June
15-18, 2010.
V. Selected Publications
[1] C
.-Y. Huang, and F.-L. Lin, Phys. Rev. A 81,
032304 (2010)
[2] C. Liu et al ., Phys. Rev. B 82, 060410 (2010)
[3] P. Chen, C.-Y. Lai, and M.-F. Yang, Phys. Rev.
B 81, 020409 (2010)
[4] W. W. Pai et al. , Phys. Rev. Lett. 104, 036103
(2010)
[5] C .-C. Lee, H. C. Hsueh, and W. Ku, Phys.
Rev. B 82, 081106 (2010)
[6] D. A. Luzhbin, and C. C. Kaun, Phys. Rev. B
81, 035424 (2010)
[7] B . Gu et al ., Phys. Rev. Lett. 105, 086401
(2010)
[8] C. C. Huang, C. H. Liu, and W. C. Wu, Phys.
Rev. A 81, 043605 (2010)
139 ‹‹- Highlights of Programs
Focus Group on Computational Materials Research
Coordinator: Ching Cheng (National Cheng Kung University; email: [email protected])
Committee members: Chun-Ming Chang (National Dong Hwa University), Feng-Chuan Chuang (National Sun Yat Sen University),
Guang-Yu Guo (National Chengchi University & National Taiwan University),
Hung-Chung Hsueh (Tamkang University), Chao-Cheng Kaun (Academia Sinica),
Ming-Hsien Lee (Tamkang University), Min-Hsiung Tsai (National Sun Yat Sen University),
Shiow-Fon Tsay (National Sun Yat Sen University)
I. Brief Description
he primary purpose of this program is to
enhance the domestic research capacity in
the computational material science based on the
first-principles quantum mechanical methods
through promoting interactions and collaborations
among local members as well as between local
members and international noted scholars, and
also through attracting outstanding young
researchers into this field.
of the activities related to the three frontiers, i.e.
HC Hsueh (TKU) for ExcS, CM Chang (NDHU)
for QMC and CC Kaun (AS) for QT, and another
six senior members as listed under the headline.
The missions of the committee are to allocate the
budget, to initiate research activities, to invite the
long-term and short-term visitors and to
recommend candidates (Ph.D. student or junior
scientist) or review applications for attending
international school, conference, or workshop
using the financial support of CMRFG.
II. Activities
The CMR focus group presently consists of
around 20 active faculty members, and around 10
postdoctor members. According to the interests
and the existing expertise of the members, we
have identified three frontiers to focus on, i.e.
calculations of the electronic excited states
(ExcS), quantum Monte Carlo methods (QMC),
and quantum transport (QT). Study-group
meetings initiated by the members involved in
these three topics become one of the main
backbone activities in promoting collaborations
among members as well as stimulating new ideas
and in-depth discussions.
The activities supported by CMRFG are listed
according to the following four categories; 1.
workshops for all members; 2. schools; 3. studygroup meetings; 4. peers interactions.
In order to train the young generation
members, the Ph.D. students, postdoctors and the
junior faculty members are encouraged to attend
international conferences, workshops and schools.
The provided fund of this year was found
insufficient. As the corresponding experience is
important for the junior researchers to broaden
their research scope, to interact with international
peers and noted scholars for inspired ideas, etc.,
we urge for a higher proportion of grant on this
category for young researchers in the coming year.
5/01-5/02 2010 : 2010
The school on First-principles Computational
Materials Research – Introductory Level
The focus group is run by a committee whose
members consists of three coordinators in charge
Highlights of Programs -›› 140
1. 7 /21-7/23 2010 : The 10th Workshop on FirstPrinciples Computational Materials Physics
9 /06-9/07 2010 : The 2nd Workshop of HighPerformance Computing on Nanoscale
Materials Research 2010
2. 4/10-4/11 2010 : 2010
The school on First-principles Computational
Materials Research – Introductory Level
7/05-7/09 2010 : 2010
The school on First-principles Computational
Materials Research – Advanced Level
3. 4/22 2010 : QMC study group meeting
4/23 2010 : Excited-state study group meeting
5 /07 2010 : Nanomaterials study group
meeting
6 /11 2010 : Nanomaterials study group
meeting
6/26 2010 : Excited-state study group meeting
8/04 2010 : QMC study group meeting
9/06 2010 : QMC study group meeting
9/24 2010 : Excited-state study group meeting
10/18 2010 : QMC study group meeting
4. 6 /25 2010: Presentation Contest of research
works by Ph.D. students and postdoctors
T h e 1 0 t h Wo r k s h o p o n F i r s t - Pr i n c i p l e s
Computational Materials Physics
his program-wide workshop was held on July
T
21-23, 2010 in the National Taitung University.
The aim of this workshop is to promote
interactions and collaborations among local
members. The CMRFG Committee also takes
this opportunity to learn about the general
interests of the community in order to organize
beneficial activities for the members in the
future. All participants, particularly PhD
students and postdoctors, are encouraged to
give a talk in this workshop.
T h e 2 n d Wo r k s h o p o f Hi g h - Pe r f o rm a n c e
Computing on Nanoscale Materials Research
his workshop is also a program-wide one as
T
most of the CMRFG members involve more or
less in the studies of nanoscale systems. The
emphasis is especially on the possible
combinations of the less CPU time-consuming
methods for larger systems with the accurate
first-principles methods to identify the crucial
mechanisms for the investigated issues. In this
year’s program, outstanding researchers from
the biology and chemistry related areas were
also invited in order to explore the possible
establishment of the interdisciplinary
collaborations.
Schools on First-Principles Computational
Materials Research
o help the newcomers in this field overcome
T
the hurdle in the beginning, both the
introductory-level spring school and the
advanced-level summer school on the firstprinciples computational materials research are
organized. The spring school, lectured by T. C.
Leung (CCU), is held in National Center for
High-Performance Computing. The summer,
also organized by T. C. Leung (CCU), is held
in NCTS (south). Both schools include the
practical hands-on sessions. The responses
from both students and non-specialist
researchers are much positive as there are more
than one hundred participants in the spring
school and more than fifty participants in the
summer school. About half of the expenses of
the summer school was provided by the
National Center for High Performance
Computing.
Excited State study group Meeting
wo study-group meetings are held for the last
T
six months. The discussions are mainly on the
applications of the present available methods,
i.e. the GW methods (VASP and Berkeley
GW), the Bethe-Salpeter methods (Berkeley
GW) and the time-dependent DFT, for the
excited-state properties of the bulk materials
and nanomaterials.
Quantum Monte Carlo study group Meeting
hree study-group meetings are held for the
T
last six months. The discussed topics cover 1)
implementation of Wannier functions into the
QMC methods 2) description of van der Waals
interactions for insulating and ionic bilayer
systems using QMC methods and their
comparisons to those using DFT methods with
different density functional schemes 3)
magnetic moments of small metallic clusters
using QMC methods.
Presentation Contest of research works by Ph.D.
students and postdoctors
ith the support by the National Cheng Kung
W
University, a joint activity of the CMR focus
group and the QIS focus group is held, i.e. the
Presentation Contest of research works by Ph.
D. students and postdoctors (http://www.ncts.
ncku.edu.tw/phys/cmr/100625/). The purpose
of this contest is to uplift the research quality
and motivation as well as to promote
interactions between the young researchers
through peers pressure and experience sharing.
III. Visitors and International
Collaborations
Examples of collaborations between CMRFG
members are listed as follows :
1. C M Chang (NDHU), C Cheng (NCKU) and
CM Wei (AS) on the applications of the
Quantum Monte Carlo methods.
141 ‹‹- Highlights of Programs
2. CY. Ren (NKNU) and C Cheng (NCKU) on the
magnetic frustrated systems.
3. B R Wu (CGU) and TC Leung (CCU) on the
electronic and optical properties of ribbon
under external electric field.
4. G Y Guo ( NTU), TC Leung (CCU) and HC
Hsueh (TKU) on the ab initio study for the
excited state of nanomaterials.
5. C C Kaun (AS) and TC Leung (CCU) on the
quantum transport in graphene nanoribbons and
in nanomachines.
International collaborations are listed as follows :
1. GY Guo (NTU) and N Nagaosa (Japan) on the
intrinsic spin Hall effect.
2. TC Leung (CCU) and CT Chan (HongKong) on
the optical properties of nanomaterials.
3. CM Wei (AS) and N Drummond (UK) on the
applications of the Quantum Monte Carlo
methods.
4. H C Hsueh (TKU) and SG Louie (USA) on
Excitonic properties calculation in
nanomaterials and defects.
5. H C Hsueh (TKU) and PH Zhang (USA) on
LDA+U+GW methods.
6. H C Hsueh (TKU) and Wei Ku (USA) on
Dynamic behaviour of strongly bounded
excitons.
IV. Highlights of Research Results
The community of the first-principles
electronic calculations for materials of this
country has flourished in the last few years. The
number of faculty members in the community
started by less than ten is now reaching more than
twenty. The members benefits extremely from the
interactions through the activities supported by the
NCTS. That the members share their individual
expertise within the community without
reservation also advances the community’s
strength as a whole. How these could lead
directly to the concrete research results, e.g.
journal publications or invited talks, is not as
straightforward to identify as might have been
implied in the performance evaluations required
by the funding agency. Not to mention that those
concrete research results also benefit vastly from
the personal NSC projects of the members as well
as, for some, the joint projects.
Highlights of Programs -›› 142
However, for the last six months, the majority
of the members have benefited enormously by the
mutual visits and the study-group meetings of the
focused topics supported by the CMRFG which
could not be acquired from other resources
otherwise. Continuous supports of these visits
and meetings with extensions through invitations
and potential collaborations with the international
leading experts are expected to lead to concrete
and eminent research results as the pursuit all the
time of the NCTS.
Excited State study group meetings
The group explores the applicability of the
established codes for the electronic excitation
using the GW, the Bethe-Salpeter and the timedependent DFT methods. Investigations are
applied to the covalent and ionic insulators as well
as the nanosystems. Extensions of these studies to
optical spectrum and absorption spectrum are also
developed.
Quantum Monte Carlo study-group meetings
To successfully apply the QMC methods to the
extended bulk systems, the generation of good
initial many-body wavefunctions is essential.
Theoretical discussions lead to the suggestion of
using the maximally localized Wannier functions
generated from the DFT calculations.
Implementation of this scheme into the presently
available QMC methods is in progress. In the
m e a n t i m e , t h e e ff e c t o f u s i n g d i ff e r e n t
approximations for the exchange and correlation
energy functional is explored and compared with
the results from QMC methods to advance the
understanding of the functional in various
materials, e.g. magnetic moments of magnetic
clusters, he stability of the surface absorption of
atoms and simple molecules, van der Waals
interaction for insulating and ionic bilayer.
Nanomaterials study-group meetings
The major issues of these meetings are to
identify the way in making use of the advantages
of the capable but coarser methods together with
the accurate first-principles methods to resolve
problems in considerably large-size systems.
V. Selected Publications
[1] " P o s s i b l e f e r r o m a g n e t i s m i n s - a n d
sp-electron element nanowires", Zhu ZZ,
Zheng JC, Guo GY, Chemical Physics Letters,
Volume: 472 Issue: 1-3 Pages: 99-103, (2009)
[2] " 13-atom metallic clusters studied by density
functional theory: Dependence on exchangecorrelation approximations and
pseudopotentials", J. P. Chou, H. Y. T. Chen,
C. R. Hsing, C. M. Chang, C. Cheng, and C.
M. Wei*, Phys. Rev. B 80, 165412 (2009)
[3] "Quantum Monte Carlo studies of covalent
and metallic clusters: Accuracy of density
functional approximations", Hsing, C. R., Wei
CM, Drummond ND, Needs RJ, Phys. Rev. B
79, 245401 (2009)
[4] " Kinetic Monte Carlo simulation of an
atomistic model for oxide island formation
and step pinning during etching by oxygen of
vicinal Si(100))", M.A. Albao, F.C. Chuang*,
and J.W. Evans, Thin Solid Films 517 1949–
1957 (2009)
[5] "A kinetic Monte Carlo study on the role of
defects and detachment in the formation and
growth of In chains on Si(100)", Marvin A
Albao, J W Evans and Feng-Chuan Chuang, J.
Phys.: Condens. Matter 21 (2009) 405002
[6] " Enhanced Spin Hall Effect by Resonant
Skew Scattering in the Orbital-Dependent
Kondo Effect", G. Y. Guo*, S. Maekawa and
N. Nagaosa, Phys. Rev. Lett. 102, 036401
(2009)
[7] " Electronic structure, linear, and nonlinear
optical responses in magnetoelectric
multiferroic material BiFeO3", S. Ju*, T.Y.
Cai, and G.Y. Guo*, J. Chem. Phys. 130,
214708 (2009)
[8] "Microscopic origin of light emission from
AlyGa1-y/GaN superlattices: Band profile
and active site", D.J. Cai, J.Y. Kang and G.Y.
Guo*, Phys. Rev. B 80, 045311 (2009)
[9] "Structural, electronic and magnetic properties
of V2O5-x: An ab initio study", Z.R. Xiao and
G.Y. Guo* , J. Chem. Phys. 130, 214704
(2009)
[10] " Tuning linear and nonlinear optical
properties of wurtzite GaN by c-axial stress",
D.J. Cai and G.Y. Guo*, J. Phys. D: Appl.
Phys. 42, 185107 (2009)
[11] "Half-metallic antiferromagnetic nature of
La2VTcO6 and La2VCuO6 from ab initio
calculations", Y. K. Wang*, P. H. Lee, and G.
Y. Guo, P Phys. Rev. B80, 224418 (2009)
[12] " S e c o n d - h a r m o n i c g e n e r a t i o n w i t h
magnetic-field controllability" , Sheng Ju,
Tian-Yi Cai, Chi-I Wei, and Guang-Yu Guo,
Optics Letters, Vol. 34, Issue 24, pp. 38603862 (2009)
[13] "Transverse force generated by an electric
field and transverse charge imbalance in
spin-orbit coupled systems", Tsung-Wei
Chen*, Hsiu-Chuan Hsu and Guang-Yu Guo,
Phys. Rev. B80, 165302 (2009)
[14] " Effects of a Modulated Electric Field on
The Optical Absorption Spectra in a SingleLayer Graphene", Y. H. Chiu, J. H. Ho, Y. H.
Ho, D. S. Chuu, and M. F. Lin*, Journal of
Nanoscience and Nanotechnology, Vol.9,
1–8 (2009)
[15] "Atomic and magnetic structures of (CuCl)
LaNb2O7 and (CuBr)LaNb2O7: Density
functional calculations", Chung-Yuan Ren
and Ching Cheng, Phys. Rev. B82 Issue: 2
Article Number: 024404 (2010)
[16] "Magnetism in two-dimensional BN1−xOx
and B1−xSixN: Polarized itinerant and local
electrons", R. F. Liu and C. Cheng, Phys.
Rev. B81, 104407 (2010)
[17] "Dynamical linear response of TDDFT with
LDA plus U functional: Strongly hybridized
Frenkel excitons in NiO", Lee CC, Hsueh
HC, Ku W, Phys. Rev. B82, 081106 R (2010)
[18] " Electronic structure of the Pb/Si(111)($sqrt{7} imessqrt{3}$) surface
reconstruction: a first-principles study",
Chia-Hsiu Hsu, F.C. Chuang*, Marvin A.
Albao, and Vincent Yeh, Phys. Rev. B 81
033407 (2010)
[19] "Magnetic moment and magnetic anisotropy
of linear and zigzag 4d and 5d transition
metal nanowires: First-principles
calculations", J. C. Tung and G. Y. Guo,
Phys. Rev. B81, 094422 (2010)
[20] "Magneto-optical selection rules in bilayer
Bernal graphene", Y. H. Ho, Y. H. Chiu*, D.
H. Lin, C. P. Chang and M. F. Lin*, ACS
Nano 4, 1465-1472 (2010)
[21] "Optical transitions between Landau levels:
AA bilayer graphene", Y. H. Ho, J. Y. Wu, R.
B. Chen, Y. H. Chiu, and M. F. Lin, Appl.
Phys. Lett. 97, 101905 (2010)
143 ‹‹- Highlights of Programs
Highlights of Programs
Particles and Fields
Focus Group on Cosmology and Particle Astrophysics
Coordinator: P isin Chen (National Taiwan University; email: [email protected], [email protected])
Summary
he NCTS Focus Group on Cosmology
and Particle Astrophysics (FGCPA) was
established in 2009 and this is the second year of
its operation. For the weekly activities, it has been
divided into three Local Chapters, in Taipei,
Hsinchu and Tainan, respectively, for seminars
and working group meetings. We further held
Joint Retreats with other NCTS Focus Groups. It
has now becoming a tradition that the Joint
Retreat with the FG on Gravitation is been held in
June and that with the FG on LHC in December
each year. We are proud to report that in this 2nd
y e a r t h e n u m b e r o f o u r N T C S a ff i l i a t e d /
acknowledged papers is 17 (as of Oct. 2010). This
is a dramatic increase from the first year.
I. Brief Description
The goals of FGCPA are as follows.
• O
rganization of summer or winter school to
offer short-term CPA courses to students and
researchers.
• I nvitation of short-term foreign visitors to
seminars or school lectures.
• E
ncouraging and promoting cooperation and/or
joint research projects among domestic research
groups.
• T
raining of graduate students and post-docs
through their attendance of international schools
Highlights of Programs -›› 144
or visits to foreign research institutes on the
longer-term basis.
• I nvitation of distinguished cosmologists and
particle astrophysicists for 3-month or longerterm visits.
• E
stablishing exchange programs with foreign
research organizations and conducting exchange
activities.
Coordinator: 陳丕燊/臺大(Pisin Chen/National
Taiwan University)
Core Members:
林貴林/交大(Guey-Lin Lin/National Chiao Tung
University),
李沃龍/師大(Wolung Lee/National Taiwan
Normal University),
耿朝強/清大(Geng,Chao-Qiang/National Tsing
Hua Univeristy),
劉國欽/淡江(Guo-Chin Liu/Tamkang Univeristy),
黃偉彥 /臺大(W-Y. Pauchy Hwang/National
Taiwan University),
吳建宏/中研院(Kin-Wang Ng/Academia Sinica),
陳泉宏/成大(Chuan-Hung Chen/National Cheng
Kung University)
In addition to the Core Members, there are
about 20 professors and researchers, 13 post-docs,
16 PhD students, 12 Master students participate in
this FG.
FGCPA is currently pursuing the following 5
research topics organized jointly with LeCosPA:
1. C
osmic Rays and Neutrinos: Guey-Lin Lin
(orgainzer)
2. B
aryon Asymmetry of the Universe (BAU):
Chao-Qiang Geng (organizer)
3. D
ark Energy Phenomenology: Je-An Gu
(organizer)
4. S
tring Cosmology: Debaprasad Maity
(organizer)
5. G
ravity and Structure Formation: Antonio
Enea Romano (organizer)
II. Activities
scientific culture and a broad spectrum of
expertise to our FG. Finally the newly arrived
member, Antonio Romano, has taken up a new
WG that focus on the connections between gravity
and quantum theories and observations.
Joint Retreats
Our FG has organized a Joint Retreats with the
FG on Gravitation co-organized by Chiang-Mai
Chen (NCU) for FG on Gravitation and Wolung
Lee for FGCPA in June 2010 at NCU. The Joint
Retreat with the FG on LHC this year is
co-organized by Tzu-Chiang Yuan (AS IoP) and
Guey-Lin Lin (NCTU) and will be held in early
December 2010 in Taipei.
Seminars
Workshops
Taipei Chapter: This seminar series is located at
NTU and organized by Pauchy
Hwang. It has been holding
s emin ar s ev er y w eek ex c e p t
during the Summer.
• 2nd International Workshop on
Hsinchu Chapter: This bi-weekly seminar series is
located at NTHU/NCTS. It is
organized jointly by ChaoQiang Geng (NTHU) and GueyLin Lin (NCTU).
Tainan Chapter: T his series is located at NCKU
and organized by Chuan-Hung
Chen. Since there are relatively
fewer FG members in southern
Taiwan, it was decided that this
series is held non-regularly and
jointly with the existing seminar
series in the Physics Department
of NCKU.
Working Groups
Among the 5 Working Groups, except that the
BAU WG organized by Chao-Qiang Geng is
conducted in Hsinchu, the rest are held in Taipei.
By far the WG on Dark Energy led by Je-An Gu
has been the most active and productive, with
non-stop weekly meetings throughout the year.
The WG on Cosmic Rays and Neutrinos led by
Guey-Lin Lin has also been very active, with a
paper already published. The new WG on String
Cosmology led by Debaprasad Maity has been
gaining momentum as well. As a new comer in
Taiwan, Debu has brought in a fresh different
" Dark Matter, Dark Energy and MatterAntimatter Asymmetry"
National Tsing Hua University, Nov. 5-6, 2010.
uilt upon the momentum gained from the
B
very successful 1st workshop held in 2009, this
2 nd workshop is again organized by ChaoQiang Geng of NTHU to further explore the
connections between dark energy and dark
matter with the matter-antimatter asymmetry.
Attendance of International Conferences
• A
PhD student, Chih-Ching Chen (NTU)
attended the international conference
ARENA in Europe in July, where he made an
oral presentation.
• O
ne post-doc, Chung-Lin Shan (NCKU),
attended the 11th International Conference
on Dark Matter (IDM 2010) in Montpelier,
France, July 26-30.
III. Visitors and International
Collaborations
With the very high degree of overlap between
FGCPA and LeCosPA in terms of research topics
and members, many international visitors and
collaborations are shared, with benefits to both.
Visitors
Dr. Mariam Lopez Bouhmadi of CENTRA
Institute in Lisbon, Portugal, visited NTU under
145 ‹‹- Highlights of Programs
the support of NCTS FG CPA, from April to June
2010. She is an expert on the Chaplygin gas
approach to dark energy and inflation.
International Collaborations
• C
ollaboration between Ron Adler (Stanford
University) and Pisin Chen (NTU) on quantum
gravitomagnetism. A paper has been published
in PRD.
• C
ollaboration between Pauchy Hwang (NTU)
and Sang Pyo Kim (Korea) on nonlinear QED
effects under Schwinger field and phase
transition in early universe.
• C
ollaboration between Pisin Chen and Johann
Rafelski (University of Arizona) and his
students on the quantum vacuum structure and
cosmology.
• C
ontinuing collaboration of Chao Qiang Geng
and Odintsov (Barcelonia, Spain) on particle
astrophysics, in particular on the ATIC/
PAMELA anomaly.
• P
isin Chen, Feng-Yin Chang (now post-doc at
LeCosPA) collaborate with Sergei Bulanov
(Advanced Photon Source, JAEA, Japan) on
plasma wakefield acceleration for the
production of ultra high energy cosmic rays.
VI. Highlights of Research Results
It is significant that members have been invited
f o r P l e n a r y Ta l k s a t m a j o r i n t e r n a t i o n a l
conferences in cosmology. Here we provide two
highlights.
• G
auge Theory of Gravity with de Sitter
Symmetry as a Solution to the Cosmological
Constant Problem and the Dark Energy Puzzle
he Coordinator of FGCPA, Pisin Chen, was a
T
Plenary Speaker at the prestigious International
Symposium to Celebrate Murray Gell-Mann’s
80th Birthday, held in Feb. 2010 in Singapore,
where 4 Nobel Laureates including Gell-Mann
himself, C. N. Yang, Gerard t’Hooft, Ken.
Wilson and numerous top physicists of the
world attended. This new solution to the CC
Problem was presented at this Symposium.
•
C osmological Constant Problem and its
Possible Solutions
Highlights of Programs -›› 146
isin Chen is a Plenary Speaker of one of the
P
w o r l d ’s l e a d i n g c o n f e r e n c e s e r i e s o n
cosmology, COMOS, which is held jointly
with the CosPA Conference series this year at
University of Tokyo, September 27- October 1,
2010. With close to 300 participants, this joint
conference is one of the largest gathering of
cosmologists and particle astrophysicists in the
world. Pisin Chen was invited to deliver one of
the key note talks at this meeting, an overview
of the cosmological constant problem and its
possible solutions, including the new solution
that he has recently proposed, where the theory
of general relativity is restructured such that
the cosmological constant becomes a constant
of integration in the new approach.
V. Publications
with NCTS as Affiliation or Acknowledgement
[1] C
. H. Chen, C. Q. Geng and D. V. Zhuridov,
"Resolving Fermi, PAMELA and ATIC
anomalies in split supersymmetry without R
parity", Eur. Phys. J. C 67, 479 (2010)
[arXiv:0905.0652 [hep-ph]]
[2] C . H. Chen and C. S. Kim, "Sommerfeld
Enhancement from Unparticle Exchange for
Dark Matter Annihilation", Phys. Lett. B 687,
232 (2010) [arXiv:0909.1878 [hep-ph]]
[3] Chia-Yu Hu, Chih-Ching Chen, Pisin Chen,
"A GPU-based Calculation Method for Near
Field Effects of Cherenkov Radiation Induced
by Ultra High Energy Cosmic Neutrinos",
arXiv: 1001.5341 [astro-ph.HE]
[4] S hu-Heng Shao and Pisin Chen, "StressEnergy Tensor Induced by Bulk Dirac Spinor
in Randall-Sundrum Model", Phys Rev D 81,
084036 (2010) [arXiv: 0910.3150 [hep-th]]
[5] S . Hoover et al. [ANITA Collaboration],
"Observation of Ultra-high-energy Cosmic
Rays with the ANITA Balloon-borne Radio
Interferometer", arXiv: 1005.0035 [astro-ph.
HE]
[6] Shu-Heng Shao and Pisin Chen, "A Naturally
Minute Qruantum Correction to the
Cosmological Constant Descended from the
Hierarchy", submitted to Phys. Rev. D [arXiv:
1005.1920 [hep-th]]
[7] D
ebaprasad Maity and Pisin Chen,
"Cosmological Behavior of a Parity and
Charge-Parity Violating Varying Alpha
Theory", submitted to Phys. Rev. D [arXiv:
1005.5104 [hep-th]]
[8] F eng-Yin Chang and Pisin Chen, "Landau
Damping of Baryon Structure Formation in
the Post-Reionization Epoch", arXiv:
1006.5777 [astro-ph.CO]
[9] C hien-I Chiang, Je-An Gu, Pisin Chen,
"Constraining the Detailed Balance Condition
in Horava Gravity with Cosmic Accelerating
Expansion", accepted for publication in J.
Cosmology and Astroparticle Physics [arXiv:
1007.0543 [astro-ph.CO]]
[10] K ung-Yi Su and Pisin Chen, "Solving the
Cusp-Core Problem with a Novel Scalar
Field Dark Matter", submitted to PRD
[arXiv: 1008.3717 [astro-ph.GA]]
[11] Y
u-Yen Chang, Rikon Chao, Wei-Hao Wang,
Pisin Chen, "Correlation between Global
Parameters of Galaxies", submitted to
Astrophysical Journal (ApJ) [arXiv:
1009.0030 [astro-ph.GA]]
[12] Kung-Yi Su and Pisin Chen, "Comments on
‘Remarks on the spherical scalar field halo in
galaxies", submitted to PRD [arXiv:
1009.0869 [astro-ph.GA]]
[13] F abio Scardigli, Christine Gruber, Pisin
Chen, "Black Hole Remnants in the Early
Universe", arXiv: 1009.0882 [gr-qc]
[14] Wei-Ting Lin, Je-An Gu, Pisin Chen,
"Cosmological and Solar-System Tests of
f(R) Modified Gravity", arXiv: 1009.3488
[astro-ph.CO]
147 ‹‹- Highlights of Programs
Focus Group on Gravitation
Coordinators: C
hiang-Mei Chen (National Central University, email: [email protected]),
James M. Nester (National Central University, email: [email protected])
I. Brief Description
he planned activities of the focus group
on Gravitation for the coming year
include the Shanghai International School/
Workshop on Gravitation at Shanghai Normal
University. This is the fifth year of the annual
international activities initiated by our FG and
organized in turn by Taiwan, Korea, China and
Japan. The other major activity this year is
IARD2010: the 7th Biennial Conference on
Classical and Quantum Relativistic Dynamics of
Particles and Fields at Dong Hwa University.
Moreover, we are planning to run several miniworkshops to enhance the interaction and
collaboration among the members of the FG. The
other highlighted effort is the student training
program. In addition to encouraging and
supporting students’ participation in international
conferences abroad we will continue the exchange
program with the Chinese Academy of Sciences at
Beijing.
Coordinators: Chiang-Mei Chen (National
Central University), James M. Nester (National
Central University)
M e m b e r s : H i n g - To n g C h o ( Ta m k a n g
University), Chung-Hsien Chou (National Cheng
Kung University), Da-Shin Lee (National Dong
Hwa University), Shih-Yuin Lin (National
Changhua University of Education), Chopin Soo
(National Cheng Kung University), I-Ching Yang
(National Taitung University), Hwei-Jang Yo
(National Cheng Kung University), Hoi-Lai Yu
(Academia Sinica)
II. Activities
We have organized IARD 2010: The 7 th
Biennial Conference on Classical and Quantum
Relativistic Dynamics of Particles and Fields from
30 May to 1 June at National Dong Hwa
Highlights of Programs -›› 148
University. The goal of the IARD meetings is to
bring together researchers from diverse fields
whose interests involve relativistic dynamics, both
classical and quantum. There were 41 participants
from the USA, Australia, Israel, Slovenia and
Taiwan. There were totally 17 talks presented at
the conference, which broadly covered relativistic
quantum information and thermodynamics,
classical and quantum field theory, and general
relativity applied to gravitation and cosmology.
Most of our members and students attended this
international conference.
There other main activity of our FG is the
annual school/workshop on gravitation. Supported
by our last year budget, we hosted the 2010
Taitung International School/Workshop on
Gravitation on 26–28 February at National
Taitung University. This regular activity gradually
is promoted to be a well recognized one for the
colleagues at Korea, Japan and China. Korea had
hosted this school in 2009 and the next school will
be at Shanghai. We have allocated our budget to
support, mainly around 10 students, to attend the
Shanghai school on 2011.
Moreover, we had a one-day joint meeting with
the FG on Cosmology and Particle Astrophysics.
Such joint meetings help to enhance the
interaction between the members in the two FGs.
III. Visitors and International
Collaborations
We have invited several visitors this year. Most
of them come to join our activities including Niall
O’ Murchadha, Maurice van Putten, William G.
Uuruh. In addition to giving lectures/talks at the
conferences, our visitors also arranged to visit
other institutes, such as Academia Sinica, National
Central University, and National Cheng Kung
University etc. to have more active scientific
exchange with local colleagues and to create the
possibility of further collaborations. Our members
have worked with their collaborators from
overseas for a long time. With the help of the FG
activities, the cooperation with colleagues from
Korea, Japan and China have been enhanced in
the past years.
IV. Highlights of Research Results
The research topics of our members mainly
include black hole physics, loop quantum gravity,
gravitational energy and cosmology. For black
hole physics, the main target is to understand
various aspects of classical and quantum black
hole physics, especially black hole
thermodynamics. An interesting new advance is
the holographic dual conformal field theory
description of the well-known charged and
rotating black holes.
In loop quantum gravity an alternative
expression for the length operator was
constructed. The operator is backgroundindependent, positive semi-definite, and well
-defined. The expression for the length can
moreover be derived both from a simple
geometrical perspective and also consistently from
regularization of the formal definition. The origin
of a common undetermined overall factor in each
derivation is also elucidated.
In the description of black holes, an
obstruction to the implementation of spatially flat
Painlevé–Gullstrand (PG) slicings was
demonstrated. Generalizations of PG slicings
which are not spatially flat but which remain
regular at the horizons are introduced. With these
generalized PG metrics, problematic contributions
to the imaginary part of the action in the Parikh–
Wilczek derivation of Hawking radiation due to
the obstruction can be avoided.
Regarding gravitational energy, we are trying
to improve the previous result by having a
systemic program for fixing the reference. Certain
expressions have been tested on some particular
solutions. In cosmology, new mechanisms for
cosmic acceleration were considered, including
the possibility of a torsion effect. This provides an
attractive alternative for the dark energy problem.
V. Selected Publications
NCTS is the affiliation
[1] " Quantum entanglement and entropy in
particle creation", Shih-Yuin Lin, ChungHsien Chou, B.L. Hu, Phys.Rev.D81:084018,
2010 [arXiv:1001.4922]
[2] "Digital origin of cosmic inflation", ChungHsien Chou & Hoi-Lai Yu, Mod.Phys.Lett.
A25:1483-1489, 2010
NCTS is acknowledged
[3] " Twofold Hidden Conformal Symmetries of
the Kerr-Newman Black Hole", Chiang-Mei
Chen, Ying-Ming Huang, Jia-Rui Sun, MingF a n Wu , S h o u - J y u n Z o u , P h y s . R e v.
D82:066004, 2010 [arXiv:1006.4097]
[4] " H i d d e n C o n f o r m a l S y m m e t r y o f t h e
Reissner-Nordstrom Black Holes", ChiangMei Chen & Jia-Rui Sun, JHEP 1008:034,
2010 [arXiv:1004.3963]
[5] " Optimal Choices of Reference for Quasilocal Energy", Chiang-Mei Chen, Jian-Liang
Liu, James M. Nester, Ming-Fan Wu, Phys.
Lett.A374:3599-3602, 2010 [arXiv:
0909.2754]
[6] " Black hole quasinormal modes using the
asymptotic iteration method", H.T. Cho, A.S.
Cornell, Jason Doukas, Wade Naylor, Class.
Q u a n t . G r a v. 2 7 : 1 5 5 0 0 4 , 2 0 1 0 [ a r X i v :
0912.2740]
[7] " New length operator for loop quantum
gravity", Yongge Ma, Chopin Soo, Jinsong
Ya n g , P h y s . R e v. D 8 1 : 1 2 4 0 2 6 , 2 0 1 0
[arXiv:1004. 1063]
[8] " A f f l e c k - D i n e B a r y o g e n e s i s , S p l i t
Supersymmetry, and Inflation", Yeo-Yie
Charng, Da-Shin Lee, Chung Ngoc Leung,
Kin-Wang Ng, Phys.Rev.D80:063519, 2009
[arXiv: 0802.1328]
[9] " Cosmological dynamics with propagating
Lorentz connection modes of spin zero", Hsin
Chen, Fei-Hung Ho, James M. Nester, ChihHung Wang, Hwei-Jang Yo, JCAP 0910:027,
2009 [arXiv:0908.3323]
[10] "Generalized Painleve-Gullstrand metrics",
Chun-Yu Lin & Chopin Soo, Phys.Lett.
B671:493-495, 2009 [arXiv:0810.2161]
149 ‹‹- Highlights of Programs
Focus Group on Lattice QCD and Hadron Physics
Coordinator: J iunn-Wei Chen (National Taiwan University; email: [email protected])
Committee members: Ting-Wai Chiu (National Taiwan University), Chung-Wen Kao (Chung-Yuan Christian University),
David Chi-Jen Lin (National Chiao-Tung University),Cheng-Pang Liu (National Dong-Hwa University)
I. Brief Description
n LQCD, the scientific goals are (a)
pursuing large-scale unquenched
calculations with optimal domain-wall quarks and
building up the capacity for large scale computing
with the new GPU technology (b) using lattice
gauge field theories to explore physics beyond
standard model, and (c) sharpening the nucleon
structure function calculations with flavor twisted
boundary conditions. In hadronic physics, the
goals are (a) understanding the impact of box
diagrams in radiative corrections to high precision
hadronic experiments (b) systematic time reversal
violation studies of nuclear and atomic systems.
Also, we would like to collaborate with string and
condensed matter theorists to study
superconductivity using AdS/CFT.
II. Activities
Lots of activities have been organized to
induce new ideas and collaborations:
Weekly/biweekly meetings: (a) Hadron physics
at NTU, video conferencing with NDHU and
NCKU (b) TWQCD collaboration at NTU (c)
Seminars Series at NDHU (biweekly), co-funded
by LQCDHP and Cosmology focus groups (d)
AdS/CFT, alternating between NTU and NTNU
(e) Joined LHC journal club with the LHC
initiative.
Schools and Workshops: (a) Miniworkshop on
Higgs-Yukawa on a Lattice, NTU, May 15, 2010.
(b) The 14 th Taiwan Nuclear Physics School
(Jan.17-22, 2011, NDHU) (c) Mini-workshop on
Beyond Standard Model Lattice Simulations
(Nov.).
Highlights of Programs -›› 150
III. Visitors and International
Collaborations
The list of visitors can be found from our focus
group website (http://phys.cts.ntu.edu.tw/en/) and
the international collaborations can be found from
o u r p u b l i c a t i o n l i s t s h o w n b e l o w. T h e
collaboration between TWQCD and JLQCD, a
well known collaboration formed by an elite
group of LQCD theorists, was formed since 2006.
This collaboration has worked out many important
results, with totally 9 papers published in PRL(2),
PRD(6), and PLB(1). C.J. David Lin has also
formed collaboration with an Oska U. group on
w a l k i n g Te c h n i c o l o r, a Ta i w a n - U K - U S
collaboration on b-baryon simulations, as well as
a Taiwan-Germany collaboration on HiggsYukawa system simulations. C.W. Kao has
collaborated with Vanderhaeghen in Mainz; C.P.
Liu and Fu-Jiun Jiang have just come back to
Taiwan within two years. Both have maintained
their collaborations with many institutes abroad.
Besides, formal postdoc alumni of our group,
Eiji Nakano and Seung-il Nam, have obtained
faculty jobs in Kochi Univ., Japan and Korea
Aerospace University, Korea, respectively. They
will also bring in new dimensions for our network.
It is also worth mentioning that Ting-Wai
Chiu’s former student/assistant Yao-Yuan Mao
was admitted to top universities such as Harvard,
Stanford, and Berkeley. He is now working on his
Ph.D in high energy theory at Stanford.
IV. Highlights of Research Results
A. Lattice QCD
Large-scale simulations of unquenched lattice
QCD with optimal domain-wall quarks:
The TWQCD collaboration led by Ting-Wai
Chiu has made a breakthrough in applying the
new GPU technology in large scale computing. It
is the first group around the world to use a GPU
cluster with sustained 36 Teraflops to perform
large-scale LQCD simulations, and is one of the
three groups (together with RBC/UKQCD,
JLQCD) that can perform large scale unquenched
simulations of lattice QCD with exact chiral
symmetry. TWQCD is now writing up papers on
the physical results of 2-flavor QCD, in particular,
the topological susceptibility, and the pion mass
and decay constant.
New strong interactions at TeV scale
In the last few years, Chi-Jen David Lin has
established collaboration with an Osaka
University group of led by Professor Tetsuya
Onogi on walking technicolour scenario. It is a
popular possibility for dynamical electroweak
symmetry breaking in which flavour-changing
neutral current processes are suppressed naturally
(dynamically). Presently, many researchers are
looking for candidate strongly-coupled gauge
theories for this scenario, which requires a quasi
non-trivial infrared fixed point. From our
simulations, we have evidence that SU(3) gauge
theory with 12 flavours develops such a fixed
point.
Higgs-Yukawa system on the lattice
Chi-Jen David Lin started collaboration with
the Zeuthen group led by Karl Jansen on lattice
simulations for the Higgs-Yukawa system. This is
also part of the recently approved Academic
Summit Project led by George W.-S. Hou at
National Taiwan University. The goal of this
programme is to study the spectrum and symmetry
breaking pattern in the presence of large Yukawa
couplings in the scalar-fermion system. In
addition to further the understanding of such field
theories in the strong coupling regime, this project
will have impact on particle physics
phenomenology of extra generations of fermions
beyond the Standard Model.
Physics related to the LHC-b program
Chi-Jen David Lin has collaboration with
colleagues in the US and the UK on the physics
related to the LHC-b program which would allow
us to probe the possible right-handed coupling
structure in physics beyond the Standard Model.
Presently, we already calculated the spectrum of
baryon containing one b quark and found it
consistent with experiment. Calculations for
relevant matrix elements are being performed.
Top Cited Articles
Five focus group articles were ranked "Top
Cited Articles" during 2009 in "hep-lat: The 400
most highly cited papers during 2009 in the heplat archive":
(a)Ranked 74: "Convergence of the chiral
expansion in two-flavor lattice QCD",
JLQCD and TWQCD Collaborations (J.
Noaki et al.), Phys. Rev. Lett.101:
202004, 2008
(b)Ranked 146: "Two-flavor lattice QCD
simulation in the epsilon-regime with
exact chiral symmetry", JLQCD
Collaboration (H. Fukaya et al.), Phys.
Rev. Lett. 98: 172001, 2007
(c)Ranked 170: "Two-flavor lattice QCD in
the epsilon-regime and chiral Random
Matrix Theory", Fukaya, Aoki, Chiu,
Hashimoto, Kaneko, Matsufuru, Noaki,
Ogawa, Onogi, Yamada, Phys. Rev. D76:
054503, 2007
(d)Ranked 211: "Topological susceptibility
in two-flavor lattice QCD with exact
chiral symmetry", JLQCD and TWQCD
Collaborations, Phys. Lett. B665: 294,
2008
(e)Ranked 241: "Universality of mixed
action extrapolation formulae", Chen,
O'Connell and Walker-Loud, JHEP
0904:090, 2009
B. 1
0 Year Review of the Solar Fusion Cross
Sections
Jiunn-Wei Chen has been a working group
leader at the Solar Fusion II Workshop (Solar
Fusion Cross Sections for the pp chain and CNO
cycle, January 2009, Seattle). The output of the
workshop is the review article "Solar fusion cross
sections II: the pp chain and CNO cycles" by E.G.
Adelberger, J.W. Chen, et al., arXiv:1004.2318
[nucl-ex] which was submitted to Rev. Mod. Phys.
The previous review (suggested by John Bahcall)
was published in 1998 with more than 250
citations so far.
151 ‹‹- Highlights of Programs
C. E
xtraction of the strangeness of the proton
In the last few years, Chung Wen Kao has
initiated a series of the extraction of the
strangeness of the proton to include state of the art
"box diagram" contributions. In their previous
work "The Two-Photon-Exchange and gamma
Z-Exchange Corrections to parity-Violating
Elastic Electron-Proton Scattering’’, Phys. Rev.
Lett .99:262001,2007, CWK and collaborators
challenged the widely used approximation of the
box diagrams by evaluating directly the twoboson exchange effects in a hadronic model and in
a partonic model. Their result shows that the twoboson exchange effects have complicated
dependence on the kinematics variables and
therefore should not be approximated as a
constant as previous analysis did. This discovery
has a wide impact on precision measurements
where theoretical radiative corrections are critical
for data interpretation. They have estimated this
effect on the extracted value of the proton
strangeness recently and are finishing up a state of
the art analysis on this quantity.
V. Selected Publications in 2010
[1] " Lambda(1520) photoproduciton off the
proton target with Regge contributions", S.
Nam and C.W. Kao, Phys. Rev. C 81, 055206
(2010)
[2] "On the two-boson exchange corrections to
parity-violating elastic electron-proton
scattering", H.Q. Zhou, C.W. Kao, S.N. Yang
Highlights of Programs -›› 152
and K. Nagata, Phys. Rev. C 81, 035208
(2010)
[3] "Towards A Holographic Model of D-Wave
Superconductors", J.W. Chen, Y.J. Kao, D.
Maity, W.Y. Wen, C.P. Yeh, Phys. Rev. D81,
106008 (2010)
[4] "Model analysis on thermal UV-cutoff effects
on the critical boundary in hot QCD", J.W.
Chen, K. Fukushima, H. Kohyama, K.
Ohnishi and U. Raha, Phys. Rev. D81, 071501
(2010)
[5] " P e a k - D i p - H u m p f r o m H o l o g r a p h i c
Superconductivity", J.W. Chen, Y.J. Kao, W.Y.
Wen, Phys. Rev. D82, 026007 (2010)
[6] "Space- and time-like electromagnetic pion
form factors in light-cone pQCD", J.W. Chen,
H. Kohyama, K. Ohnishi, U. Raha, Y.L. Shen,
Phys. Lett. B 693, 102 (2010)
[7] " Shear Viscosity of a Gluon Plasma in
Perturbative QCD", J.W. Chen, H. Dong, K.
Ohnishi, Q. Wang, Phys. Lett. B685, 277
(2010)
[8] "Chiral restoration at finite temperature with
meson loop corrections", S. Nam, C.W. Kao,
arXiv:1005.1689 [hep-ph]
[9] "Model analysis of thermal UV-cutoff effects
on the chiral critical surface at finite
temperature and chemical potential", J.W.
Chen, H. Kohyama, U. Raha,
arXiv:1009.4456 [hep-ph]
[10] "Space-and Time-like Electromagnetic Kaon
Form Factors", U. Raha, H. Kohyama,
e-Print: arXiv:1005.1673 [hep-ph]
Focus Group on Lattice QCD and Hadron Physics
Coordinator: J iunn-Wei Chen (National Taiwan University; email: [email protected])
Committee members: Ting-Wai Chiu (National Taiwan University), Chung-Wen Kao (Chung-Yuan Christian University),
David Chi-Jen Lin (National Chiao-Tung University),Cheng-Pang Liu (National Dong-Hwa University)
I. Brief Description
n LQCD, the scientific goals are (a)
p u r s u i n g l a rg e - s c a l e u n q u e n c h e d
calculations with optimal domain-wall quarks and
building up the capacity for large scale computing
with the new GPU technology (b) using lattice
gauge field theories to explore physics beyond
standard model, and (c) sharpening the nucleon
structure function calculations with flavor twisted
boundary conditions. In hadronic physics, the
goals are (a) understanding the impact of box
diagrams in radiative corrections to high precision
hadronic experiments (b) systematic time reversal
violation studies of nuclear and atomic systems.
Also, we would like to collaborate with string and
condensed matter theorists to study
superconductivity using AdS/CFT.
II. Activities
Lots of activities have been organized to
induce new ideas and collaborations:
Weekly/biweekly meetings: (a) Hadron physics
at NTU, video conferencing with NDHU and
NCKU (b) TWQCD collaboration at NTU (c)
Seminars Series at NDHU (biweekly), co-funded
by LQCDHP and Cosmology focus groups (d)
AdS/CFT, alternating between NTU and NTNU
(e) Joined LHC journal club with the LHC
initiative.
Schools and Workshops: (a) Miniworkshop on
Higgs-Yukawa on a Lattice, NTU, May 15, 2010.
(b) The 14 th Taiwan Nuclear Physics School
(Jan.17-22, 2011, NDHU) (c) Mini-workshop on
Beyond Standard Model Lattice Simulations
(Nov.).
III. Visitors and International
Collaborations
The list of visitors can be found from our focus
group website (http://phys.cts.ntu.edu.tw/en/) and
the international collaborations can be found from
o u r p u b l i c a t i o n l i s t s h o w n b e l o w. T h e
collaboration between TWQCD and JLQCD, a
well known collaboration formed by an elite
group of LQCD theorists, was formed since 2006.
This collaboration has worked out many important
results, with totally 9 papers published in PRL(2),
PRD(6), and PLB(1). C.J. David Lin has also
formed collaboration with an Oska U. group on
w a l k i n g Te c h n i c o l o r, a Ta i w a n - U K - U S
collaboration on b-baryon simulations, as well as
a Taiwan-Germany collaboration on HiggsYukawa system simulations. C.W. Kao has
collaborated with Vanderhaeghen in Mainz; C.P.
Liu and Fu-Jiun Jiang have just come back to
Taiwan within two years. Both have maintained
their collaborations with many institutes abroad.
Besides, formal postdoc alumni of our group,
Eiji Nakano and Seung-il Nam, have obtained
faculty jobs in Kochi Univ., Japan and Korea
Aerospace University, Korea, respectively. They
will also bring in new dimensions for our network.
It is also worth mentioning that Ting-Wai
Chiu’s former student/assistant Yao-Yuan Mao
was admitted to top universities such as Harvard,
Stanford, and Berkeley. He is now working on his
Ph.D in high energy theory at Stanford.
IV. Highlights of Research Results
A. Lattice QCD
Large-scale simulations of unquenched lattice
QCD with optimal domain-wall quarks:
The TWQCD collaboration led by Ting-Wai
153 ‹‹- Highlights of Programs
Chiu has made a breakthrough in applying the
new GPU technology in large scale computing. It
is the first group around the world to use a GPU
cluster with sustained 36 Teraflops to perform
large-scale LQCD simulations, and is one of the
three groups (together with RBC/UKQCD,
JLQCD) that can perform large scale unquenched
simulations of lattice QCD with exact chiral
symmetry. TWQCD is now writing up papers on
the physical results of 2-flavor QCD, in particular,
the topological susceptibility, and the pion mass
and decay constant.
New strong interactions at TeV scale
In the last few years, Chi-Jen David Lin has
established collaboration with an Osaka
University group of led by Professor Tetsuya
Onogi on walking technicolour scenario. It is a
popular possibility for dynamical electroweak
symmetry breaking in which flavour-changing
neutral current processes are suppressed naturally
(dynamically). Presently, many researchers are
looking for candidate strongly-coupled gauge
theories for this scenario, which requires a quasi
non-trivial infrared fixed point. From our
simulations, we have evidence that SU(3) gauge
theory with 12 flavours develops such a fixed
point.
Higgs-Yukawa system on the lattice
Chi-Jen David Lin started collaboration with
the Zeuthen group led by Karl Jansen on lattice
simulations for the Higgs-Yukawa system. This is
also part of the recently approved Academic
Summit Project led by George W.-S. Hou at
National Taiwan University. The goal of this
programme is to study the spectrum and symmetry
breaking pattern in the presence of large Yukawa
couplings in the scalar-fermion system. In
addition to further the understanding of such field
theories in the strong coupling regime, this project
will have impact on particle physics
phenomenology of extra generations of fermions
beyond the Standard Model.
Physics related to the LHC-b program
Chi-Jen David Lin has collaboration with
colleagues in the US and the UK on the physics
related to the LHC-b program which would allow
us to probe the possible right-handed coupling
structure in physics beyond the Standard Model.
Highlights of Programs -›› 154
Presently, we already calculated the spectrum of
baryon containing one b quark and found it
consistent with experiment. Calculations for
relevant matrix elements are being performed.
Top Cited Articles
Five focus group articles were ranked "Top
Cited Articles" during 2009 in "hep-lat: The 400
most highly cited papers during 2009 in the heplat archive":
(a)Ranked 74: "Convergence of the chiral
expansion in two-flavor lattice QCD",
JLQCD and TWQCD Collaborations (J.
Noaki et al.), Phys. Rev. Lett.101:
202004, 2008
(b)Ranked 146: "Two-flavor lattice QCD
simulation in the epsilon-regime with
exact chiral symmetry", JLQCD
Collaboration (H. Fukaya et al.), Phys.
Rev. Lett. 98: 172001, 2007
(c)Ranked 170: "Two-flavor lattice QCD in
the epsilon-regime and chiral Random
Matrix Theory", Fukaya, Aoki, Chiu,
Hashimoto, Kaneko, Matsufuru, Noaki,
Ogawa, Onogi, Yamada, Phys. Rev. D76:
054503, 2007
(d)Ranked 211: "Topological susceptibility
in two-flavor lattice QCD with exact
chiral symmetry", JLQCD and TWQCD
Collaborations, Phys. Lett. B665: 294,
2008
(e)Ranked 241: "Universality of mixed
action extrapolation formulae", Chen,
O'Connell and Walker-Loud, JHEP
0904:090, 2009
B. 1
0 Year Review of the Solar Fusion Cross
Sections
Jiunn-Wei Chen has been a working group
leader at the Solar Fusion II Workshop (Solar
Fusion Cross Sections for the pp chain and CNO
cycle, January 2009, Seattle). The output of the
workshop is the review article "Solar fusion cross
sections II: the pp chain and CNO cycles" by E.G.
Adelberger, J.W. Chen, et al., arXiv:1004.2318
[nucl-ex] which was submitted to Rev. Mod. Phys.
The previous review (suggested by John Bahcall)
was published in 1998 with more than 250
citations so far.
C. E
xtraction of the strangeness of the proton
In the last few years, Chung Wen Kao has
initiated a series of the extraction of the
strangeness of the proton to include state of the art
"box diagram" contributions. In their previous
work "The Two-Photon-Exchange and gamma
Z-Exchange Corrections to parity-Violating
Elastic Electron-Proton Scattering’’, Phys. Rev.
Lett .99:262001,2007, CWK and collaborators
challenged the widely used approximation of the
box diagrams by evaluating directly the twoboson exchange effects in a hadronic model and in
a partonic model. Their result shows that the twoboson exchange effects have complicated
dependence on the kinematics variables and
therefore should not be approximated as a
constant as previous analysis did. This discovery
has a wide impact on precision measurements
where theoretical radiative corrections are critical
for data interpretation. They have estimated this
effect on the extracted value of the proton
strangeness recently and are finishing up a state of
the art analysis on this quantity.
V. Selected Publications in 2010
[1] " Lambda(1520) photoproduciton off the
proton target with Regge contributions", S.
Nam and C.W. Kao, Phys. Rev. C 81, 055206
(2010)
[2] "On the two-boson exchange corrections to
parity-violating elastic electron-proton
scattering", H.Q. Zhou, C.W. Kao, S.N. Yang
and K. Nagata, Phys. Rev. C 81, 035208
(2010)
[3] " Towards A Holographic Model of D-Wave
Superconductors", J.W. Chen, Y.J. Kao, D.
Maity, W.Y. Wen, C.P. Yeh, Phys. Rev. D81,
106008 (2010)
[4] "Model analysis on thermal UV-cutoff effects
on the critical boundary in hot QCD", J.W.
Chen, K. Fukushima, H. Kohyama, K.
Ohnishi and U. Raha, Phys. Rev. D81, 071501
(2010)
[5] " P e a k - D i p - H u m p f r o m H o l o g r a p h i c
Superconductivity", J.W. Chen, Y.J. Kao, W.Y.
Wen, Phys. Rev. D82, 026007 (2010)
[6] "Space- and time-like electromagnetic pion
form factors in light-cone pQCD", J.W. Chen,
H. Kohyama, K. Ohnishi, U. Raha, Y.L. Shen,
Phys. Lett. B 693, 102 (2010)
[7] " Shear Viscosity of a Gluon Plasma in
Perturbative QCD", J.W. Chen, H. Dong, K.
Ohnishi, Q. Wang, Phys. Lett. B685, 277
(2010)
[8] "Chiral restoration at finite temperature with
meson loop corrections", S. Nam, C.W. Kao,
arXiv:1005.1689 [hep-ph]
[9] "Model analysis of thermal UV-cutoff effects
on the chiral critical surface at finite
temperature and chemical potential", J.W.
Chen, H. Kohyama, U. Raha,
arXiv:1009.4456 [hep-ph]
[10] "Space-and Time-like Electromagnetic Kaon
Form Factors", U. Raha, H. Kohyama,
e-Print: arXiv:1005.1673 [hep-ph]
155 ‹‹- Highlights of Programs
Focus Group on LHC Physics
Coordinator: Tzu-Chiang Yuan (Academic Sinica; email: [email protected])
I. Brief Description
t the end of 2009, the large hadron
collider (LHC) at CERN was getting fired
up and the first collisions at energy of 3.5 TeV per
beam took place on 30th March 2010. It marks the
beginning of the LHC era. LHC physics will
become one of the most important fields in
particle physics in the next couple of decades.
The LHC physics focus group, formed early
last year, consists of six coordinators from 5
different universities and one institute. Each year,
we have one chief coordinator who will take care
all the detailed matter for that year. This year’s
chief coordinator is Tzu-Chiang Yuan (AS) while
last year was Xiao-Gang He (NTU). Next 4 years’
chief coordinators will be consecutively ChengWei Chiang (NCU), Kwei-Chou Yang (CYCU),
Chuan-Hung Chen (NCKU) and Kingman Cheung
(NTHU).
The goals of this focus group are (1) to
establish an environment for our theoretical
physicists and our two LHC experimental groups
within Taiwan to work together; (2) to train young
postdocs and PhD students to get into this high
energy frontier effectively; and (3) to respond to
hot and important ideas in the field and make
contributions in a timely fashion. The following 4
directions have been singled out to focus on in our
proposal for the foreseeable future
• I nvestigation of Physics of Electroweak
Symmetry Breaking and Higgs Mechanism
• Physics Beyond the Standard Model
• Probing the Nature of Dark Matter
• Flavor Physics and CP Violation
Members of our group, listed at the end of the
NSC report, consist of 27 faculties (18 theorists
and 9 experimentalists), 20 postdocs and
numerous master and PhD students from these
group members.
Highlights of Programs -›› 156
II. Activities
This year our focus group has organized
various activities to benefit students, young
postdocs and ourselves. These activities are
sketched as follows:
• S
eminars or journal clubs are scheduled on a
weekly basis at NTU, NTHU, NCU and CYCU,
which are supported by the focus group. This
year as of to date we have a total of 73 seminars
delivered at these 4 universities. More seminars
and journal clubs will be organized for the rest
of the semester.
• T
wo mini-workshops have been organized so
far. The first one was held at AS, while the
second one at CYCU. We are planning a third
one as a joint retreat with cosmology focus
group to be held at NCKU near the end of the
year. The number of participants for each of the
mini-workshops was well over 40. This
indicates more people are getting involved with
our focus group. For each of these miniworkshops, we have invited experimentalists to
present their works and these are beneficial to
all of us.
• W
ithin each member group, there are numerous
group meetings among students, postdocs and
faculties. These kinds of meetings stimulate
ideas and discussions and have produced many
research papers, in particular for the two groups
led by our coordinators He at NTU and Cheung
at NTHU.
• T
he 23rd Spring School on Particle Physics was
held at NCKU this year and our focus group had
provided partial support for this meeting.
Excellent lecturers invited by our NCTS
director this year had made this spring school
the most successful one in the last five years, as
judged by the numbers of audiences at the last
day of the school and the many wonderful
questions asked by the students instead of by the
faculties this year.
• T
his year we have supported 3 persons to Korea
for the YongPyong APCTP international
conference and 3 persons to participate the
Summer Institute 2010 on Particle Physics
Phenomenology at Fuji-Yoshida, Japan.
III. V isitors and International
Collaborations
We have invited Professor Tony Zee and
professor Wai-Yee Keung to visit us using the
NCTS multi-year senior visitor program. Zee gave
lectures on Quantum Field Theory at NTU and
Keung presented mini-courses on LHC physics at
NTHU. Besides lecturing, they also collaborate
with some members of our group. In addition, we
have invited 8 short-term visitors to visit us,
presenting seminars and collaborating with us.
Some of these short-term visitors had initiated
new projects during their visits and even worked
together with our young postdocs.
Many of our coordinators and group members
have international collaborations. This is one of
our strengths as compared with other disciplines.
Our collaborators are distributed in many
countries all over the world including US, Canada,
China, Japan, Korea, Egypt, Morocco as well as
various countries in Europe.
The exchange program with KEK theory group
in Japan continues like last year. We have already
sent 3 young researchers to KEK this year and we
still have one more quota to be used for the year.
We are closely working with the topical
program this year at NCTS, and will contribute
0.5 millions to support this program with over 30
visitors from abroad.
IV. Highlights of Research Results
During the past year, our focus group has made
important progresses in the various directions
mentioned in our proposal. We now summarize
these works below:
• Dark Matter
In the years of 2009 and 2010 we have been
entertained by excitements from a number of
astronomical and astro-particle experiments, e.g.,
PAMELA, ATIC, FERMI-LAT, CDMS, XENON,
CoGeNT, DAMA/LIBRA etc. All the new results
give hints to the nature of the dark matter if
indeed interpreted as dark matter signals.
Cheung and Yuan used the new limit of the
direct detection of dark matter from CDMS to put
a new bound on the Higgs-dark-matter coupling,
which is then implied to an upper limit on the
Higgs boson invisible width. They found that the
invisible width to be of order of O(10) MeV at mH
= 120− 140 GeV, then the invisible decay of the
Higgs boson can be dominant. This will have
nontrivial efects on the search for the intermediate
Higgs boson at colliders.
In the scenario of SO(5) x U(1) gauge-Higgs
unification model based on the Randall-Sundrum
warped space, Higgs can be a dark matter
candidate due to the presence of the H parity.
Cheung and his collaborators studied the positron
and antiproton spectra from annihilation of the
gauge-Higgs dark matter in the halo in this model.
They found that the Higgs boson mass of 90 GeV
or more is inevitably ruled out by the observed
data at PAMELA. Cheung presented this work at
the SUSY 2010 conference at Bonn, Germany.
I n a r e c e n t w o r k , C h e u n g , Yu a n a n d
collaborators investigated a scenario that the top
quark is the only window to the dark matter
particle using the effective Lagrangian approach.
Requiring the dark matter satisfying the relic
density they obtain the size of the effective
interaction. They showed that the scenario can be
made consistent with the direct and indirect
detection experiments by adjusting the size of the
effective coupling. Finally, they calculated the
production cross section for t anti-t + χ anti-χ at
the LHC, which will give rise to an interesting
signature of a top-pair plus large missing energy.
He’s group at NTU concentrated on the
simplest dark model dubbed as the Darkon model,
the SM with an extra real scalar singlet. They
were the first group to study the implications of
this model for recent data from CDMSII, Xenon,
and CoGeNT experiments. They showed that
current direct search of dark matter can restrict the
parameter space, but allow dark matter mass from
as low as a few GeV to TeV region.
Chen and company had studied the
Sommerfeld enhancement effects from unparticle
to explain the positron excess of PAMELA.
Yang and Cheung have also explored their new
research directions of cosmology with the
postdocs.
157 ‹‹- Highlights of Programs
• Physics Beyond the Standard Model (SM)
Chen and his collaborators had also studied
nonuniversal Z' model in bs l+ l- decays in order to
explain the large CP asymmetry in B S system
observed at D0 and CDF.
In a recent work, Cheung with his NCTS
postdocs J. S. Lee, E. Senaha and PhD student T.
J. Hou include CP phases in the µ and other soft
parameters in the NMSSM. They study the
NMSSM Higgs sector with CP violation. They
calculate the whole mass spectrum of the Higgs
sector as well as the couplings to the vector gauge
bosons, which will dictate the production and
decay patterns of the Higgs bosons. They include
the important corrections to the Higgs spectrum,
the full one-loop corrections to the Higgs boson
masses, and logarithmically enhanced two-loop
corrections of order O(g S) and O(h 6) with the
renormalization group (RG) improvement and
minimization of the two-loop corrections. They
found that the RG-improved corrections have
significant reduction in the allowed parameter
space with respect to the LEP limits, the global
minimum condition, and the positivity of the
Higgs-mass squared. This work becomes Hou’s
PhD thesis.
• Collider Physics
Starting from last year, Chiang and his postdoc
A. Akeroyd studied intensively the Higgs Triplet
Model. Besides offering an attractive mechanism
to provide Majorana masses to neutrinos, such a
model has a very clean signature of like-sign
decays from the doubly charged Higgs boson.
Their work emphasized on the parameter space
where its leptonic decays are dominant and
studied the discovery reach at the LHC.
In the study of neutrinos seesaw models, He
and his team at NTU concentrated possible
experimental signatures at the LHC and also
LHeC (the e P mode). They showed that the LHC
could probe the seesaw scale as low as several
hundred GeV.
The forward-backward asymmetry in top quark
pair production was measured at the Tevatron.
While the Standard Model (SM) only predicts a
level as small as a few percent arising from the
higher-order QCD corrections, the measurement
by CDF, however, is as large as Afb = 0.19 ± 0.065
Highlights of Programs -›› 158
(stat) ± 0.024 (syst). If the asymmetry is true, it
will indicate the presence of new physics, because
within the SM the asymmetry is only up to about
5%. Cheung, Keung and Yuan proposed an extra
W-like boson W that only couples to the d and t
quarks so as to produce the forward-backward
asymmetry as reported by the CDF Collaboration,
while Chen and his collaborator use color triplet
and sextet scalars as well as unparticles to do the
job.
• Flavor Physics and CP Violation
While both were visitors at IPMU, He and
Frampton studied a new graphic representation of
KM matrix by proposing the unitarity boomerang
diagram to describe physics contained in the KM
matrix, and implications of recent data from BS –
anti-BS mixing on new physics beyond the SM.
In recent years, both B factories and CLEO-c
have collected ample data regarding charm
physics. It is therefore timely to study the new
data and analyze their implications. Recently,
Cheng (IoP, AS) and Chiang had just carried out
this analysis. They studied the two-body hadronic
charmed meson decays, including both the PP and
VP modes. They observed that significant SU(3)
breaking effects in some of singly-Cabibbosuppressed channels. In the case of VP modes,
they pointed out that the A P and AV amplitudes
cannot be completely determined based on
currently available data. Subsequently, they also
studied the hadronic D meson decays into a
pseudoscalar meson P and an even-parity meson
M, where M represents a scalar meson S, an axialvector meson A, or a tensor meson T. Current
measurements on the AP decays are insufficient
for a meaningful analysis while some TP data are
inconsistent with the others. In certain cases, the
W-annihilation diagrams indicated by the data are
unexpectedly large.
V. Publication
We have published 37 SCI papers in total with
16 using NCTS in their addresses and 21 having
NCTS in the acknowledgment. In addition, 16
preprints have been written and submitted to the
various journals for publications with 8 of them
used NCTS address and 8 acknowledged NCTS.
Detailed list of the publication can be found in the
complete report prepared for the NSC.
Focus Group on String Theory
Coordinator: F eng-Li Lin (National Taiwan Normal University, email: [email protected])
I. Brief Description
he string focus group is coordinated by
Feng-Li Lin (NTNU) this year. There are
currently 10 committee members, they are ChuanChung Chan (THU), Chiang-Mei Chen (NCU),
Wu-Yen Chuang (NTU), Kazuyuki Furuuchi
(NCTS), Choon-Lin Ho (TKU), Pei-Ming Ho
(NTU), Hsien-Chung Kao (NTNU), Jen-Chi Lee
(NCTU), Feng-Li Lin (NTNU), Yi Yang (NCTU).
Besides, we have about 14 postdocs: Hirotaka Irie
(NTU), Hiroshi Isono (NTU), Tomohisa Takimi
(NTU), Shoichi Kawamoto (NTNU), Wen-Yu
Wen (NTU), Chen-Pin Yeh (NTU), Dam Tomino
(NCTS), Chih-Wei Wang (NCTS), Takayuki
Hirayama (NCTS), Jia-Rui Sun (NCU), ShouHuang Dai (NTNU), Masafumi Ishihara
(NCTU),Yoshihiro Mitsuka (NCTU), Keijiro
Takahashi (NCTU); and about 6 PhD students. In
total, we have about 30 members in our group.
There are mainly 3 current research topics in
our group: (a) 3-algebra and BLG theory related,
(b) holographic principle and its applications, (c)
fundamental aspects of string theory.
II. Activities
The main activities of our group is the weekly
string seminar held at NTU and NCTS (Hsinchu),
for the details please see http://web.phys.ntu.edu.
tw/string/index.htm and http://phys.cts.nthu.edu.
tw/%7Estring/schedule.html. Besides, our focus
group also support the high energy physics
seminar at NTNU, for the details see http://www2.
phy.ntnu.edu.tw/~highenergy/seminars.html .
The string seminar usually takes 2-3 hours so
that participants can really learn from the speakers
by very stimulating Q&A interactions. Especially,
the young members get the chances to know
different topics and speakers from the seminar,
and sometimes they also talk about their own
works and get the responses to improve
furthermore. Moreover, occasionally members
also form the working group after someone’s
talks, and then organize the group meeting among
themselves. In the last year, there are quite fruitful
publications stimulated by the string seminars,
such as the collaboration between the NTU group
leaded by Pei-Ming Ho and NCTS group leaded
by Kazuyuki Furuuchi on the topics (a), between
Juinn-Wei Chen (NTU, Nuclear theory Focus
group) and Wen-Yu Wen (NTU) and Chen-Pin
Yeh (NTU) on topics (b), and between Hirotaka
Irie (NTU) and Chuan-Chung Chan (THU) on the
topics (c). Besides, Juinn-Wei Chen (NTU) and
Feng-Li Lin (NTNU) also co-organized the
bi-weekly AdS/CMT seminar for one semester to
stimulate the discussions on the topics.
We also organize the annual Taiwan String
Theory Workshop by inviting the foreign speakers
to lecture on the recent development of string
theory. In the past two years the workshop is
organized mainly by Feng-Li Lin (NTNU) and
Shoichi Kawamoto (NTNU) with the help from
Hsien-Chung Kao (NTNU), Chiang-Mei Chen
(NCU), Kazuyuki Furuuchi (NCTS), and ShouHuang Dai (NTNU), for the details see http://
www2.phy.ntnu.edu.tw/~highenergy/events.html.
This winter the 3rd annual workshop will be
organized by Chuan-Chung Chan (THU).
Each year we encourage our members to
participate the schools or workshops of string
theory held at the nearby institutes in the Asia,
such as India, Japan, Korea and China. Last year
we have supported some of our postdoc members
to participate the 4th Asian Winter School on
Strings, Particles and Cosmology at ICTS, India,
and the workshop on AdS/CMT at IPMU, Japan.
In the future, we hope NCTS can support our
focus group to co-organize the annual Asian
Wi n t e r S c h o o l o n S t r i n g s , P a r t i c l e s a n d
Cosmology, which is currently hosted in turn by
India, Japan, Korea and China.
159 ‹‹- Highlights of Programs
III. V isitors and International
Collaborations
In average we have more than one foreign
visitor per month supported by NCTS, for
example, during the last June and July we have 5
foreign visitors among the 9 talks (see http://web.
phys.ntu.edu.tw/string/activities0310.html). Most
of the visitors come from Japan, indicating that we
have strong connection with Japanese string
theory community. This is also reflected with the
fact that we have many Japanese postdocs, and
collaboration with Japanese string theorists.
Recently, for examples, Pei-Ming Ho (NTU) is
collaborating with Yutaka Matsuo (Tokyo U),
Kazuyuki Furuuchi (NCTS) with Kazumi
Okuyama (Shinshu U), Chiang-Mei Chen (NCU)
with Nobuyoshi Ohta (Kinki U), and Feng-Li Lin
(NTNU) with Shin Nakamura (Kyoto U). All the
foreign collaborators have been the visitors and
speakers of the string seminar.
IV. H
ighlights of Research Results
In the past year, we have quite fruitful
publications according to the above 3 categories
of the topics.
In (a) Pei-Ming Ho(NTU), Kazuyuki Furruchi
(NCTS), Tomohisa Takimi (NTU), Dan Tomino
(NCTS) and their students at NTU have continued
their works of previous year on the Lie 3-algebra
and the Nambu-Poisson formulation of M5-brane
theory. In total, they finished quite amount of
works on the subject, which make peculiar impact
in formulating the M5-brane theory stimulated by
BLG theory.
In (b) Chiang-Mei Chen (NCU), Jia-Rui Sun
(NCU) and their students at NCU published a
series of papers on AdS_2/CFT_1 for RN black
hole inspired by the recent Kerr/CFT works by
Strominger et al. Hsien-Chung Kao (NTNU) and
Wen-Yu Wen (NTU) also published a paper on the
subject.
Juinn-Wei Chen (NTU, Nuclear theory focus
group), Wen-Yu Wen (NTU) and Chen-Pin Yeh
(NTU) along with two other colleagues at NTU
had published two inspiring papers on holographic
superconductors, one of them is the original
proposal for the holographic d-wave
superconductors.
Highlights of Programs -›› 160
Feng-Li Lin (NTNU), Shoichi Kawamoto
(NTNU), Takayuki Hirayama (NCTS), Wu-Yen
Chuang (NTU), Chen-Pin Yeh (NTU) and ShouHuang Dai (NTNU) have altogether finished some
works on the Unruh effect and dynamical
instability of holographic QCD, and some
interesting construction of the holographic
anyons.
In (c) Jen-Chi Lee (NCTU), Yi Yang (NCTU)
and Keijiro Takahashi (NCTU) continue their
study on the Regge limit of the string scattering
amplitude. Chuan-Chung Chan (THU), Hirotaka
Irie (NTU) and their students at NTU had worked
on the multi-cut matrix model formulation of 3D
M theory.
Besides, Choon-Lin Ho (TKU), Hsien-Chung
Kao (NTNU) and Feng-Li Lin (NTNU) also
worked on some QFT or string theory-inspired
problems on condensed matters and quantum
information sciences.
Some of the above works have been presented
in some workshops and conferences, for
examples, Hirotaka Irie (NTU) and Shoichi
Kawamoto (NTNU) received best poster prizes in
KEK annual workshop in string theory, Kazuyuki
F u r r u c h i ( N C T S ) a ls o g a v e a t a l k a t t h a t
workshop. Juinn-Wei Chen (NTNU), HsienChung Kao (NTNU) and Feng-Li Lin (NTNU)
also presented their works at the workshop of
``HEP meets CMT" held at IPMU. In this
November, some of our members will attend the
AdS/QCD and AdS/CMT workshop at KITPC,
and present their works there.
V. Publications
Aug. 2009 ~ Sep. 2010, with acknowledgement to
NCTS
[1] "Absorption cross section in warped AdS(3)
black hole revisited", Hsien-Chung Kao, WenYu Wen, JHEP 0909:102, 2009
[2] " Pattens of High energy Massive String
Scatterings in the Regge regime", Sheng-Lan
Ko, Jen-Chi Lee, Yi Yang, JHEP 0906:028,
2009
[3] "String solitons in the M5-brane worldvolume
action with Nambu-Poisson structure and
Seiberg-Witten map", Kazuyuki Furuuchi,
Tomohisa Takimi, JHEP 0908:050, 2009
[4] " High Energy Symmetry of Bosonic Open
String Theory in the Light-like Linear Dilaton
Background", Chuan-Tsung Chan, Wei-Ming
Chen, JHEP 0911:081, 2009
[5] "Membrane scattering from Bagger-Lambert
theory", Takayuki Hirayama, Dan Tomino,
JHEP 0908:071, 2009
[6] "A No-Go Theorem for M5-brane Theory",
Chien-Ho Chen, Pei-Ming Ho, Tomohisa
Takimi, JHEP 1003:104, 2010
[7] "Lagrangian Formulations of Self-dual Gauge
Theories in Diverse Dimensions", Wei-Ming
Chen, Pei-Ming Ho, Nucl. Phys. B837:1-21,
2010
[8] "A UV completion of scalar field theory in
arbitrary even dimensions", Pei-Ming Ho,
Xue-Yan Lin, JHEP 1001:032, 2010
[9] "Holographic Anyons in the ABJM Theory",
Shoichi Kawamoto, Feng-Li Lin, JHEP
1002:059, 2010
[10] "Twofold Hidden Conformal Symmetries of
the Kerr-Newman Black Hole", Chiang-Mei
Chen, Ying-Ming Huang, Jia-Rui Sun, MingFan Wu, Shou-Jyun Zou, Phys.Rev.D82
066004, 2010
[11] " On Holographic Dual of the Dyonic
Reissner-Nordstrom Black Hole", ChiangMei Chen, Ying-Ming Huang, Jia-Rui Sun,
Ming-Fan Wu, Shou-Jyun Zou, Phys.Rev.
D82 066003, 2010
[12] " Hidden Conformal Symmetry of the
Reissner-Nordstrom Black Holes", ChiangMei Chen, Jia-Rui Sun, JHEP 1008:034,
2010
[13] " Holography of Charged Dilaton Black
Holes in General Dimensions", Chiang-Mei
Chen, Da-Wei Pang, JHEP 1006:093, 2010
[14] " Holographic Duals of Near-extremal
Reissner-Nordstrom Black Holes", ChiangMei Chen, Ying-Ming Huang, Shou-Jyun
Zou, JHEP 1003:123, 2010
[15] " Global solutions for higher-dimensional
stretched small black holes", Chiang-Mei
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
Chen, Dmitri V. Gal'tsov, Nobuyoshi Ohta,
Dmitry G. Orlov Phys.Rev.D81 024002,
2010 [arXiv:0910.3488]
"The RN/CFT Correspondence Revisited",
Chiang-Mei Chen, Jia-Rui Sun, Shou-Jyun
Zou, JHEP 1001 057, 2010
"Holographic Duals of Black Holes in Fivedimensional Minimal Supergravity", ChiangMei Chen, John E. Wang, Class. Quant.
Grav. 27:075004, 2010
" Regge Closed String Scattering and its
Implication on Fixed angle Closed String
Scattering", Jen-Chi Lee, Yi Yang, Phys.
Lett. B687:84-88, 2010
"Non-Linearly Extended Self-Dual Relations
From The Nambu -Bracket Description Of
M5-Brane In A Constant C-Field
Background", Kazuyuki Furuuchi, JHEP
1003:127, 2010
"Fractional-Superstring Amplitudes, MultiCut Matrix Models and Non-Critical M
Theory", Chuan-Tsung Chan, Hirotaka Irie,
Chi-Hsien Yeh, Nucl.Phys.B838 75-118,
2010
"Macroscopic loop amplitudes in the multicut two-matrix models", Chuan-Tsung Chan,
Hirotaka Irie, Sheng-Yu Darren Shih, ChiHsien Yeh, Nucl.Phys.B828 536-580, 2010
"Towards A Holographic Model of D-Wave
Superconductors", Jiunn-Wei Chen, Ying-Jer
Kao, Debaprasad Maity, Wen-Yu Wen,
Chen-Pin Yeh, Phys.Rev.D81 106008, 2010
" P e a k - D i p - H u m p f r o m H o l o g r a p h i c
Superconductivity", Jiunn-Wei Chen, YingJer Kao, Wen-Yu Wen, Phys.Rev.D82
026007, 2010
" Q u a r k M a s s D e p e n d e n c e o f H a d r o n
Spectrum in Holographic QCD", Koji
Hashimoto, Takayuki Hirayama, Deog Ki
Hong, Phys.Rev.D81 045016, 2010
" Classical Solutions of a Torsion Gravity
from Large N Matrix Model", Hiroshi Isono,
Dan Tomino, Phys.Rev.D81 084049, 2010
161 ‹‹- Highlights of Programs
Highlights of Programs
Interdisciplinary Fields
Focus Group on Atomic, Molecular and Optical Physics
Coordinator: D
aw-Wei Wang (National Tsing Hua University; email: [email protected])
I. Brief Description
MO focus group is to coordinate the
researchers in AMO-related community in
Taiwan to work together in several frontier
directions.
Coordinator: Daw-Wei Wang (National Tsing
Hua University)
Committee members: Wen-Chin Wu (NTNU),
Shih-Chuan Gou (NCUE), Chung-Hou Cheng
(NCTU), Jiang-Nan Liu (FCU), Yi-Wei Liu
(NTHU), Ying-Cheng Chen (IAMS), Te-Kuei
Fang (FCU), Wei-Chi Liu (NTNU)
Group size: Active faculty members are about 20,
including experimentalists.
Goal: 1)To encourage more cooperation between
faculty in this community, especially cooperation
between different institutes and between theorists
a n d e x p e r i m e n t a l i s t s . 2 ) To a t t r a c t m o r e
researchers/ students to join related research and
to form a stable research environment. 3) To
enhance the research quality by actively
cooperating with international frontier researchers.
Research direction: (1) Strongly correlated
effects in cold atoms/molecules, (2) Dynamical
properties of weakly interacting Bose gases, (3)
Atomic structure theory and spectroscopy. Besides
these three major subjects, we also partially
support researches in high intensity laser, cold
atom experiments, and quantum optics etc.
Highlights of Programs -›› 162
II. Activities
International Workshop: In the June 2010, we
held an International Workshop on Ultracold
Atoms and Molecules in Institute of Atomic and
Molecular Sciences, organized by Daw-Wei Wang
and Ying-Chen Chen. We invited several worldleading-edge theorists and experimental groups to
introduce their work on ultracold atoms and
molecules. This includes Prof. Gora Shylapnikov
(LTPMS, Orsay), Miguel A. Cazalilla (DICP,
Spain), John Barry (Yale U.), Mark Eng Hiang
Yeo (JILA) etc.
Before the workshop, we had a satellite
meeting for our local researchers to present their
works in front of our invited speakers and got
valuable feedback. For example, Prof. ChungChun Hou (NCTU) had fruitful discussions
with one of the speakers--Miguel Cazalilla on
the quantum phases of the Bose-Fermi mixture
in 2D optical lattices. They have developed a
feasible theoretical approach to address this issue,
and will continue the collaboration along this line.
Group-participation of ICAP 2010: In July
2010, several active members of AMO focus
group (5 professors, 1 postdoc, and 6 students)
participate the most important cold atom
conference, ICAP 2010, in Austria. Our focus
group provided financial support to some of them.
We also got deep connection with Prof. G.
Shlyapnikov(LTPMS) as well as Prof. E. Demler
(Harvard) etc. For example, during that
conference, Prof. G. Shlyapnikov invited Prof. Ite
Yu and Daw-Wei Wang to give lectures in ICTP
conference in 2011. Daw-Wei Wang also had
several projects with Demler’s research group in
Harvard University. Several of us were invited to
participate the cross-strait conference in Beijing,
China. Prof. Po-Chung Chen also invited an
expert on quantum Monte Carlo calculation to
visit Taiwan in this year.
AMO Summer School: In Sep. 2010, we held
the 7th AMO summer school in National ChengKong University, organized by Prof. Chin-Chung
Tsai. This year, besides of active researchers in the
AMO field, we also invited several speakers from
the AMO-related industry, international speaker,
and postdocs from US school to broaden the
knowledge horizon of students. From students’
feedback, we know that this format worked very
well, and will attract more perspective students to
join this community in the future.
III. V isitors and International
Collaborations
Visitors
In the previous year, we invited Prof. G.
Shylapnikov (LTPMS), E. Yeo (JILA), John Barry
(Yale), Miguel Cazalilla (DIPS, Spain), to stay
NCTS/NTHU for a few days before or after the
International Workshop of ultracold atoms/
molecules. They also discuss with local
researchers for their work.
We also invited Prof. Makoto Tsubota from
Osaka City University, Japan (Nov 2009). Prof.
Tsubota has pioneered in the studies of quantum
turbulence in trapped BEC. Prof. Shi-Chuan Kuo
(NCUE) have been inspired via discussions with
Prof. Tsubota on the hydrodynamical properties of
trapped BECs, in particular, the problem of vortex
reconnection in such systems. Besides, we also
invited Prof. Blair Blakie from University of
Otago, New Zealand (May 2010), to develop a
long term collaboration with on the subject of
SPGPE (stochastic projected Gross-Pitaevskii
equation). On this basis, SC Gou will be invited to
visit Otago's group in next January. We are
looking forward to have graduate students
exchanged in the upcoming years. As a regular short-term visitor to NCTS each
year, Professor Tu-nan Chang (USC) continually
leads the joint experimental and theoretical team
(including T. S. Yih, C. C. Chu, and J. I. Lo at the
National Central University, H. S. Fung and Y. Y.
Lee at the NSRRC, and T. K. Fang and C. H.
Chen at Fujen University) on atomic structure
study. Recent include i) spin-mixed doubly
excited resonances in Ca and Sr spectra, ii)
column density and temperature effects on narrow
resonance structures in atomic photoionization/
photoabsorption, and iii) photoionization of Ca in
static electric field. In addition, they have recently
started theoretical works on the atomic transitions
in plasma environment and the multi-photon
processes with soft x-ray lasers.
International Cooperation
D . - W. Wa n g ( N T H U ) r e c e n t l y h a s
collaboration with Prof. E. Demler (Harvard) on
dipolar atoms, with G. Shyalpnikov (LPTMS) on
supersoilid phase in polar molecules, with Cheng
Chin and Pingnan Ma on the first comparison
between QMC and the in situ experiments near
quantum phase transition, and with prof. S. Das
Sarma (UMCP) on fermionic polar molecules. In
fact, Prof. Wang has overseen several postdocs in
Harvard. U and U. of Maryland to study exotic
phases of polar molecules. Prof. Chung-Hou
Chung (NCTU) has a collaboration with Yong
Baek Kim (U. Toronto) on the supersolid phase in
frustrated system and with Prof. M. Cazalilla on
Bose-Fermi mixture. Prof. T.-K, Fang (FJU)
collaborates with Prof. T.-N. Chang (USC) in
atomic structure theory. Prof. Shih-Chuan Gou
collaborates with Prof. Makoto Tsubota (Osaka
City U., Japan) and Blair Blakie (U. Otago, New
Zealand) on quantum turbulence and quantum
dynamics in cold atoms.
IV. Highlights of Research Results
Exotic quantum phases of cold atoms and polar
molecules
(1) Prof. D.-W. Wang (NTHU) and his group
develop the first theoretical prediction about the
ferro-electricity of polar molecules in a trapped
system [1]. (2) Prof. Wang worked with Prof. S.
Das Sarma and his postdoc in U. of Maryland on
the first complete quantum phase diagram for
Bose-Fermi mixture of dipolar atoms/molecules in
1D optical lattice [2]. The result shows a BoseFermi solid in strongly interacting regime and has
a nontrivial quantum melting. (3) Prof. W.-C. Wu
(NTNU) and D.-W. Wang (NTHU) have a
collaboration on the condensate wave function
and elementary excitations of bosonic polar
molecules in a harmonic trap, treating the
scattering amplitude beyond the standard first
Born approximation [3].
163 ‹‹- Highlights of Programs
Quantum dynamics of Bose-Einstein Condensate
(1) Prof. D.-W. Wang (NTHU) and R.-K. Lee
(NTHU) developed a powerful numerical method
to study the quantum dynamics of a BEC
including quantum fluctuations. They applied this
method to give the first study in the world on the
expansion dynamics for atoms released from the
optical lattice [4]. (2) W.-C. Wu (NTNU) and his
group have recently investigated the behaviors of
a rapidly rotating BEC under extreme elongation
in a two-dimensional anisotropic harmonic plus
quartic trap [5]. When g is present, the interplay
between g and the quartic trap potential can lead
to rich vortex lattice transition states as a function
of Ω, to which vortex lattices vanish eventually at
some higher Ω. (3) Prof. S.-C. Guo have devoted
to investigate the non-equilibrium dynamics of a
fast-rotating BEC in the rapid-quenched limit by
s o l v i n g t h e S P G P E . R e c e n t l y, t h e y h a v e
successfully applied the formalism of SPGPE to
study the magnetic properties of a rotating spinor
BEC with F=1 [6]. Their results have been
presented in several international workshops and
conferences.
Manipulation of coherent atom waves in optical
lattice
Prof. S.-T. Wu (NCCU) and D.-J. Han (NCCU)
study the dynamics of Bose-Einstein condensates
in accelerated two-dimensional optical square
lattices by numerically solving the GrossPitaevskii equation [7]. Aside from conceiving
realization of a pulsed two-dimensional atom
laser, they demonstrate that Landau-Zener
tunnelling and Bragg reflection of the condensate
inside the optical lattice can provide means for
manipulation of coherent atom waves. This result
shall be valuable for beam splitting in atom
interferometry and possibly also for quantum
information sciences.
Atomic structure and spectroscopy
A joint experimental and theoretical
investigation on column density and temperature
effects on photoionization and photoabsorption
spectra has led to new physical insight in peak
cross sections of the narrow resonances. Prof.
T.-K. Fang (FJU) and T.-N. Chang (USC) have
investigated in detail the effect on the resonance
structure due to the Doppler effect at finite
temperature. Another joint theoretical and
Highlights of Programs -›› 164
experimental work on the effect of spin-dependent
interaction on doubly excited spectra of Ca and Sr
across several ionization thresholds has identified
the inversion of energy levels between members
of a number of multiplets. This project has clearly
demonstrated the breakdown of the LS coupling
for resonances series with higher orbital angular
momenta. [8]
Developing numerical method for strongly
interacting bosons
D.-W. Wang (NTHU) and P.-C. Chen (NTHU)
sent students to Hong Kong U. to learn worm
algorithm of quantum Monte Carlo calculation,
the world’s most efficient code in large size
simulation. Their ab inito results can be used to
directly compare to the in situ experimental data
in Cheng Chin’s group (U. Chicago), showing the
world’s first quantitative comparison between
theory and experiment in quantum many-body
physics of cold atoms (paper has been sent to
Phys. Rev. Lett.). They are also the first group to
numerically study the quantum criticality near the
SF-MI transition.
V. Selected Publications
[1] C.-H. Lin, Y.-T. Hsu, H. Lee, and D.-W. Wang,
Phys. Rev. A 81, 031601(R) (2010)
[2] Bin Wang, Daw-Wei Wang, and S. Das Sarma,
Phys. Rev. A 82, 021602(R) (2010)
[3] C .-C. Huang, D.-W. Wang, and W. C. Wu,
Phys. Rev. A 81, 043629 (2010)
[4] Shiang Fang, Ray-Kuang Lee, and Daw-Wei
Wang, Phys. Rev. A 82, 031601(R) (2010)
[5] C.-C. Huang, C.H. Liu, and W. C. Wu, Phys.
Rev. A 81, 043605 (2010)
[6] T.-L. Horng, S.-C. Gou, T.-C. Lin, G.A. El, A.
Itin, and A.M. Kamchatnov, Phys. Rev. A 79,
053619 (2009); T.-L. Horng, C.-H. Hsueh,
S.-W. Su, Y.-M. Kao, and S.-C. Gou, Phys.
Rev. A 80, 023618 (2009)
[7] Wei-Chih Ting, Dian-Jiun Han, and Shin-Tza
Wu, New J. Phys. 12, 083059 (2010)
[8] J. H. Chen, T. K. Fang, C. C. Chu, T. S. Yih,
and T. N. Chang, Phys. Rev. A 80, 042509
(2009); J. I. Lo, T. S. Yih, Y. X. Luo, H. S.
Fung, Y. Y. Lee, and T. N. Chang, Phys. Rev. A
82, 012504 (2010)
Focus Group on Plasma Science
A. Laser/Maser Plasma Science
Coordinator: Shih-Hung
Chen (National Central University; email: [email protected])
I. Brief Description
he Laser/Maser Plasma Science program
is coordinated by Prof. Shih-Hung Chen
from National Central University. The program
provides a platform to integrate the research and
training activities of two groups, whose research
topics are the laser plasma physics and relativistic
vacuum electronics, respectively.
The first group, High-Field Physics and
Ultrafast Technology Laboratory at the Institute of
Atomic and Molecular Sciences, Academia Sinica,
constructed a high-quality 10-terawatt laser
system in 2004 and complete the construction of a
100-TW laser at National Central University by
the end of 2007. They utilized the laser facility to
conduct pioneering experiments in high-field
science.
The second group, High Frequency
Electromagnetic Laboratory at National Tsing Hua
University, has been devoted to the study of the
Electron Cyclotron Maser during the past twenty
years. They have taken the lead in the
international microwave/plasma community by
addressing these physics groundwork that have
been resulted in great advancements. The recent
investigations conducted in NTHU group also
awake a general interest in a relatively dormant
subject, gyrotron backward wave oscillator (gyroBWO).
Facilitated by these two groups, a "theoretical
study and simulation group", which has intensive
collaborations with the two groups, was formed at
National Central University. The new group
comprises participants from several research
institutions and universities. The operations of this
group are concordant with the goals and vision of
the NCTS program. Over the past few years, the
group has built capacities of the theoretical
analysis and the large-scale simulation for the
study of the laser/maser plasma science. The
forming of the topical program can provide a
more solid foundation and operation mechanism
for the theoretical and simulation group.
These three groups represent the local
community of laser/maser plasma science, and
they have gained lots of scientific achievements of
the international visibility. The proposed laser/
maser plasma science topical program intends to
establish a platform to serve the community and to
couple all sub-areas through common interest in
simulation, theory and education, and to interact
with experimentalists under the support of NCTS.
The key members include Prof. Kwo Ray Chu
(National Tsing Hua University), Prof. Yu-Ren
Linliu (National Central University), Prof.
Jyhpyng Wang (IAMS, Academia Sinica), Prof.
Gin-Yih Tsaur (Tunghai University), Ling-Hsiao
Lyu (National Central University), Weicheng
Huang (National Center for High-performance
Computing) and Prof. You- Hsien Shiau (National
Chengchi University) et al. There are 8
researchers/professors, 3 post doctors, 5 Ph.D.
students and 14 Master students joined in the
program.
The laser/maser plasma physics is the area to
study the highly nonlinear and highly relativistic
system. The coupling between the electromagnetic
field and various degrees of freedom of plasma is
highly nonlinear, hence parametric instabilities are
ubiquitous. Whether the effects are useful or
detrimental, it is essential to control these
instabilities. The onset of instability can usually be
studied analytically by perturbation techniques,
but the saturation or stabilization of these effects
may not. Computer simulation can serve as
numerical experiments to explore the control
methods with low cost and great flexibility in the
parameter space. The nonlinear theory is an
essential guideline and acts as the complementary
tool for the study of these problems. In the
program, the focused research topics includes the
laser wakefield electron accelerators, laser-based
proton accelerators, radiation sources based on the
laser-plasma interactions and electron cyclotron
resonance and plasma-based nonlinear optics et al .
165 ‹‹- Highlights of Programs
II. Activities
One of the major activities of the topical
program is the training and education of students
and junior researchers. During the summer
vacation, we invited Prof. Ling-Hsiao Lyu to give
a workshop on introducing the fluid simulation on
the study of laser-produced plasmas. The courses
demonstrate the fundamental concept of the fluid
model and the numerical algorithm for solving the
fluid equations. The integration of the fluid
simulation and the radiation model will be applied
on the study of the EUV and X-ray light sources
induced by laser-produced plasmas. Recently, we
started a new collaboration with Prof. Sheng-Lung
Huang from National Taiwan University for the
development of the EUV light sources based on
the laser-solid interactions, and the proposal has
been approved and funded by Taiwan National
Science and Technology Program for Nanoscience
and Nanotechnology since Aug. 2010.
The Asia Summer School and Symposium
(ASS&S) on Laser-Plasma Acceleration and
Radiation is a supplementary training activity to
the topical program. The topical program
supported two graduate students to attend the 5th
Asia Summer School and Symposium (http://
www.opticsjournal.net/ass2010.htm), Shanghai
Institute of Optics and Fine Mechanics (SIOM),
CAS, Shanghai, China from Aug. 16 through 20,
2010. The purpose of the school is to promote the
research activities in the field of laser-plasma
acceleration and radiation and provide an
excellent opportunity for graduate students, postdocs and fresh researchers in Asian countries to
learn and communicate.
In order to complement the local plasma
physics courses, Prof. Liu Chen (University of
California, Irvine, USA) still come to visit us and
to give seminars on nonlinear plasma physics
during Apr. 4-10, and he will visit us again during
Nov. 5-12. The seminars include the research
topics we are studying now, e.g. nonlinear modemode coupling, parametric interactions, and threewave interactions et al. The nonlinear analysis can
provide more precise guideline for the computer
simulation and experimental designs, as compared
to the linear theory. Therefore, we are organizing a
summer school on theoretical analysis and
computer simulation of plasma science for
delivering complete and integrated courses on
Highlights of Programs -›› 166
theory and simulation for the study of laser/maser
plasma science. The summer school is scheduled
to be held during the summer of 2011.
Except the training courses, the journal club
for studying the newest publications on the
journals of high impact is regularly held at
National Central University. The journal club can
keep our students and researchers updated with
the newly development of the laser/maser plasma
science and provide them an excellent
opportunity to give presentations.
The core members of the topical program are
frequently invited by international research
institutes and universities to give seminars or
training courses and perform joint researches. The
exchange visiting activities and communication
enhance the international visibility and the
research quality of the local research societies.
The research results of the topical program are
presented on local conferences, e.g. Annual
Meeting of Chinese Physical Society, and
international conferences, e.g. APS Meeting of
Plasma Division, IVEC, ICOPS et al . The topical
p r o g r a m i s o rg a n i z i n g 2 0 11 C r o s s - S t r a i t
Symposium on the Fusion Energy and Plasma
Science (will be held at National Central
University), and help organize IVEC 2011 as
international committee members.
III. Visitors and International
Collaborations
We are collaborating with Prof. Lay Kee Ang
(Nanyang Technological University, Singapore)
and Dr. Wee Shing Koh (Institute of High
Performance Computing, Singapore) to study the
electromagnetic Child-Langmuir (CL) Law for
evaluation of the space charge limited current
density with considering the relativistic effects.
The research works require the extension of the
electrostatic model to the relativistic
electromagnetic model. Our computer simulation
results give the parametric studies and physical
explanations for examining the difference between
the electrostatic model and the electromagnetic
model. The study also provides a good starting
point for the derivation of the general
electromagnetic CL law. The paper for the joint
work is in revision and will be submitted to an
international journal of high impact. Prof. Lay
Kee Ang visited NCU during Jun. 20-25 and gave
seminars at NCU and NTHU, respectively, to
introduce their works on the study of quantum CL
law. Dr. Wee Shing Koh visited NCU during Aug.
19 - 25 and he proposed a research project for the
study of nonlinear effects in surface plasmonics
and include us as international collaborators.
Prof. Prof. Liu Chen visited us during Apr.
4-10 and will visit NCU on Nov. 5-12, 2010. He
gave seminars at National Central University
during his stay and had discussions with local
researchers about the application of the nonlinear
analysis on the study of the laser/maser plasma
interactions. We are collaborating in the analysis
of the stability of gyrotron backward-wave
oscillators (gyro-BWO) and obtain the possible
physical reasons for its non-stationary behaviors.
The experiences of the nonlinear analysis will be
extended to other topics, e.g. the relativistic high
harmonics generation from the interactions
between the laser and solid targets et al .
We collaborated with Prof. Chuan Sheng Liu
(University of Maryland, USA) on the study of the
LWFA and laser-based proton accelerators, and
the recent works on the study of the beam energy
scaling of laser wakefield accelerators (LWFA)
have been published on Physics of Plasmas (Phys.
Plasmas 17, 063109 (2010)). We also invited Dr.
Stefan Sneip from Dept. of Physics, Imperial
College London, to visit us and he gave a seminar
to introduce the research works in LWFA during
the past few years.
The joint works with scientists in the Institute
of Plasma Physics, Chinese Academy of Sciences,
Hefei, are to develop a fully relativistic FokkerPlanck code for studying electron cyclotron wave
heating in tokamak, an axisymmetric magnetic
confinement device for magnetic fusion energy
research. The code can also be used to study the
problems of electron transport in fast-ignition
plasmas in laser fusion. Prof. Yue-Ren. Linliu has
joined the development works and has a solid
collaboration with the Research Institute at Hefei.
IV. Highlights of Research Results
Optical-field ionization by femtosecond multiterawatt laser pulses is an efficient method for
creating a plasma of hot electrons and close-shell
ions in the sub-picosecond timescale. The hot
electrons in such a plasma collide with the ions to
produce population inversion that leads to x-ray
lasing. A major limitation of this x-ray laser
pumping scheme is the defocusing of the pump
pulse by ionization-induced refraction. Our
solution to this problem is fabricating a transient
plasma waveguide into the gain medium to
confine the pump pulse. By this method we
achieved dramatic enhancement of 32.8-nm x-ray
lasing in an optically preformed krypton plasma
waveguide. An output level of 8x1010 photon/shot
was reached at an energy conversion efficiency of
2x10 -6. The same method was used to achieve
x-ray lasing for the high-threshold low-gain
transition of 46.9 nm in neon-like argon. We have
also demonstrated seeding of Ni-like Kr lasing at
32.8 nm by high harmonic generation. Seeding
with high harmonics yields much smaller
divergence, enhanced spatial coherence, and
controlled polarization. In application, we
demonstrated single-shot digital holographic
microscopy with an adjustable field of view and
magnification by using the plasma-waveguide
based 32.8-nm x-ray laser. A new configuration of
imaging was developed to overcome the pixel-size
limit of the recording device without reducing the
effective numerical aperture. The ultrashort x-ray
pulse duration combined with the single-shot
capability offers great advantage for flash imaging
of delicate samples. (Jyhpyng Wang et al , invited
talk on International Symposium on Chirped
Pulsed Amplification, Laval University, Quebec
City, Canada, Nov. 17-21, 2010.)
Large amplitude electrostatic waves have been
observed in the electron foreshock region
upstream from the planetary bow shocks,
interplanetary shocks, and the solar wind
termination shock. The observed electrostatic
waves include electron acoustic waves, ion
acoustic waves, and double layers. Since the
electron acoustic waves are the electron-timescale phenomena, but the ion acoustic waves and
the double layers are the ion-time-scale
phenomena, we need a reliable cross-scale
simulation code to simulate the cross-scale
evolution of these nonlinear electrostatic waves.
A low-noise Vlasov simulation code is developed
to simulate the cross-scale evolution of the
electrostatic waves in the collisionless plasma. We
have successfully simulated the cross-scale
evolution of the electrostatic waves from the
electron acoustic waves to the ion acoustic waves.
Additional secondary electron acoustic waves are
167 ‹‹- Highlights of Programs
generated in the nonlinear stage of the ion
acoustic waves and result in the formation of ion
acoustic double layers. (Ling-Hsiao Lyu, invited
talk at West Lake International Symposium on
Space Plasma Physics , Hangzhou, P.R. China,
2010.)
Two-dimensional particle-in-cell simulations
were performed to demonstrate the fluctuation of
the maximum beam energy while varying the
plasma density in a laser wakefield accelerator
(LWFA) under the transition from mildly
relativistic regime to relativistic regime. The
fluctuation of the beam energy is induced by the
unstable accelerating structure, which length is
dynamically oscillating between the plasma
wavelength and the relativistic plasma
wavelength. The simulation results also reveal the
existence of the parameter space for the stable
operation of a LWFA. An empirical formulation
was derived by the curve fitting of the simulated
radius of curvature of the returning electrons
along the boundary of the plasma bubble in a
stably operated LWFA. The comparisons between
the energy scaling law derived from the empirical
formulation, the two-dimensional and threedimensional PIC simulations, and previous
experimental results with self-guided laser pulses
show good agreement. The scaling law derived in
the study can provide a correct estimation of the
maximum beam energy for a newly designed
LWFA experiment with an optimal configuration
of the laser pulse. (S. H. Chen et al, Phys. Plasmas
17, 063109(2010))
Field-induced birefringence, also known as
cross-polarization wave generation, has played an
important role in ultrafast nonlinear optics. In this
paper we analyze birefringence induced by
relativistic collective motion of electrons driven
by high-intensity laser field. An analytical
expression for the phase difference between the
parallel and perpendicular polarizations of a weak
probe pulse with respect to the polarization of a
strong pump pulse as a function of intensity,
density, and wavelengths is derived. It is shown
that under typical experimental conditions of
high-eld physics, the effect is well above detection
threshold. The analysis is compared with particlein-cell simulation, and the agreement provides
good support for the theory. (G. Tsaur et al ,
submitted to Phys. Rev. A.)
Highlights of Programs -›› 168
As an intense laser pulse propagates through an
underdense plasma, the strong ponderomotive
force pushes away the electrons and produces a
trailing plasma bubble. In the meantime the pulse
itself undergoes extreme nonlinear evolution that
results in strong spectral broadening toward the
long-wavelength side. By experiment we
demonstrate that this process can be utilized to
generate ultrashort mid-infrared pulses with an
energy three orders of magnitude larger than that
was produced by crystal-based nonlinear optics.
The infrared pulse is encapsulated in the bubble
before exiting the plasma, hence is not absorbed
by the plasma. The process is analyzed
experimentally with laser-plasma tomographic
measurements and numerically with
3-dimensional particle-in-cell simulation. Good
agreement is found between theoretical
estimation, numerical simulation, and
experimental results. (C.-H. Pai et al, submitted to
Phys. Rev. A)
We are studying the thermal relaxation
phenomenon due to electron-ion collision in fully
ionized plasmas by using a 1-dimensional PIC
simulation code. The collision is modeled by
successive small-angle scatterings of electrons by
a fixed positive ion background using a MonteCarlo procedure. The breakdown of the ND2 law
in the 1-D simulation is also observed. The
phenomenon of numerical thermalization in the
PIC simulation of a Lorentz plasma is
investigated. The thermalization time of the
simulation is reduced in the presence of the
additional Monte-Carlo collision which simulates
the electron-ion pitch angle scattering. (Yu-Ren
Linliu et al , Accepted for presentation on 52nd
Annual Meeting of the APS Division of Plasma
Physics, November 8-12, 2010, Chicago, IL,
USA)
V. Publications [1] S
. H. Chen, L. C. Tai, C. S. Liu and Y. R.
Linliu, Phys. Plasmas 17, 063109 (2010)
[2] C.-H. Pai, Y.-Y. Chang, L.-C. Ha, Z.-H. Xie,
M.-W. Lin, J.-M. Lin, Y.-M. Chen, G. Tsaur,
H.-H. Chu, S.-H. Chen, J.-Y. Lin, J. Wang,
and S.-Y. Chen, submitted to Phys. Rev. A.
[3] G. Tsaur, N.-H. Kang, Z.-H. Xie, S.-H. Chen,
J. Wang, submitted to Phys. Rev. A.
[4] Yu, H. S., L. H. Lyu, and S. T. Wu, submitted
to Astrophys. J.
Focus Group on Plasma Science
B. Plasma Science
Coordinators: Chio-Zong
(Frank) Cheng (National Cheng Kung University, email: [email protected])
I. Brief Description
oals:
1. Organize NCTS Plasma Science Workshop;
2. O
rganize a summer/winter school to offer short
courses to students and researchers;
3. I nvite short-term foreign visitors to give
lectures in summer/winter school or NCTS
Plasma Science Workshop;
4. E
ncourage cooperation and/or joint research
projects among domestic research groups;
15.
16.
17.
18.
19.
20.
21.
ing-Hsiao Lyu (NCU)
L
Yasutaro Nishimura (NCKU)
Kouichiro Oyama (NCKU)
Ker-Chung Shaing (NCKU)
Han-Tzong Su (NCKU)
Sunny W. Y. Tam (NCKU)
C hin-Ching Tzeng (INER - Institute of
Nuclear Energy Research)
22. Kai-Ti Wang (NCKU)
23. Ya-Hui Yang (NCKU)
Focused Research Topics:
5. I nvite distinguished foreign plasma theory
researchers for a 3-month or longer term
Taiwan visit;
The focused research topics include basic
magnetized plasma physics with applications in
magnetic confinement fusion plasmas, space
p l a s m a s , l a b o r a t o r y p l a s m as , a n d p l as m a
applications.
6. E
stablish collaborations and conduct exchange
programs with distinguished foreign plasma
research organizations.
II. Activities
Names of Coordinators: Chio-Zong (Frank)
Cheng
ames of Group Committee Members or Key
N
Members:
1. Tsun-Hsu Chang (NTHU)
2. Alfred B. Chen (NCKU)
3. Kuan-Ren Chen (NCKU)
4. C. Z. (Frank) Cheng (NCKU)
5. Kwo-Ray Chu (NTHU)
6. Lin-Ni Hau (NCU)
7. Rue-Ron Hsu (NCKU)
8. Lin I (NCU)
9. Eiichirou Kawamori (NCKU)
10. Yoichi Kazama (NCKU)
11. Chwung- Shan Kou (NTHU)
12. Yung-Chiang Lan (NCKU)
13. Ker-Chung Leou (NTHU)
14. Yuh-Ren Lin-Liu (NCU)
We organized the 2010 Plasma Science
Summer School, which was held at National
Cheng Kung University during July 18-25, 2010.
In total, 17 lecturers, who are experts on different
plasma science area, are invited from Academia
Sinica, National Central University (NCU),
National Chung Cheng University (CCU), and
National Cheng Kung University (NCKU) to give
lectures in the school. The lectures provide
overviews of the major applications of plasma
science and technology to undergraduate and
graduate students who show interest in this field.
About 50 students participated in this summer
school. The school provides opportunity for
students and young researchers to present their
research on poster boards. There was a dedicated
poster paper presentation time slot everyday
during the 5-day school and 10 poster papers were
presented.
The 2010 International Space Plasma
Symposium (ISPS), which is co-sponsored by
NCTS, was held at NCKU during June 27 – 30,
169 ‹‹- Highlights of Programs
2010. There were 52 oral paper presentations and
25 poster papers. Experts in space plasma sciences
around the world gathered in Taiwan and 32
world-leading plasma experts from foreign
institutions will attend the workshop and give
invited talks. It is a great opportunity for our
young scientists and students to learn new trends
in frontiers of space and fusion plasma sciences
and technologies and exchange ideas with these
scholars. In total, about 80 scientists and students
attended this event. This workshop greatly
enhanced the visibility of Taiwan plasma research
activity in the international plasma community.
III. V isitors and International
Collaborations
On the invitation of foreign scientists to visit
Taiwan, we invited Prof. Gwangson Choe of
School of Space Research, Kyung Hee University,
Korea to visit Taiwan during June 27-30, 2010
and attend the ISPS meeting and discuss with the
plasma physicists at NCKU. Prof. Choe is the
world-leading expert in the MHD simulation of
the solar and magnetospheric plasmas. His visit
provides an excellent opportunity for Taiwan
plasma scientists and students to interact with him
on the theory of solar corona, flares and coronal
mass ejections. Prof. Choe presented an invited
talk on "Development of ballooning instability by
flux rope merging in solar atmosphere" at the
2010 ISPS.
We have collaboration with Princeton Plasma
Physics Laboratory on (1) the stability of Toroidal
Alfven Eigenmodes (TAEs), Compressional
Alfven Eigenmodes (CAEs), and other Afven
eigenmodes due to interaction with alpha particles
in tokamaks; (2) the stability of ballooning modes;
and (3) kinetic-MHD model of magnetized
plasmas. As a result of the collaboration a joint
paper paper on "Transport of Energetic Ions due to
Microturbulence, Sawteeth, and Alfven
Eigenmodes" by D.C. Pace, C.Z. Cheng, R.K.
Fisher, M. Garcia-Munoz, W.W. Heidbrink, Z.
Lin, G.R. McKee, M. Murakami, C.M.
Muscatello, R. Nazikian, J.M. Park, C.C. Petty,
T.L. Rhodes, M.A. Van Zeeland, R.E. Waltz, R.B.
White, J.H. Yu, W. Zhang, and Y.B. Zhu was
submitted to the 23 rd IAEA Fusion Energy
Conference to be held at Daejeon, Korea during
Highlights of Programs -›› 170
11-16 October, 2010. This is an international
fusion energy conference sponsored by the
International Atomic Energy Agency (IAEA) once
every two years.
We have collaboration with Prof. Y. Ono of
U n i v e r s i t y o f To k y o , J a p a n o n m a g n e t i c
reconnection theory and experiment. As a result of
the collaboration a joint paper on "Double Null
Merging Start-up Experiments in the University of
Tokyo Spherical Tokamak" by T. Yamada, R.
Imazawa, S. Kamio, R. Hihara, K. Abe, M.
Sakumura, Q. H. Cao, H. Sakakita, H. Koguchi, S.
Kiyama, Y. Hirano, C. Z. Cheng, Y. Takase, Y.
Ono was submitted to the 23 rd IAEA Fusion
Energy Conference to be held at Daejeon, Korea
d u r i n g 11 - 1 6 O c t o b e r, 2 0 1 0 . T h i s i s a n
international fusion energy conference sponsored
by the International Atomic Energy Agency
(IAEA) once every two years.
We plan to invite Prof. George Parks of Space
Science Laboratory, University of California at
Berkeley, USA to visit Taiwan during OctoberDecember, 2010. Professor Parks is an expert in
space plasma physics and space instruments, and
satellite missions. In addition to many journal
publications, he has also published a popular text
book on "Physics of Space Plasmas."
We plan to invite an expert in laboratory and
fusion plasma physics from Princeton Plasma
Physics Laboratory and/or Tokyo University to
visit Taiwan during October-December, 2010.
IV. Highlights of Research Results
We have organized a plasma science summer
school and an International Space Plasma
Symposium. We have established and conducted
collaborations with Princeton Plasma Physics
Laboratory, Princeton University, USA on theory
of energetic particles in tokamak fusion plasmas
and with University of Tokyo on magnetic
reconnection physics. We have also invited Prof.
Gwangson Choe of School of Space Research,
Kyung Hee University, Korea to visit Taiwan
during June 27-30, 2010. Prof. Choe is a worldleading expert in the MHD simulation of the solar
and magnetospheric plasmas.
We also plan to provide NCTS foreign travel
fund to support Dr. Marty Chou, an NSC postdoc
stationed at NCKU, to attend the 2010 Fall AGU
meeting, which is held at San Francisco during
Dec. 13-17, 2010. Dr. Marty Chou will present a
paper on "Modeling of Saturn’s magnetosphere
with anisotropic equilibrium." Dr. Marty Chou has
published a paper on "Modeling of Saturn
magnetosphere during Voyager 1 and Voyager 2
encounters" in J. Geophysical Research in 2010
with acknowledgments to NCTS. Prof. C. Z.
Cheng (NCKU) will also attend the 23 rd IAEA
Fusion Energy Conference to be held at Daejeon,
Korea during 11-16 October, 2010. Prof. Cheng is
a co-author of two papers: one paper is on
"Transport of Energetic Ions due to
Microturbulence, Sawteeth, and Alfven
Eigenmodes" by D.C. Pace, C.Z. Cheng, R.K.
Fisher, M. Garcia-Munoz, W.W. Heidbrink, Z.
Lin, G.R. McKee, M. Murakami, C.M.
Muscatello, R. Nazikian, J.M. Park, C.C. Petty,
T.L. Rhodes, M.A. Van Zeeland, R.E. Waltz, R.B.
White, J.H. Yu, W. Zhang, and Y.B. Zhu (USA),
and the other paper is on "Double Null Merging
Start-up Experiments in the University of Tokyo
Spherical Tokamak" by T. Yamada, R. Imazawa,
S. Kamio, R. Hihara, K. Abe, M. Sakumura, Q. H.
Cao, H. Sakakita, H. Koguchi, S. Kiyama, Y.
Hirano, C. Z. Cheng, Y. Takase, Y. Ono (Japan).
V. Publication
[1] M
. Chou and C. Z. Cheng, Modeling of
Saturn magnetosphere during Voyager 1 and
Voyager 2 encounters, J. Geophys. Res., 115,
A08202, doi:10.1029/2009JA015124 (Aug.,
2010)
171 ‹‹- Highlights of Programs
Focus Group on Quantum Information Science
Coordinators: Yueh-Nan
Chen (National Cheng Kung University; email: [email protected]),
Hsi-Sheng Goan (National Taiwan University; email: [email protected])
I. Brief Description
5. M
ini-workshops and seminars at NCKU, NTU,
and CYCU.
Beneficiaries
he main mission of the Quantum
Information Science (QIS) focus group is
to build a platform of communication and
discussion for researchers in this area in Taiwan.
In the last few years, we have brought QIS
researchers in Taiwan to work and discuss
research together and to hold activities, such as
scientific seminars, workshops and short-term
schools. We have also been seeking to establish
links and exchanges as well as to initiate
collaborations with other QIS researchers
worldwide.
Coordinators: Hsi-Sheng Goan (NTU) and YuehNan Chen (NCKU)
Committee members:Yia-Chung Chang (AS),
Wei-Min Zhang (NCKU), Chi-Yee Chueng (AS),
Zheng-Yao Su (NCHC), Alec Maassen van den
Brink (AS), Pochung Chen (NTHU), Li-Yi Hsu
(CYCU), Chung-Hsien Chou (NCKU), Shih-Yuin
Lin (NCUE)
Focused topics: Quantum Decoherence,
Measurement, Entanglement, and
Communication.
II. A ctivities and Beneficiaries
Activities
1. I nternational Workshop on Relativistic RQI,
Hualien, May 28~30 (2010).
2. M
ini-course on Superconducting Quantum
Devices, Taipei, July 26~29 (2010).
3. S
ummer Lectures on QIS, Tainan, Aug. 28~29
(2010).
4. T
he 5th Winter School on QIS to be held in
Kenting, Jan. 15 ~ 18 (2011).
Highlights of Programs -›› 172
1. T
he Workshop on RQI held in Hualien helped
to introduce the new research field of RQI to
the physicists in quantum information,
gravitation, and quantum fields in Taiwan.
During the panel discussion, a new association
named the International Society on Relativistic
Quantum Information (ISRQI) was founded to
promote this new interdisciplinary field. The
executive and council members were elected,
and the international activities in this new field
in the coming years were planned. Our
Workshop on RQI thus became the first in a
series of annual events of the ISRQI. The next
Workshop on RQI will be held in Madrid,
Spain in summer 2011.
2. W
e were invited to join a large project
proposed by Prof. Buchleitner (the main
lecturer of the Summer Lecturer on QIS) and
his colleagues at Freiburg. If this large project
proposal (for 「Clusters of excellence」 in
Germany) would be approved, an intensive
collaboration could be expected. We also
invited Prof. Y. C. Cheng to give summer
lectures about their works on Quantum
Coherence in Photosynthesis to introduce the
new research direction of Quantum Biology to
the people in QIS.
Training of young-generation physicists
1. F
inancial supports for international
conferences
We plan to support students and postdocs to
attend the 4th International Workshop on SolidState Quantum Computing to be held in Shanghai,
Dec. 13~16 (2010).
III. V isitors and International
Collaborations
IV. Highlights of Research Results
Visitors
1. Decoherence and Measurements
1. P
rof. B. L. Hu, Univ. of Maryland, USA (June
3~11, 2010)
A. D istinguishing quantum and classical
transport through nanostructures
2. P
rof. Daniel Terno, Macquarie, Australia (May
23-27, 2010)
3. P
rof. A. Buchleitner, Universität Freiburg
(Aug. 26 ~ Sep. 9, 2010)
4. D
r. Min-Hsiu Hsieh, ERATO, Japan (June
10~17, 2010)
5. Dr. J. Bae, KIAS, Korea (March. 4 ~10, 2010)
6. D
r. N. Lambert, Riken, Japan (November
11-18, 2010)
International Collaborations
1. P
rof. W. M. Zhang & Prof. Aharony and Prof.
Entin-Wohlman (Isarel): Dephasing problem in
quantum transport and molecular electronics.
2. P
rof. W. M. Zhang & Prof. Yan (Hong-Kong)
and Prof. Jin (Hangzhou): Transient quantum
transport problems in nanoscale devices.
3. P
rof. C. Y. Cheung & Prof. Zhang (Anhui):
quantum bit commitment.
4. P
r o f . L . Y. H s u & D r. H s i e h ( J a p a n ) :
Entanglement in entanglement-assisted
quantum low-density parity-check codes.
5. P
rofs. C. H. Chou, Y. N. Chen & Prof.
Buchleitner (Freiburg): (1) Research Visit (2)
Joint Proposal for Clusters of excellence」 in
Germany.
6. P
rof. Y. N. Chen & Prof. Nori (Riken, Japan):
Research visiting: Prof. Y. N. Chen and Dr.
Lambert. Focus on Quantum Measurement.
7. D
r. C. M. Li, Prof. Y. N. Chen & Prof. J. W.
Pan: (1) Research visiting of Dr. C. M. Li; (2)
Project on Quantum Entanglement.
8. P
rof. H.-S. Goan & Prof. Todd. A Brun (USC):
Single spin measurement using magnetic
resonance force microscopy (MRFM).
9. P
rof. H.-S. Goan & Prof. X.Z. Yuan (Shanghai
J i a o To n g U . ) : S p i n q u b i t c o u p l e d t o
antiferomagnetic environment.
Research results
We consider the question of how to distinguish
quantum from classical transport through
nanostructures. To address this issue we have
derived two inequalities for temporal correlations
in non-equilibrium transport in nanostructures
weakly coupled to leads. The first inequality
concerns local charge measurements and is of
general validity; the second concerns the current
flow through the device and is relevant for double
quantum dots. Violation of either of these
inequalities indicates that physics beyond that of a
classical Markovian model is occurring in the
nanostructure [1].
B. Nonequilibrium quantum transport theory
for nanodevices
We developed a nonequilibrium quantum
theory for transient electron dynamics in
nanodevices. Applying the exact master equation
for nanodevices we recently developed to the more
general case in which all constituents of a device
vary in time in response to time-dependent
external voltages, we obtained nonperturbatively
the transient quantum transport theory in terms of
the reduced density matrix. The theory enables us
to study transient quantum transport in
nanostructures with back-reaction effects from the
contacts, including non-Markovian dissipation and
decoherence, being fully taken into account [5].
C. N on-Markovian two-time correlation
functions of system operators
We obtain, valid to second order in the systemenvironment interaction Hamiltonian, a nonMarkovian evolution equation of two-time CF’s of
the system operators at finite environment
temperatures for both Hermitian and nonHermitian system coupling operators and for any
initially separable system-environment state [9].
The evolution equation generalizing the quantum
regression theory to the non-Markovian finitetemperature case will have applications in many
different branches of physics.
173 ‹‹- Highlights of Programs
2. Quantum Entanglement
A. Entanglement creation between two causally
disconnected objects
We considered the entanglement dynamics
between two Unruh-DeWitt detectors at rest
separated at a distance d . We found that there is
spatial dependence of quantum entanglement in the
stable regime. In [13], the case with two uniformly
accelerated Unruh-DeWitt detectors moving backto-back in the field vacuum was considered. In this
setup each detector never enters the other's light
cone. We found that the created entanglement lasts
only a finite duration, and always disappears at late
times. The entanglement dynamics depend on the
fiducial time, i.e. intrinsically non-Markovian.
B. Q uantum entanglement and entropy in
particle creation
We investigated the basic theoretical issues in
the quantum entanglement of particle pairs created
from the vacuum in a time-dependent background
field. [14] We discussed the conditions of
separability of quantum states in particle creation
processes and point out the differences in how the
von Neumann entropy is used as a measure of
entropy generation versus for entanglement
dynamics. We show by an explicit construction
that adoption of a different set of physical variables
yields a different entanglement entropy.
3. Quantum Communication
A. Criterion for faithful teleportation with an
arbitrary multiparticle channel
We present a tripartite protocol which splits a
qutrit state via two GHZ states. The scheme is then
generalized to splitting a qudit state among any
number of receivers. We show this scheme is
applicable to splitting arbitrary multi-particle
entangled states. [15]
B. S tabilized multipartite unlockable bound
entanglement
We investigate multipartite unlockable
stabilized bound entanglement. First, the
mathematical structure of these stabilized bound
entangled states is studied. Second, since stabilizer
states are the local equivalent to the graph states,
we study them in the graph-state formalism. As a
result, the unlockable stabilized bound entangled
Highlights of Programs -›› 174
states can be graphically depicted and decomposed
in the product form. [16]
Invited presentations
1. P
rof. H.-S. Goan at the 5th Asia-Pacific
Conference in QIS, Taiyuan, Aug., 2010.
2. P
rof. W. Zhang, Prof. H.-S. Goan, and Prof. Y.
N. Chen at the 4th International Workshop on
Solid-State Quantum Computing, to be held in
Shanghai, Dec., 2010.
Cooperation with Experimental Group
Dr. Che-Ming Li, a former postdoc to Prof. Y.
N. Chen, at NCKU/NCTS(south) spent almost two
years at Heidelberg with Prof. J. W. Pan. Their
work, "Experimental demonstration of a heralded
entanglement source", was recently published in
high-impact journal [17]. Further theoretical work
[18] cooperated with the experimental group is
expected to have more impact in this field.
V. Publications
[1] N
. Lambert, C. Emary, Y. N. Chen, and F.
Nori, Phys. Rev. Lett. 105, 176801 (2010)
[2] W. Chen, G. Y. Chen, and Y. N. Chen, Opt.
Express 18, 10360 (2010)
[3] Y. Y. Liao and Y. N. Chen, Phys. Rev. B 81,
153301 (2010)
[4] Y. N. Chen, N. Lambert, and F. Nori, Phys.
Rev. B 80, 235335 (2009)
[5] J. S. Jin, M. W.Y. Tu, W. M. Zhang, and Y.
Yan, New J. Phys. 12, 083013 (2010)
[6] X. T. Liang, W. M. Zhang, and Y. Z. Zhuo,
Phys. Rev. E 81, 011906 (2010)
[7] M. H. Wu, C. U. Lei, W. M. Zhang, and H. N.
Xiong, Opt. Express 18, 18407 (2010)
[8] H. N. Xiong, W. M. Zhang, X. G. Wang, and
M. H. Wu, Phys. Rev. A 82, 012105 (2010)
[9] H.-S. Goan, C.-C. Jian and P.-W. Chen, Phys.
Rev. A 82, 012111 (2010)
[10] M d. M. Ali, P.-W. Chen and H.-S. Goan,
Phys. Rev. A 82, 022103 (2010)
[11] X
. Z. Yuan, H.-S. Goan and K. D. Zhu, Phys.
Rev. A 81, 034102 (2010)
[12] C.-A. Yen, S.-J. Horng, H.-S. Goan, T.-W.
Kao, Opt. Commun. 283, 3202 (2010)
[13] S
. Y. Lin and B. L. Hu, Phys. Rev. D 81,
045019 (2010)
[14] S. Y. Lin, C. H. Chou and B. L. Hu, Phys.
Rev. D 81, 084018 (2010)
[15] W. Zhang, Y. M. Liu, Z. J. Zhang, and C. Y.
Cheung, Opt. Commun. 283, 628 (2010)
[16] L. Y. Hsu and K. S. Wu, Phys. Rev. A 80,
042324 (2009)
[17] C. Wagenknecht, C. M. Li, A. Reingruber, X.
H. Bao, A. Goebel, Y. A. Chen, Q. Zhang, K.
Chen, and J. W. Pan, Nature Photonics 4,
549 (2010)
[18] C . M. Li, K. Chen, A. Reingruber, Y. N.
Chen, and J. W. Pan, Verifying of genuine
high-order entanglement, Phys. Rev. Lett.,
accepted (2010)
175 ‹‹- Highlights of Programs
Highlights of Programs
Initiative (sub-project I): Build-up of Theory Support for LHC Physics
Coordinator: Wei-Shu Hou (National Taiwan University; email: [email protected])
I. Brief Description
oal: The aim of this "TH-LHC Initiative"
is to bring in strong theory manpower, to
enhance contact with cutting-edge experiment for
mutual benefit. It also complements the theory
part of the NTU 拔尖 Project "Scaling the Particle
Frontier", which is a form of matching fund from
NTU and MOE. NSC further approved in 2010
the 攻頂計畫 "Beyond Kobayashi-Maskawa",
targeting physics at the LHC. The Coordinator is
the CI/PI of both large projects, and there is
clearly synergy and confluence of resources,
where this Initiative can play a crucial "extra piece
of coal" role, to kindle the flame into a stronger
fire—the goal.
Coordinator: George W.S. Hou
Key Members: Xiao-Gang He, F. Borzumati/Y.
Mimura (NTU拔尖), Johan Alwall (NCTSn),
D a v i d L i n (N C T U/N C T S); i n t e r f a c e w i t h
experimental colleagues (mostly CMS) KaiFeng Chen, Paoti Chang, Minzu Wang, Bob
Hsiung (NTU), Yuan Chao, Rong-Shyang Lu
(special NSC appointments), Paolo Bartalini
(NTU拔尖), Yuan-Hann Chang, Shin-Shan Yu,
Chia-Ming Kuo (NCU), and Song-Ming Wang of
AS in ATLAS [underlined are the "EC" members]
Group Size: above, plus postdocs (see II.),
students and visitors, altogether well over a dozen
theorists
Research Focus (from Phase-III 6-year
proposal of NCTS filed in Fall 2008):
Highlights of Programs -›› 176
Before 2012 H
elp find t' and b' quarks at LHC,
and elucidate associated Flavor and
CP Violation physics (other topics of
course pursued)
Before 2015 H
elp elucidate the impact on CPV
for BAU, EWSB and New
Resonances, and prepare for Super B
factory and ILC
II. Activities
A forum of contact established in the past is the
"Particle Physics Journal Club" (PP-JC, or just JC)
held each Monday lunchtime at NTU, and
sponsored by LHC FG. This JC is unusual in
Taiwan, as both theorists and experimentalists are
present in good numbers, ranging from mature
researchers to beginning students. It is a legacy of
the Belle era, exemplary for the good TH-EXP
cross-fertilization. In anticipation of the LHC era,
the JC was broadened to Particle Physics a few
years ago. The NTUHEP group is well funded by
NSC and NTU, and has significant manpower
base. The purpose of this TH-LHC Initiative is to
try to replicate the success of the Belle era,
catalyzing passage into the LHC era, to put
Taiwan on the map of LHC physics.
Following the planning in the 6-year proposal
filed in late 2008 (see http://phys.cts.ntu.edu.tw/
data/proposal.pdf), the Second Workshop on
Beyond 3 Generation Standard Model (2BSM3)
h t t p : / / i n d i c o . c e r n . c h / c o n f e r e n c e D i s p l a y.
py?confId=68036 was held January 14-16 2010
on NTU campus rather successfully. This is a
follow-up of the first workshop, http://indico.cern.
ch/conferenceDisplay.py?confId=33285, held at
CERN in Sept. 2008, and is a mid-size
international workshop with subtitle "New
Fermions at the Crossroads of Tevatron and
LHC", because of the slow start of LHC. The
workshop brought in over two dozen international
researchers with active interests in the 4th
generation, to establish an "international
consortium" (wording from 6-year proposal), with
Taiwan as a main hub of activity. Practically all
international participants attended the workshop
using their own funds. This is one thing we wish
to introduce into Taiwan in general, and NCTS
funded meetings in particular — people attend our
workshop because it is interesting, not because
their expenses are paid for! Emphatically we do
not take the latter approach to exhaust the
Initiative funds for sake of accounting. We have
seen a rather visible increase this year in interest
in, and activity on, the 4th generation.
Being hit on the head in 12/2009 by NSC’s ad
hoc Review Committee, slashing the TH-LHC
Initiative from two to just one Assistant Fellow,
the Coordinator worked hard with Prof. X.G. He
during Jan./Feb. in recruiting theory manpower,
independent of NCTS funding , to really fulfill the
purpose of the TH-LHC Initiative. Thus, Y.
Mimura was brought in under 拔尖 Project as
Associate Fellow, replacing F. Borzumati (left for
Tohoku U.) since April, and M. Kohda, F. Xu
(under the Coordinator) and E. Tsedenbaljir
(under X.G. He) arrived as NSC postdocs in May
and August. There would further be S.K. Majee
(courtesy NTUHEP) and K. Tsumura (under X.G.
He) arriving in October, also as regular NSC
postdocs. A further offer was to H. Yokoya as
Assistant Fellow under 拔尖 Project, replacing
Sechul Oh (moved to AS). However, since
(unfortunately) Johan Alwall will leave, we feel
we should have Yokoya moved to this TH-LHC
Initiative as Assistant Fellow under NCTS North.
In any case, altogether we have put together 7-8
doctoral level theorists towards a new Theory
G r o u p a ff i l i a t e d t o t h e N C T S n /拔尖/攻頂
consortium, in accord with the true goal of this
TH-LHC Initiative. That is, we have expanded the
platform greatly.
One major line of development, with
associated activities, is the "Lattice HiggsYukawa" line of research. This originated as a
dialogue out of curiosity by the Coordinator with
local lattice community (T.W. Chiu and David
Lin) since 2008. Thus, one feature of the abovementioned 2BSM3 workshop held in January was
a Forum on the subject. Through this we identified
the work of Karl Jansen and Philipp Gerhold as
already providing a workable framework. The
point is how Electroweak symmetry breaking
could be accomplished by fourth generation quark
condensates, without need for an elementary
Higgs boson. This scenario, which requires
relatively heavy fourth generation quarks, will be
particularly difficult to disentangle at the LHC,
and will therefore be an important line of research
in the group, both theoretically and
experimentally. Noting this importance, it was
brought under the 攻頂計畫 as a research arm,
and right at the time of filing the proposal, a oneday mini-workshop was held in mid-May (http://
p h y s . c t s . n t u . e d u . t w /
workshop/2010/990515ILHC/), with another one
to follow in November when Jansen comes for a
visit. A research program has started (synergy of
TH-LHC Initiative, Lattice/HP FG and 攻頂計
畫), where both David Lin and the Coordinator
visited DESY-Zeuthen in July, and with Gerhold
(will quit physics, despite an offer from 攻頂計
畫) brought to Taiwan in Sept-Oct to tutor two
postdocs, B. Smigielski (under Jiunn-Wei Chen)
and K. Ogawa (under David Lin), both regular
NSC postdocs. The GPU Initiative, eliminated by
the 12/2009 ad hoc Committee, could also be put
to use, since GPU computing may turn out needed
both for CMS data production, and the LatticeYukawa work.
In regards student training, the Coordinator
was invited by the Summer Institute 2010
(SI2010, http://muse.sc.niigata-u.ac.jp/SI2010/),
held at Fuji-Yoshida, Japan (hosted by Taiwan in
2008) to give a 90 min. lecture on the LHC and
CMS physics, and joining also as an organizer.
With coordination between NCTS Hsinchu and
NCTS North, many students were selected and
supported by Taiwan funds to attend.
In September, a new "LHC Journal Club"
(LHC-JC) was initiated, which focuses on
theoretical and experimental paper reading (the
original meaning of JC), starting with aspects of
fourth generation studies. The is mainly to "bring
the group together", i.e. group building and bring
the many new members up to date with the
theoretical and experimental developments, given
that LHC has started accumulating data. The first
177 ‹‹- Highlights of Programs
few theory meetings, together with an
experimental one on t’ search focus on
understanding how Electroweak symmetry
breaking can be accomplished by fourth
generation quark condensates, without need for an
elementary Higgs boson.
III. V isitors and International
Collaborations
Prof. Abdesslam Arhrib was brought in again
for 2BSM3 workshop (many visitors, as can be
found from webpage), and for collaboration work.
Short term visitors are variably sponsored
between TH-LHC Initiative, LHC FG, CTS of
NTU (college funded), and NTUHEP, where
examples are Jansen and Gerhold (given
previously) and Chung Kao, Hsin-Chia Cheng,
Ian Low, and Daisuke Kadoh.
Through Dr. Johan Alwall, we establish contact
with MadGraph (with Louvain, Illinois, and
NIKHEF) consortium, where Version 5, a major
update, has just come out. The Lattice-Yukawa
effort is forming collaboration with DESYZeuthen.
With the slashing of one 5-year term position
by NSC committee, we have resourcefully
brought in a rather international presence
(Japanese, Chinese, Indian, Mongolian and
American) of postdocs, as outlined in II.. We
expect activities to rise in late 2010 when the new
Theory Group fully forms.
The Coordinator was invited to a plenary talk
on the 4th generation at TOP2010, a very good sign
that the "thermometer" for 4th generation is going
up. At ICHEP2010 in Paris, he was drawn into a
new, developing international consortium,
tentatively called CKM4-Fitter, and he will return
to Paris in October for further discussions.
Please do appreciate that the aim of NCTS
North TH-LHC Initiative is to be internationally
visible, rather than just "national". This is the true
nature of particle physics itself, and Taiwan ought
to be not self-limiting.
IV. Highlights of Research Results
The coordination, in large part through
interface of TH-LHC Initiative and experiment, to
have an approved 攻頂計畫, to further augment
the goals, is the chief highlight, though not yet
Highlights of Programs -›› 178
quite a "research result". But given that NCTS
Phase III and 攻頂計畫 are both long term, this is
a great development, readying Taiwan for the
LHC era. Two lines directly link to TH-LHC, as
already mentioned: LHC phenomenology that
support experiment (lead by Johan Alwall), and
the new development of Lattice-Yukawa (lead by
David Lin). This is now a joint enterprise between
TH-LHC Initiative and 攻頂計畫.
One highlight is the successful development of
a completely new matrix element generator,
MadGraph 5, written in Python and a completely
general, automatic matrix element generator. From
the latter, for any physics model that can be
written in the form of a Lagrangean, it can then
calculates cross sections/generate events. The
work has been presented at many workshops. The
Lattice-Yukawa team has also formed and started.
It is understood that, by the 2013 LHC run, the
results from Lattice-Yukawa are needed to
facilitate continued search, and interpretation.
Both Alwall and collaborators, and the
Coordinator and collaborators, have published
papers related to fourth generation, as well as
other topics. Xiao-Gang He, the ever productive
researcher, also has multiple papers.
V. Selected Publications
[1] J . Alwall, J.L. Feng, J. Kumar, S. Su, "Dark
Matter-Motivated Searches for Exotic 4th
Generation Quarks in Tevatron and Early
LHC Data", Phys. Rev. D 81, 114027 (2010).
[2] J . Alwall, M. Herquet, F. Maltoni, O.
Mattelaer and T. Stelzer, "MadGraph 5", to be
submitted to JHEP.
[3] X.-G. He, T. Li, X.-Q. Li, J. Tandean, H.-C.
Tsai, "The Simplest Dark-Matter Model,
CDMS II Results, and Higgs Detection at
LHC", Phys. Lett. B 688, 332 (2010).
[4] X.-G. He, S.-Y. Ho, J. Tandean, H.-C. Tsai,
"Scalar Dark Matter and Standard Model with
Four Generations", Phys. Rev. D 82, 035016
(2010).
[5] W.-S. Hou and C.-Y. Ma, "Flavor and CP
Violation with Fourth Generations Revisited",
Phys. Rev. D 82, 036002 (2010).
[6] W. - S . H o u , Y. Y. M a o a n d C . H . S h e n ,
"Leading Effect of CP Violation with Four
Generations", Phys. Rev. D 82, 036005
(2010).
Initiative (sub-project I): Theory and Simulation of Plasmonic Metamaterials
Coordinator: Guang-Yu
Guo (National Chengchi University/National Taiwan University, email: [email protected])
Committee members: Ming-Wen Chu and Michitoshi Hayashi (National Taiwan University),
Wei-Chih Liu (National Taiwan Normal University)
I. Brief Description
urface plasmon polaritons (SPPs) are
electromagnetic waves confined to a
metal-dielectric interface and coupled to the
quantized collective oscillation of free charge
carriers. The low-dimension nature of SPPs and
the strong electromagnetic field at the interface
are responsible for a number of fascinating
phenomena in fundamental science and exciting
opportunities for technological applications such
as enhancing Raman scattering by astronomical
orders, enabling extraordinary transmission of
light through nanoholes, guiding electromagnetic
waves with SPPs beyond the diffraction limit.
Therefore, plasmonic nanostructures have been
attracting an enormous amount of experimental
and theoretical interest worldwide in recent years.
Indeed, a large number of experimental groups
in Taiwan, in particular, the prominent groups of
Cheng-Hsuan Chen (NTU-CCMS), Yang-Fang
Chen and Ding-Ping Tsai (NTU-Physics) in the
Condensed Matter and New Physics Building in
NTU, have already begun to conduct research in
plasmonics-related nano-sciences and
nanotechnologies in recent years. For example,
Cheng-Hsuan Chen’s group has established the
combined technique of scanning transmission
electron microscopy (STEM) in conjunction with
electron energy-loss spectroscopy (EELS) and its
applications for mapping and probing plasmonics
modes in individual Ag and Au nanoparticles
(NPs). The plasmonics critically relies on the
detailed knowledge of electric near fields
associated with various surface-plasmon (SP)
modes on metallic NPs. The STEM-EELS
routinely provides the nanometer spatial
resolution by focusing a subnanometer electron
beam (~2 Å) on NPs and analyzing the energy
losses of the electrons to the NPs. A nanometerscale resolutio is difficult to attain by
conventional, popular optical approaches such as
scanning near-field optical microscopy that
marginally attains a spatial resolution of ~20 nm.
While experiments plunge ahead, they need
strong theory support. Having identified this
direction as promising, and with Taipei taking the
lead, we wish to enhance Theory Support, to make
a difference over the next years.
Therefore, the main purpose this year and also
next year is to build up internationally
competative Theory Support for Plasmonic
Metamaterials. To this end, we have proceeded in
two directions: (1) to hunt for quality overseas
scientists to work in the NCTSn as either long
term fellows/postdocs or short term visiting
scientists, and (2) to build up in-house expertise of
theory and simulation of plasmonic metamaterials.
(3) to provide a platform where local
experimentalists and theoreticians can get together
to interact and collaborate.
II. Activities
To provide a platform for local professors,
postdocs and students to have discussions, to
exchange ideas and to learn related theoretical
methods and experimental techniques, we have
organized a series of monthly meetings. For
example, in the meeting last May, Ming-Wen Chu
gave a talk on "Optical Excitations in Electron
Microscopy" and also the new faculty member of
CCMS-NTU, Chih-Wei Chang gave a talk on
"Beyond Natural Materials: New Properties of
Metamaterials". In the June meeting, Masud
Mansuripur gave a talk on "Energy, Meomentum,
Force and Torque in Classical Electrodynamics:
179 ‹‹- Highlights of Programs
Application to Negative-index Media", and the
new postdoc of NCTSn, Shulin Sun gave a talk on
"Theoretical and Simulation Research on
Electromagnetic Metamaterials".
As mentioned above, plasmonics and
metamaterials are currently a very hot field and
therefore there are many experimental and
theoretical groups in other Taiwan institutions
actively working on it. Therefore, like last year,
we will organize a workshop titled "Plasmonics
and Metamaterials: Experiment and Theory", Oct.
15-16, 2010 in NTU, to provide an opportunity for
domestic scientists to present latest results, to
exchange ideas and experience, and lastly but not
the least, to educate our young researchers
(students, postdocs and faculty members). There
will be about ten invited speakers including Prof.
C. Davis of U. of Maryland.
Like last year, we have been actively trained
our young researchers with widely used
theoretical methods and also ourselves with new
theoretical techniques. For example, Michitoshi
Hayashi has been teaching one student, one
research assistant and one postdoc how to perform
excited state calculations for metallic
nanoparticle-molecular systems in order to reveal
the microscopic mechanism of SERS. Guang-Yu
Guo has been teaching two students how to use
the DDA and KKR methods to calculate
electromagnetic responses of metallic nanoparticle
clusters. The students who are learning the KKR
method. Ming-Wen Chu and Guang-Yu Guo has
been training a student to develop a theory to
describe interaction of relativistic electron beam
with plasmons on metal surfaces. Ding-Ping Tsai
also has one postdoc and one PhD student
learning how to simulate nanoplasmonics using
the FDTD method. Encouragingly, our team
members have mastered a few basic theories and
computational methods, and are working with our
experimental colleagues as well as our
distinguished foreign visitors to tackle some
fascinating issues in the field of plasmonics and
metamaterials, as indicated by our publication list
below.
III. V isitors and International
Collaborations
Highlights of Programs -›› 180
We have been extremely lucky that upon Prof.
D. P. Tsai’s invitation, Prof. Masud Mansuripur
(Chair of Optical Data Storage, College of Optical
Sciences, U. of Arizona) visited D. of Physics,
NTU and NCTSn from 2010/2/1-2010/07/31 as a
chair visiting professor supported by NSC. During
his stay, he gave a one-semester course titled
"Classical Electrodynamics with Applications in
Optics" which was attended by 33 graduate
students. He also gave several interesting seminars
such as "Energy, Momentum, Force, and Torque
in Classical Electrodynamics: Application to
Negative-index Media". He had extensive
interactions with local scientists. Indeed, his visit
has been extremely useful to graduate students,
postdocs as well as faculty members in the field.
We have been able to invite prominent
scientists in the field, Prof. Che-Ting Chan (D. of
Physics, Hong Kong U. of Science and
Technology) (2010/7/9-13), Prof. Pui-Tak Leung
(D. of Physics, Portland State U.) (2010/7/15-31),
and Prof. Christopher Davis (U. of Maryland)
(2010/10/10-17). Their visits have been very
7helpful and fruitful. Prof. Chan gave a
fascinating seminar titled "A Metamaterial Slab as
a Lens, a Cloak and Something in Between". Prof.
Leung also gave a talk titled "Plasmonic effects on
lateral displacements of light beam at material
interfaces" in a monthly meeting and was an oral
examiner of two master students’ theses. Indeed,
during his stay, a joint paper on "accurate
description of the optical response of a
matryushka in the long wavelength
approximation" was completed [2, 2010], and a
couple of new collaborative projects were
initiated. Prof. C. Davis will give a talk in the
workshop on "Plasmonics and Metamaterials:
Experiments and Theory", Oct. 15-16, NTU.
IV. Highlights of Research Results
Circularly surface plasmon modes in layered
meta-materials
Traditionally, in non-magnetic layered
structure only TM surface plasmon mode exists in
the interface of metal and dielectric layer, because
of negative permittivity of metal in specific
frequency region. To introduce TE and circular
surface plasmon modes, negative permeability is
necessary. The dispersion relations of circularly
polarized surface plasmon modes are solved
analytically for layered structure consisting of
chirally structural material and anisotropic
metamaterial. The chiral structure could be made
of liquid crystal, therefore its properties could be
controlled by external electric field, which
provides feasible controllability of those circular
surface plasmon modes. We have recently
demonstrated that the dispersion curve for surface
plasmon mode splits into upper branch (left
circularly polarized surface plasmon, LCPSP) and
lower branch (right circularly polarized surface
plasmon, RCPSP). The RCPSP mode has weak
resonate at ω=ωSP . On the other hand, the LCPSP
mode resonates much stronger. The difference of
propagating constants between two branches
provides a way to build polarization rotator for
linear polarized surface plasmon. When chiralty
factor is large enough, lower branch becomes
localized mode, and upper branch is still in
circularly polarized surface plasmon mode. This
fact enable us to make circularly polarized filter to
block right-handed circularly polarized surface
plasmon shown in lower branch.
Novel collectivity analysis of electronic motion
and plasmonic excitations in sodium clusters
We h a v e r e c e n t l y d e v e l o p e d a n o v e l
collectivity analysis of the electronic motion of
finite systems based on both the linear response
density functional theory (LRDFT) and the
collectivity index defined by the transition density
matrix [3, 2010]. We characterize the computed
excitations by analyzing the transition density for
the excitation, which is proportional to the Fourier
component of the time-dependent electronic
d e n s i t y. T h e r e f o r e , w e c a n g r a s p s p a t i a l
information of the electronic motion during the
excitation by inspecting the transition density.
The transition density has dynamical information
and is often more useful than the static electronic
density difference. Within the linear response
TD-DFT, the transition density is given by
electron and hole orbitals that are determined by
Kohn-Sham equation.
We have demonstrated a collectivity analysis
on the size-dependent peaks of electronic
excitations of small sodium clusters (rings and
linear chains). We find the excitation-mode
d e p e n d e n c e o f t h e c o l l e c t i v i t y a n d l a rg e
collectivities for the higher-energy plasmonic
excitations. The collectivity analysis also clarifies
the existence of the non-dipolar collective motion
at the energies very close to the higher-energy
plasmonic excitations. The importance of the nondipolar motion is pointed out in light of nanooptics. The results of the collectivity analysis of
the electronic motion of (Na)n ring-cluster are
presented in this paper [3, 2010].
STEM-EELS mapping of surface plasmon modes
and surface exciton polaritons
Another major accomplishment in the past year
have been the probing and mapping of surfaceplasmon modes in individual Ag nanoparticles
[Nanotechnology 20, 235705 (2009)] and probing
of surface exciton polaritons in HfO 2 [New. J.
Phys. 11, 103009 (2009)] using electron energyloss spectroscopy (EELS) in conjunction with
scanning transmission electron microscopy
(STEM) featuring an 0.2-nm electron probe. In
addition, we have established the only functional
spherical-aberration-corrected scanning
transmission electron microscope (Cs-STEM) in
Taiwan. This facility features a ~0.1-nm electron
probe with a superb stability of <0.1-nm sample/
probe drift per minute. Meanwhile, this oneangstrom electron probe is characterized by a
probe current of ~55 pA, which is much larger
than that (~10 pA) of a conventional STEM with a
characteristic probe size of >0.2 nm. Using
Cs-STEM in combination with energy dispersive
X-ray spectroscopy (EDX), we have successfully
demonstrated the chemical mapping of atomic
columns down to 0.147 nm in spatial resolution
for the first time [Phys. Rev. Lett. 104, 196101
(2010)]. The results on probing surface exciton
polaritons in HfO 2 and STEM-EDX chemical
mapping are outlined in this paper.
We have recently revisited the conventional
understanding in surface exciton polaritons (SEPs)
and established their excitations in materials
displaying an otherwise weak excitonic oscillator
strength. The existence of SEPs is thus not limited
to materials with a sharp excitonic absorption, and
the collective nature of SEPs upon weak excitonic
absorption originates from oscillations of loosely
defined delocalized excitons, which are correlated
with broad interband transitions in materials. The
181 ‹‹- Highlights of Programs
weak excitonic absorption and the associated
interband transitions can be observed in
practically all semiconductors and insulators
above the band gap, suggesting the existence of
SEPs in the materials. Using STEM in
conjunction with EELS with an ultimate spatial
resolution of 0.2-2 nm, we have firmly established
the existence of SEP (~7.5 eV) in monoclinic,
insulating HfO2 upon the weak excitonic
excitation, ~6.2 eV, above the optical band gap
(~5.1 eV). Interband transitions can be found in
almost all semiconductors and insulators above
the band gap, and this work could stimulate future
interests in SEPs in various materials, where the
SEP excitations may find unexpected optics
applications via manipulations of their surface
wave fields analogous to surface plasmons for
plasmonics.
V. Publications
[1] H
. Y. Xie, P. T. Leung and D. P. Tsai, "General
proof of optical reciprocity for nonlocal
electrodynamics," J. Phys. A: Math. Theor.
42, 045402 (2009)
[2] H. Y. Xie, P. T. Leung, D. P. Tsai, "Molecular
decay rates and emission frequencies in the
vicinity of an anisotropic metamaterial," Solid
State Commun. 149, 625 (2009)
[3] K. P. Chiu, K. F. Lai, S. C. Yen, D. P. Tsai,
"Surface plasmon polariton coupling between
nano recording marks and their effect on
optical read-out signal," Opt. Rev. 16, 326
(2009)
[4] H . Y. X i e , P. T. L e u n g , D . P. Ts a i ,
"Clarification and extension of the optical
reciprocity theorem," J. Math. Phys. 50,
072901 (2009)
Highlights of Programs -›› 182
[5] K
. P. Chiu, N. L. Wu, C. S. Wu, Y. H. Fu, C.
H. Chu, H. Y. Chung, F. H. Chen, L. D. Lin,
L. H. Huang, C. D. Shue, and D. P. Tsai,
"Plasmonic nanostructures for photo-catalytic
reactors," Proceedings of SPIE 7392, 73920B
(2009)
[6] H. Y. Xie, H. Y. Chung, P. T. Leung, and D. P.
Tsai, "Plasmonic enhancement of Foester
energy transfer between two molecules in the
vicinity of a metallic nanoparticle: Nonlocal
optical effects", Phys. Rev. B 80, 155448
(2009)
[7] H . Y. Chung, P. T. Leung, and D. P. Tsai,
"Dynamic modifications of polarizability for
large metallic spheroidal nanoshells", J.
Chem. Phys. 131, 124122 (2009)
[8] H. Y. Chung, H. Y. Xie, P. T. Leung and D. P.
Tsai, "Optical properties of metallic nanoshell
composites: The effects of temperature and
particle clustering", Solid State Commun.
149, 2151 (2009)
[9] H. Y. Xie, P. T. Leung, D. P. Tsai, "Reciprocity
theorem for nonlocal optics: Completion of
proof and application to spectroscopic
analysis", J. Optics 12, 035006 (2010)
[10] H. Y. Chung, G. Y. Guo, H.-P. Chiang, D. P.
Tsai, and P. T. Leung, "Accurate description
of the optical response of a multilayered
spherical system in the long wavelength
approximation", Phys. Rev. B 82 (2010, in
press) (BV11426)
[11] T. Yasuike, K. Nobusada, and M. Hayashi,
"Collectivity of plasmonic excitations in
small sodium clusters", J. Chem. Phys.
(under review)
[12] V. Klimov and G.-Y. Guo, "Bright and dark
Plasmon modes in three cylinder
nanocylinder cluster", J. Phys. Chem. C
(under review)
Research Activities of Individuals
Research Activities on Collider Phenomenology and HEP Software Development
Johan Alwall (email: [email protected])
Assistant research scholar, 2010/1/1~2010/10/12
y research during the Academic year
2009-2010 has been in the areas of
hadron collider phenomenology and development
of software for simulation of high-energy
collisions. Of my main projects, several are
finished or close to being finished:
• D
etermination of discovery and exclusion limits
at the Tevatron and the LHC for exotic fourth
generation quarks decaying to third generation
quarks and Dark matter (in collaboration with
profs. J.L. Feng (UC Irvine, CA), J. Kumar (U
of Hawaii) and S. Su (U of Arizona))
• I mprovement of the Matrix Element method for
analysis of experimental data (with prof. A.
Freitas, U. of Pittsburgh, PA and O. Mattelaer,
UC Louvain, Belgium)
• D
evelopment of a matrix element generator,
MadGraph 5, which replaces the exceptionally
successful and widely used matrix element
generator MadGraph 4 (in collaboration with
the MadGraph team: Prof. F. Maltoni (UCL,
Belgium), Prof. Timothy Stelzer (UIUC, IL), Dr.
M. Herquet (previously NIKHEF, Netherlands)
and Dr. O. Mattelaer (UCL, Belgium)). This is a
completely new code with improvements in
every direction, compared to previous versions.
The successful completion of the development
of this core code is a milestone, which will
allow a large range of exceptional developments
in the near future.
Among projects that are still ongoing, in a
more or less advanced state, are:
• D
istinction between signals for a standard
sequential fourth generation and
supersymmetric scenarios, in particular
scenarios where supersymmetric top and bottom
quarks mimic the decay structure of fourth
generation quarks (with Prof. K.-F. Chen and
Y.-W. Chang, both at NTU). While this
distinction would be trivial with large amounts
of data, the situation in early stages of the LHC
experiment will be very different. The main
signal for both these scenarios will be same-sign
dilepton and trilepton signals, as well as signals
of jets and missing energy. In this project, we
are investigating which observables will be
most sensitive to the differences between these
two broad scenarios, by using scans over large
regions of the parameters space of
supersymmetric extensions of the Standard
Model.
• T
he development of a fast decay width
calculator and decay generator within the
MadGraph 5 framework (with C.-H. Shen,
NTU). By using maximum model information
and fast, analytical, approximative calculations
of partial decay widths, it is possible to take into
account only decays with substantial
contributions to the full decay width. These
decay widths can then be calculated to high
precision using Monte Carlo simulation. This
also allows for fast simulation of spin-correlated
decays of events which have been generated
using a matrix element Monte Carlo simulation
package such as MadGraph/MadEvent.
183 ‹‹- Research Activities of Individuals
• I nvestigation and analysis of single fourth
generation quark production in the parameter
regime where the fourth generation quarks are
experiencing strong coupling effects (with Prof.
G . W. - S . H o u , N T U ) . I n t h i s r e g i m e , a
perturbative treatment of fourth generation
quark pair production breaks down, and
extraction of properties for the fourth generation
quarks from studies of pair production will be
difficult and the results uncertain. Single
production, however, does not suffer from
strong coupling effects, since all relevant
couplings in this case are perturbative. The idea
was therefore to investigate the feasibility of
observing single fourth generation quark
production, and to extract properties of the
heavy quarks from the observed events.
Unfortunately, initial investigations indicate that
severe Standard Model backgrounds, in
combination with small production cross
sections for the relevant modes of single heavy
quark production, will make even the
observation of this production mode quite
challenging.
I will now give more details about the finished
or nearly finished projects mentioned above.
Exotic fourth generation quarks decaying to
third generation quarks and Dark matter
The scenario investigated in this study, with
chiral fourth generation quarks carrying some
"dark" quantum number which forces them to
decay exclusively to dark matter and third
generation quarks, is motivated by a class of
models for dark matter, called WIMPless models,
which can be used to explain the famous DAMA
anomaly. In this scenario, the dark matter can have
any mass, and we therefore made a very general
study, which applies to any model where chiral
quarks are pair produced through QCD
interactions at the Tevatron or the LHC, and then
decays to third generation quarks and an invisible
particle (i.e., a particle with negligible interactions
with the detector material). In the first publication
[1], we treated the case where the produced quarks
decay to top quarks and dark matter. A second
publication is in progress, where we investigate
the corresponding (but very different) case when
the produced quark decay to a b quark and Dark
matter.
Research Activities of Individuals -›› 184
Improvement of the Matrix Element method
The Matrix Element method is a method for
analysis of experimental events. It uses the
squared matrix element for a particular process,
model, and given model parameters to assign a
value to each experimental event, which can be
interpreted as the probability that this event was
produced according to the corresponding matrix
element. By combining these values for multiple
events into a likelihood, it is possible to select
between different model assumptions, and within
each model between different model parameter
ranges. This method has been used extensively for
determination of the top quark mass at the
Tevatron, as well as for the very difficult
extraction of single top processes at the Tevatron,
and is responsible for the most precise top quark
mass measurement to date.
One drawback with the method is that only
events with final states identical to those of the
matrix element can be used. This means in
particular that events with extra hadronic jet
activity must be discarded, which reduces the
statistical sample of useful events, hence the
statistical sensitivity of the method. Extra
hadronic activity has another important effect on
experimental events: QCD radiation from the
incident legs in the interaction (initial-state
radiation) tends to give the produced particle
system a momentum in the direction transverse to
the incoming beam. Such a boost is not taken into
account in the standard application of the Matrix
Element method, and can strongly distort the
results and give unknown systematic effects in the
analysis.
In [2], we develop and investigate different
methods to account for such initial-state radiation.
The simplest method investigated is to sum up the
momentum of any additional jet activity in the
detector event by event, make the assumption that
this is due to initial state radiation, and account for
it by boosting the matrix element by the inverse of
this momentum (or, equivalently, boost the
experimental event by the momentum). In the
ideal case where all additional jet activity is
recorded by the detector, already this method is
surprisingly effective, giving measured mass
results which reproduce the masses used for the
simulation of the events used as experimental
data. However, in the realistic case of a detector
with limited acceptance, some radiation will
always be missed. For this case, we improved the
method by introducing an integration over
distributions of initial state momenta, which are
fitted to Monte Carlo simulation data. With this
addition, we get excellent agreement between the
input masses and those reconstructed by the
method, even in a realistic case. Also other
improvements were tested, some of which might
also be of interest for experimental applications.
This work is in the final stages of completion, and
should be available at the arXiv preprint servers
within a week.
MadGraph 5, an all-new matrix elem e n t
generator
The last work that I will report on here is also
the largest, and has been taking the majority of my
efforts during this year. In November 2009, I,
together with my colleages in the MadGraph
team, started development of a completely new
generation of the MadGraph matrix element
generator. MadGraph, which is one of the most
widely used matrix element generators in High
Energy Physics (with over 1500 registered users,
besides all the major experimental collaborations),
was originally written starting in 1994, and using
the Fortran 77 programming language. While this
language is fast, it has many intrinsic limitations.
In order to allow new developments, it was clear
that something new was needed, and we chose to
use the fourth generation programming language
Python to develop a completely new version of
the matrix element generator program from
scratch, with completely new algorithms for
almost every aspect of the operation.
Thanks to an excellent programming
framework, modern programming methods, an
extremely competent team and a lot of hard work,
we succeeded in less than six months to create a
code which could not only do everything that the
old MadGraph 4 could do, but also improved the
speed of the program by up to orders of
magnitude, while at the same time improving
stability compared to the old code.
Just reproducing what the old code was doing
(but better) was of course not our goal – the idea
with the new code was to create a flexible
framework which allows easy implementation of
completely new developments. In the further
development of the core code, the main
achievement has been to allow for automatic
creation of so-called Helicity amplitude routines
for any model which can be written in terms of a
Langrangian. This allows completely automatic
generation of fast simulation code for cross
section calculation and event simulation for any
model, which is something that has never been
achieved before. We have also added many new
features and new output formats, including an
interface for generation of matrix elements in C++
for the widely used Monte Carlo simulation
program Pythia, new QCD color structures, and
advanced checks for the consistency of new
models. The writeup of this work is in progress,
and will get submitted to JHEP within a few
weeks.
I would finally like to express my great sense
of gratitude for this year at NCTS-North and the
NTU Physics department, in particular to Prof.
George Hou, but also to Chiachi Liu for her
unfailing willingness to help with any
administrative matter, and to the members of the
CMS and Theory groups for their welcoming and
appreciative spirit.
References
[1] J . Alwall, J.L. Feng, J. Kumar, S. Su, "Dark
Matter-Motivated Searches for Exotic 4th
Generation Quarks in Tevatron and Early
LHC Data", Phys. Rev. D 81, 114027 (2010)
[2] J. Alwall, A. Freitas and O. Mattelaer, "The
Matrix Element Method in presence of Initial
state radiation", to be submitted to Phys.Rev.
D.
[3] J . Alwall, M. Herquet, F. Maltoni, O.
Mattelaer and T. Stelzer, "MadGraph 5", to be
submitted to JHEP.
185 ‹‹- Research Activities of Individuals
Research Activities on Biophysics
Chun-Chung Chen (email: [email protected])
Assistant research scholar, 2009/10/1~2011/9/30
n the past year, my research has focused
on simulations of plastic neural network
and on cyclic competition in evolutionary
dynamics. I have worked to improve the accuracy
and efficiency of the event-driven simulation code
for plastic neural network. With the deployment of
the new computer cluster, I have performed
extensive simulations to investigate the full
parameter space of the model. These simulations
confirmed, in the stable phases of the system, the
narrow synaptic weight distribution predicted by
mean-field analysis [1] and revealed emergent
structures in the transition region of the network
(see Figure 1) that has not been reported in the
literature. I am currently preparing manuscripts to
reported these findings.
Figure 2: Stationary system of 2 dimensional cyclic competition
between three species (Red, Green and Blue)
without mobility.
Figure 1: E mergent structures of plastic neural networks.
Numbers indicate values of plasticity parameter
controlling the preferred synaptic strength.
For evolutionary dynamics, I worked with
Prof. Hsiu-Hau Lin's group to investigate the
subjects of error threshold and cyclic competition.
The quasispecies model proposed
Research Activities of Individuals -›› 186
by Eigen [2] describes molecular evolution
through point mutation. We found that the
dynamics of the model can be mapped to the
dynamics described by an effective Hamiltonian.
Applying variational ansatz on the Hamiltonian,
we obtained a good estimate of the error
threshold, which partly confirmed the first order
nature of the quasispecies transition. We also
found that for a symmetric fitness landscape, we
could use an S-wave decomposition to reduce the
dimension of mutation matrix from exponential to
linear in the sequence length. Such reduction
enabled numerically exact diagonalization of the
quasispecies equation for long sequence length.
For cyclic competition, we developed simulation
code to investigate the extinction time for three
species competition in 1 and 2 dimensions (see
Figure 2) as well as a globally coupled systems.
We have identified different powerlaw scalings of
the extinction time with respect to the system size
for all cases except for the extinction of the first
species in 2D, which was found to increase
exponentially with the system size. Such
exponential scaling explains the protection of
biodiversity in 2D rock-paper-scissors games with
low mobility as reported in the literature [3]. We
were able to relate this exponential divergence to a
finite correlation length in the system due to
localized dynamic patterns of activities. Such
finite correlation partitions the system into
uncorrelated blocks and the extinction of the first
species requires simultaneous extinguishment of
this species for all the blocks. This requirement
leads to the observed exponential growth of first
extinction time in 2D with respect to system size.
We are confirming such an understanding through
numerical verifications.
[2] M
. Eigen, Molekulare selbstorganisation und
evolution, Naturwissenschaften, 58:465, 1971.
[3] T. Reichenbach, M. Mobilia, and E. Frey,
Mobility promotes and jeopardizes
biodiversity in rock-paper-scissors games,
Nature, 448:1046, 2007.
References
[1] C
.-C. Chen and D. Jasnow, Mean-field theory
of a plastic network of integrate-and-fire
neurons, Phys. Rev. E, 81:011907, 2010.
187 ‹‹- Research Activities of Individuals
Research Activities on Quantum Transport and Measurement
Yueh-Nan Chen (Department of Physics, National Cheng-Kung University; email: [email protected])
Center scientist, 2009/10/1~2011/9/30
n 2010, my research activity in NCTS has
been focused on the theory of quantum
transport and measurement. There are three major
results in the past year:
• C
oherent transport of nanowire surface
plasmons coupled to quantum dots
The coherent transport of surface plasmons
with nonlinear dispersion relations on a metal
nanowire coupled to two-level emitters is
investigated theoretically as shown in Fig. 1. Realspace Hamiltonians are used to obtain the
transmission and reflection spectra of the surface
plasmons. For the double-dot case, we obtain the
interference behavior in transmission and
reflection spectra, similar to that in resonant
tunneling through a double-barrier potential.
quadratic dispersion relation. All these peculiar
behaviors indicate that the dot-nanowire system
provides a one-dimensional platform to
demonstrate the bandgap feature widely observed
in photonic crystal.
• D
istinguishing quantum and classical
transport through nanostructures
We consider the question of how to distinguish
quantum from classical transport through
nanostructures. To address this issue we have
derived two inequalities for temporal correlations
in non-equilibrium transport in nanostructures
weakly coupled to leads. The first inequality
concerns local charge measurements and is of
general validity; the second concerns the current
flow through the device and is relevant for double
quantum dots. Violation of either of these
inequalities indicates that physics beyond that of a
classical Markovian model is occurring in the
nanostructure.
TQ npef
Fig. 2 (a) shows a generic single-charge nanostructure. The
single-charge can occupy one of N internal states. Local
charge occupation of one or more sites is measured
using a charge detector (CD) Eq. (2), e.g. a quantum
point contact. (b) shows a schematic of a double
quantum dot, the main example we discuss here.
• P
ure dephasing of double-quantum-dot charge
qubits in free-standing slabs
Fig.1 ( a) Schematic view of the model: a silver nanowire
coupled to two QDs. (b) Dispersion relations of the
nanowire surface plasmons for the modes n = 0 to n = 3.
M o r e o v e r, F a n o - l i k e l i n e s h a p e o f t h e
transmission spectrum is obtained due to the
Research Activities of Individuals -›› 188
We study phonon-induced pure dephasing in a
double-quantum-dot qubit that is embedded in a
free-standing slab (Fig. 3).
References
[1] W
. Chen, G. Y. Chen, and Y. N. Chen, Opt.
Express 18, 10360 (2010)
[2] N . Lambert, C. Emary, Y. N. Chen, and F.
Nori, Phys. Rev. Lett. 105, 176801 (2010)
[3] Y. Y. Liao and Y. N. Chen, Phys. Rev. B 81,
153301 (2010)
[4] Y. Y. Liao, Y. N. Chen, and S. R. Jian, J. Phys.
C. 22, 045301 (2010)
Fig.3 Schematic illustration of the double-quantum-dot charge
qubit embedded in a free-standing slab of width W.
Dashed circles represent two identical quantum dots with
dot radii a and center-to-center distance d.
The dispersion relations are evaluated to probe
the phonon characteristics of the slab. The pure
dephasing factor in the off-diagonal elements of
the density matrix is calculated. Numerical results
demonstrate that time-evolution of this factor
exhibits a non-monotonic feature, resulting from
the phonon confinement effect. Significant
contribution from individual phonon mode is
analyzed in detail. We also study effects of
temperature and double-dot position on the pure
d e p h a s i n g . I n p a r t i c u l a r, t w o r e m a r k a b l e
oscillations are observed due to phonon van Hove
singularities.
189 ‹‹- Research Activities of Individuals
Research Activities on Particle Physics Phenomenology
Kingman Cheung (Department of Physics, National Tsing Hua University; email: [email protected])
Center scientist, 2006/11/1~2008/10/31, 2009/2/1~2011/1/31
have been in the Center as a Center
Scientist since November 2006. I am also
one of the coordinators for the Focus group on the
LHC Physics. My research area is in particle
physics phenomenology. In the following, I
highlight some works done in 2010.
Dark Matter
The year 2009 and 2010 have been filled with
excitements from a number of astronomy and
astroparticle experiments, e.g., PAMELA, ATIC,
CDMS, XENON, say to name a few. All the new
results give hints to the nature of the dark matter if
interpreted as signals of the dark matter. As we
have understood since a decade ago, about 25% of
the matter of the whole Universe is constituted by
a substance that has no or very small interaction
with visible matters and has only gravitation
effects in the structure formation, known as dark
matter. This dark matter cannot be any particle
that we know in the standard model (SM). It is
clear that new physics models are needed to
explain the existence of the dark matter, which is
stable over cosmological time scale, very weak
interactions with matters, and electrically neutral
(to a large extent). The most studied candidate for
the dark matter is the neutralino in the
supersymmetric models. In recent years, a new
crop of dark matter models were also proposed.
One of the most direct detection methods of
the dark matter is through a set of direct search
experiments. The dark matter particles move at a
velocity relative to the detecting materials. It will
recoil against the nucleons, and create a phonontype signal, which can be amplified by electronics.
Just very recently the CDMSII finalized their
search. When they opened the black box in their
blind analysis, they found two candidate events,
which are consistent with background fluctuation
at a probability level of about 23%. Nevertheless,
the signal is not conclusive. The CDMS then
improves upon the upper limit on the spinindependent cross section
to 3.8 x 10-44 cm2 for
Research Activities of Individuals -›› 190
m χ ≈ 70 GeV. In the work[1], we use this new
limit to put a new bound on the Higgs-dark-matter
coupling, which is then implied to an upper limit
on the Higgs boson invisible width. We found that
the invisible width to be of order of O(10) MeV at
mh = 120—140 GeV, then the invisible decay of
the Higgs boson can be dominant. This will have
nontrivial effects on the search for the
intermediate Higgs boson at colliders.
In another scenario[2,3],the SO(5)×U(1)gaugeHiggs unification model based on the RandallSundrum warped space provides a dark matter
candidate. The dark matter is the Higgs boson,
which is a part of the fifth component of a gauge
boson field in the model. It was shown that at the
value of θH = ±π/2 the effective potential of the
Higgs boson is minimized. Furthermore, the
invariance of the effective interactions under H
→-H prohibits triple vertices such as WWH, ZZH,
and ffH, which is true to all orders in perturbation
theory. Thus, the Higgs boson is stable and can be
a dark matter candidate.
Focused on 4-point vertices of HHW+W- and
HHZZ, we study the collider signatures of this
dark matter model [2] Our main process is the
production of a pair of the Higgs bosons
associated with a W or Z boson. The final state
consists of charged leptons plus large missing
energy. However, the detection of this signal is
very challenging. The signal cross section is
generically small due to the 2 → 3 process with
the weak coupling. In addition, only one single
observable particle in the final state provides very
limited kinematics, which could be used to reduce
the SM background. We found that the signal at
the LHC is too small to be useful. On the other
hand, the International Linear Collider with high
beam polarization can substantially improve the
sensitivity to the signal.
In another work[3], we study the positron and
antiproton spectra from annihilation of the gaugeHiggs dark matter in the halo. We use the cosmic
ray propagation code Galprop to calculate the
propagation of the positron and antiproton from
the halo to the Earth, and compare with the
spectra measured by PAMELA. The most
dominant annihilation channel for mh ≥ 70 GeV is
HH → W+W-, followed by the subsequent decays
of the W bosons into positrons or quarks. The
quarks undergo fragmentation into antiproton. We
use the PAMELA data as the constraints on the
model: the resulting spectra obtained from the
CDM annihilation should not exceed the ones
m e a s u r e d b y PA M E L A. T h e H i g g s b o s o n
annihilation rate is shown to increase with
increasing Higgs boson mass. The mh = 82GeV is
marginally consistent with both the observed
positron and antiproton spectra. However, the
Higgs boson mass of 90 GeV or more is obviously
ruled out by the observed data.
Supersymmetry
The anomalous magnetic dipole moment of the
muon, aµ , has provided one of the most sensitive
test grounds for the validity of the Standard
Model. There is currently a 3.7σ discrepancy
between the experimental result and the SM
prediction, which can be attributed to possible
contributions from physics beyond the SM
EXP
SM
-10
ΔaEXP
µ ≡ aµ — aµ = 30.7(8.2) × 10 .
One of the most appealing scenarios for
physics beyond the SM is augmented with a softly
broken supersymmetry (SUSY) around the TeV
scale. The supersymmetric contributions to aµ
from such models are known up to two-loop level.
It is well-known that the dominant two-loop
contribution comes from Higgs-mediated BarrZee diagrams. On the other hand, the SUSY
augmented models can contain additional
CP-violating phases beyond the SM CabibboKobayashi-Maskawa(CKM) phase leading to
sizable EDMs. In a work[4], we study the
correlation between the muon EDM and MDM in
the CP-violating MSSM. We present the relation
between the one-loop chargino-and neutralinomediated EDM and MDM of the muon. We also
derive an analytic relation between them in the
two-loop contributions from the dominant
Higgs-mediated Barr-Zee diagrams. We
improve the earlier results by including
CP-violating Higgs-boson mixing effects in the
Barr-Zee diagrams and resumming the threshold
corrections to the muon, tau, and bottom-quark
Yukawa couplings in the one-and two-loop
graphs. We then focus our numerical studies on
three types of scenarios in which (i) the muon
EDM and MDM are dominated by the one-loop
contributions, (ii) thelightest Higgs boson is
mostly CP odd and lighter than ∼ 50GeV, and
(iii) the dominant contributions to the muon EDM
and MDM come from the two-loop Barr-Zee
graphs.
Supersymmetry predicts the existence of
SUSY partners. In particular, the colored ones,
like squarks and gluinos, are produced abundantly
at the LHC. The squarks are pair produced via
QCD interactions, which are independent of
tanβ. Mixed top and bottom squark production is
via an intermediate W boson in the2 → 2
subprocess or via gW fusion in the 2 → 3
subprocess. In a work[5], we point out that
production via a charged Higgs boson can become
dominant in the large tanβ region. With large
tanβ not only can the smallness of the Yukawa
coupling and the small parton luminosity of the
incoming bottom quark be compensated, but also
the charged-Higgs sbottom-stop vertex can be
enhanced. Furthermore, with the intermediate
charged Higgs boson all left-and right-handed
squark pairs ˜tL,R b̃ L, R can be produced while only
t̃ Lb̃ L can be produced via the intermediate W
exchange. Thus, we anticipate the production via
intermediate charged Higgs boson could be
dominant in some region of parameter space.
An extension with an extra singlet superfield,
known as the next-to-minimal supersymmetric
standard model(NMSSM) was motivated to
provide a natural solution to the µ problem. In the
NMSSM, the µ term is generated dynamically
through the vacuum-expectation-value(VEV), vS,
of the scalar component of the additional Higgs
field S, which is naturally of the order of the
S U S Y b r e a k i n g s c a l e. I n S U S Y m o d e l s,
CP-violating phases naturally appear in the µ term
of the superpotential and in the soft-SUSY
breaking terms. The non-vanishing CP phases
could radiatively induce significant mixing
between the CP-even and CP-odd states, giving
rise to a number of interesting CP violating
phenomena and substantial modifications to
Higgs-boson phenomenology. In a recent work[6],
we marry these two ideas by allowing CP phases
in the µ and other soft parameters in the NMSSM.
191 ‹‹- Research Activities of Individuals
We study the NMSSM Higgs sector with CP
violation. In the CP-conserving limit, the neutral
Higgs sector in the NMSSM includes two CP-odd
and three CP-even states. With CP violation the 5
neutral Higgs bosons lose their CP parities and all
mix together. We anticipate a whole new set of
phenomena associated with the singlet extension
of the MSSM in the presence of nontrivial
CP-violating phases in the VEVs, and the µ and
soft SUSY breaking parameters. As the first step
toward this new extension, we calculate the whole
mass spectrum of the Higgs sector as well as the
couplings to the vector gauge bosons, which will
dictate the production and decay patterns of the
H i g g s b o s o n s. We i n c l u d e t h e i m p o r t a n t
corrections to the Higgs spectrum, the full oneloop corrections to the Higgs boson masses, and
logarithmically enhanced two-loop corrections of
order O(gs2h4)and O(h6) with the renormalization
group (RG) improvement and minimization of the
two-loop corrections. We also impose highly
desirable conditions to limit the parameter space:
(i) the LEP limits including the Higgs-boson mass,
chargino mass, and neutralino mass bounds,
(ii) the global minimum condition–the local
minimum that we obtain is indeed the global
minimum, and(iii) the positivity of the square of
the Higgs-boson masses. We found that the
RG-improved corrections have significant
reduction in the allowed parameter space with
respect to the LEP limits, the global minimum
condition, and the positivity of the Higgs-mass
squared.
Collider
The forward-backward asymmetry in top quark
pair production was measured at the Tevatron.
While the Standard Model (SM) only predicts a
level as small as a few percent arising from the
higher-loop contributions, the measurement by
CDF, however, is as large as
Nt(cosθ> 0) — Nt(cosθ< 0)
Nt(cosθ> 0) ┼ Nt(cosθ< 0)
= 0.19 ± 0.065 (stat) ± 0.024 (syst) ,
Afb ≡
where θ is the production angle of the top
quark t in the tt̄ rest frame. If the asymmetry is
true, it will indicate the presence of new physics,
because within the SM the asymmetry is only up
to about 5%. In a work [7], we proposed an extra
W-like boson W′that only couples to the d and t
Research Activities of Individuals -›› 192
quarks. Thus, the dd̄ initial state' turns into the tt¯
final state via a charge-current exchange of the
W′boson in the t-channel. This process can be
used to produce the forward-backward asymmetry
as reported by the CDF Collaboration.
There are some other works [8,9,10],but
because of space limitation they are omitted here.
References
[1] K
. Cheung and T. C. Yuan, Phys. Lett. B 685,
182 (2010) [arXiv:0912.4599 [hep-ph]]
[2] K . Cheung and J. Song, Phys. Rev. D 81,
097703(2010)[Erratum-ibid. D 81,
119905(2010)][arXiv:1004.2783[hep-ph]]
[3] K . C h e u n g , J . S o n g a n d P. Y. Ts e n g ,
arXiv:1007.0282 [hep-ph] (accepted for
publication in JCAP)
[4] K . Cheung, O. C. W. Kong and J. S. Lee,
J H E P 0 9 0 6 , 0 2 0 ( 2 0 0 9 )
[arXiv:0904.4352[hep-ph]]
[5] A. Arhrib, R. Benbrik, K. Cheung and T. C.
Yu a n , J H E P 1 0 0 2 , 0 4 8 ( 2 0 1 0 )
[arXiv:0911.1820[hep-ph]]
[6] K .Cheung, T.J.Hou, J.S.Lee and E.Senaha,
arXiv:1006.1458[hep-ph]
[7] K . Cheung, W. Y. Keung and T. C. Yuan,
Phys. Lett. B 682, 287 (2009)
[arXiv:0908.2589 [hep-ph]]
[8] K .Cheung,C.W.Chiang,Y.K.HsiaoandT.
C . Yu a n , P h y s . R e v. D 8 1 , 0 5 3 0 0 1 ( 2 0 1 0 )
[arXiv:0911.0734 [hep-ph]]
[9] C. M. Lin and K. Cheung, Mod. Phys. Lett. A
25, 2231(2010) [arXiv:0911.4749 [hep-ph]]
[10] L. Y. Lee, K. Cheung and C. M. Lin, Mod.
Phys. Lett. A 25, 2105 (2010)
[arXiv:0912.5423 [hep-ph]]
Research Activities on Quantum Information Science
Chung-Hsien Chou (Department of Physics, National Cheng Kung University; email: [email protected])
Center scientist, 2007/8/1~2009/7/31, 2010/2/1~2012/1/31
In 2010 my research activity in NCTS has
been focused on quantum information
science, especially the quantum field theoretical
treatment of issues in relativistic quantum
information (RQI).
Usually entanglement is discussed in the
framework of non-relativistic quantum mechanics,
but for a quantity to have physical meaning one
needs to know how it transforms in different
reference frames, e.g., for two observers moving
at relative constant speed how is the quantity one
observer reports as entanglement between two
parties in its system related to that reported by the
other observer in its system? This is the starting
point of relativistic quantum information (RQI).
When a quantum field is involved, one needs to
upgrade the treatment to that of relativistic
quantum field theory. This is the platform we have
adopted for our research program on RQI.
The simplest process which distinguishes a
quantum field theoretical process from a quantum
mechanical one is particle creation. The
investigation of quantum entanglement in the
particle creation process -- how to define
entanglement, between what parties, and how it
evolves in time -- are the first order of business
toward establishing a RQI theory for quantum
field processes. In the work [1] collaborated with
Prof. S.Y. Lin of NCUE and Prof. B.L. Hu of
UMD, we study the issue of quantum
entanglement and entropy in particle creation.
Quantum entanglement depends crucially on
the choice of physical variables and the way the
two parties whose entanglement is the object of
interest are defined. Quantum entanglement can
be measured in many ways. For the bipartite
system the von Neumann (vN) entropy is quite
commonly used. We show that the way the vN
entropy is used and what results it yields for these
two processes, one pertaining to entanglement
dynamics, the other for entropy considerations in
nonequilibrium statistical mechanics are quite
different, both in terms of whether and how
coarse-graining is introduced, and for what
reasons. A particle pair with some 3-momentum
(k, -k) created from the vacuum is habitually
regarded as perfectly entangled. We show by
explicit construction that adoption of a different
set of physical variables with the same
3-momentum (k, -k) makes a difference in the
entanglement dynamics.
We are focusing on the simplest cases with free
quantum fields in a dynamical background. We
describe the particle creation process of real and
complex scalar fields, respectively, in the
Schrodinger representation. We investigate the
behavior of particle numbers and quantum phase
exploring the theoretical issues for the quantum
entanglement of particle creation in a timedependent background. The main results of
entanglement dynamics are presented using
Wigner functions. After the theoretical issues are
explored and analysis performed we study such
processes in the early universe. We find that for
the vacuum state of a free real scalar field in an
expanding universe, once the physical variables
are correctly chosen, it is possible to partition the
degrees of freedom of a (k, -k) mode pair into k
and – k particles, and the degree of entanglement
between them can be calculated accordingly.
Based on these results we are able to look into
how the particle number and the quantum phase
enter the entanglement dynamics in cosmological
particle production.
As a next step toward a quantum field
theoretical approach of RQI, we are now working
the effect that gravitational interaction would play
in the process of quantum teleportation.
In the past year I also did some work about
cosmology trying to give a digital origin of
cosmic inflation.
193 ‹‹- Research Activities of Individuals
Ever since Wheeler proposed the working
hypothesis: it from bit , various attempts have been
made to elucidate the proposal that the physical
universe can be viewed as just a continuum
approximation to some underlying microscopic
information-theoretic or digital principles.
Therefore, bit gives rise to it. To take this
proposal seriously, one can take dual approaches
to uncover these microscopic bit-level principles,
we shall call them digital principles. First of all,
the very act of computation is by itself a physical
process which should be subjected to the known
physical constraints. One can calculate the limits
on the capacity of computation, or on the speed of
computation based on known physical principles.
Given that the known physical description of the
world is supposed to emerge out of an underlying
digital description, it is reasonable to use such
limits based on known physics as an estimate.
In the work [2] done in collaboration with Prof.
H.L. Yu at IPAS, we argue that based on the
kinematic information calculated earlier, one can
naturally arrive at the conclusion that the cosmic
inflation is unavoidable due to a simple digital
principle.
Assuming our physical universe processes and
registers information to determine its dynamical
evolution, one can put serious constraints on the
cosmology that our universe can bear, in
particular, the origin of cosmic inflation. The
universe evolves to gain her computation capacity
which is linear in time t. On the other hand, the
growth in content of degrees of freedom (i.e., by
integrating in more galaxies) is as t 3/2 through
expansion. When the in flux of degrees of
Research Activities of Individuals -›› 194
freedom of the universe grows beyond some
value, the computation capacity of the universe
becomes insufficient to determine its evolution,
the universe fixes its Hubble radius and inflates
away its degrees of freedom within its horizon to
regain dynamical evolution. We predict that there
can be multiple cosmic inflations. The next
inflation era will stop after inflating for a period of
1019 sec if the past inflation period of our universe
was 10-33 sec.
Reference
[1]. S
hih-Yuin Lin, Chung-Hsien Chou and B. L.
Hu, Phys. Rev. D 81, 084018 (2010)
[2]. Chung-Hsien Chou and Hoi-Lai Yu, Modern
Phys. Lett. A 25, 1483-1489 (2010)
Research Activities on Strings
Kazuyuki Furuuchi (email: [email protected])
Staff scientist, 2007/8/1~present
projects.
In this academic year, my research was
mainly focused on the following two
I. Study of M-theory branes through
3-algebra
This is a continuation of the studies in previous
two years (see Refs. [1]). String theory is a most
promising framework for the unified description
of all the forces in the Nature. However, it is
known that there are five types of superstring
theory in ten space-time dimensions. M-theory is
a hypothetical theory in eleven dimensions which
is expected to unify these five types of superstring
theory. But its microscopic definition has not been
given yet. Recently, theoretical evidences that an
algebraic structure called Lie 3-algebra (or
Filippov algebra) is relevant for describing branes
in M-theory (M-branes) have been found. Lie
3-algebra is a natural extension of the familiar Lie
algebra which was relevant for the description of
multiple D-brane system in string theory. In
particular, Prof. Pei-Ming Ho at NTU together
with Prof. Yutaka Matsuo, Prof. Yosuke Imamura
and Dr. Shotaro Shiba at University of Tokyo
proposed in 2008 that M-theory five-brane
(M5-brane) in a large constant C-field background
can be described by an action with a NambuPoisson structure (NP M5-brane theory). NambuPoisson structure is an example of the infinite
dimensional Lie 3-algebra. They conjectured that
this new theory is related to the previously known
M5-brane theory by a map called Seiberg-Witten
map. Seiberg-Witten map relates commutativeand non-commutative descriptions of D-branes in
a large B-field background, and their conjecture is
an uplift of such system to M-theory. Although the
two descriptions of the M5-brane are expected to
be (S-matrix) equivalent due to the Seiberg-Witten
map, the NP M5-brane theory should provide
more economical description of the system, like
the non-commutative description of D-branes in a
large B-field background. Our previous works [1]
have given non-trivial evidences for the
conjecture.
A salient feature of the M5-brane theory is
that it contains a self-dual two-form gauge field.
In Ref. [2] I clarified how the self-dual relations
of the two-form gauge field are encoded in the
new NP M5-brane theory. Using this result, I
extended the previous analysis of the BPS string
solitons in two M5-brane theories through
Seiberg-Witten map in the third reference of [1]. I
found a complete match between the two
descriptions within the approximation considered.
This result provides further support for the
conjectured equivalence of the two M5-brane
theories.
The results of Ref. [3] can be roughly divided
into three parts. Firstly, we gave a precise
identification of the scaling limit in which the
description by NP M5-theory becomes
appropriate. Secondly, we made the background
independence of the theory manifest. And finally,
we obtained the all-order solution to the SeibergWitten map. All these results are vital for showing
the conjectural equivalence of the two M5-brane
theories.
Taiwan String Theory Group is making
unique and major contributions in the study of the
NP M5-brane theory which is internationally
recognized.
Preliminary results of Ref. [2] were presented
in Taiwan String Theory Workshop 2010 held at
NTNU in December 2009. Preliminary results of
Ref. [3] were presented by me as a plenary talk at
K E K T h e o r y Wo r k s h o p 2 0 1 0 i n M a r c h .
Discussions during the invited stay at the YITP
workshop "Branes, Strings and Black Holes" in
October 2010 were useful.
195 ‹‹- Research Activities of Individuals
II. D
-branes wrapped on fuzzy extra
dimensions and towards its
application to particle physics
phenomenology
This is a joint work with Prof. Kazumi
Okuyama at Shinshu University. Recently, Grand
Unified Theory (GUT) model building in F-theory
appeared as an promising direction to connect
string theory to particle physics. F-theory, like
M-theory, is related to the five types of superstring
theory by duality, and in particular it can be
regarded as a non-perturbative completion of type
IIB superstring theory. A notable feature of the
F-theory GUT model is the appearance of the
exceptional groups, which is rather constraining
compared with other GUT model buildings in
string theory framework, and thus more
predictive. It is quite natural, though not
necessary, to assume the hierarchy between the
GUT scale and the Planck scale and decouple
gravity in the F-theory GUT models. Recently
Verlinde and Wijnholt pointed out that if we
require the hierarchy between the GUT scale and
the Planck scale, the subspace which 7-branes in
F-theory wrap is naturally explained by noncommutative geometry, or "fuzzy" space.
However, they did not give a precise derivation of
the theory of 7-branes on the fuzzy space, instead
they took a practical approach and proposed a low
energy effective model of 7-branes of the fuzzy
space, hoping that it will be derived from string
theory. Kazumi and I realized D-branes wrapped
on fuzzy extra dimensions as classical vacua of
quiver gauge theories on D-branes probing a
singularity of a Calabi-Yau space in type IIB
superstring theory. In particular, the fuzzy extra
dimensions constructed are the fuzzy version of
del Pezzo surfaces, which are required to decouple
gravity in the F-theory GUT model building. This
new type of vacua are also interesting from the
quiver gauge theory perspective. We also explored
Research Activities of Individuals -›› 196
a possible application of our solutions for the
explanation of the structure of the Yukawa
couplings in the standard model of particle
physics.
The informal F-theory GUT study group at
NCTS led by Dr. Keijiro Takahashi (NCTU) was
extremely useful for this project. The lectures at
the String Theory Focus Group given by Dr.
Miranda C. N. Cheng (Harvard) and Dr. Wu-Yen
Chuang (Rutgers) were also helpful.
References
[1] K
. Furuuchi, S.-Y. D. Shih, T. Takimi,
"M-Theory Superalgebra From Multiple
Membranes" JHEP 0808:072 (2008); K.
Furuuchi and D. Tomino, "Supersymmetric
reduced models with a symmetry based on
Filippov algebra," JHEP 0905:070 (2009); K.
Furuuchi and T. Takimi, "String solitons in the
M5-brane worldvolume with a NambuPoisson structure and Seiberg-Witten map,"
JHEP 0908:050 (2009)
[2] K. Furuuchi, "Non-Linearly Extended SelfDual Relations From The Nambu-Bracket
Description Of M5-Brane In A Constant
C-Field Background,'' JHEP 1003:127 (2010)
[3] C . H. Chen, K. Furuuchi, P. M. Ho and T.
Takimi, "More on the Nambu-Poisson
M5-brane Theory: Scaling limit, background
independence and an all order solution to the
Seiberg-Witten map,'' arXiv:1006.5291 [hepth], accepted for publication in JHEP (in
press)
[4] K . Furuuchi and K. Okuyama, "D-branes
Wrapped on Fuzzy del Pezzo Surfaces,''
arXiv:1008.5012 [hep-th]
Research Activities on Condensed Matter Physics
Vidar Gudmundsson (Science Institute, University of Iceland, email: [email protected])
Visiting professor, 2009/9/1~12/20, 2010/2/28~5/20
Formalism for time-dependent transport
leads imposes correlations on the many-electron
states in the finite system [1].
n September 2009 I in cooperation with
Prof. Andrei Manolescu at the Reykjavik
University, Dr. Valeriu Moldoveanu at the
National Institute of Materials Physics in
Bucharest, and Prof. Chi-Shung Tang at the
National United University in MiaoLi prepared
for publication our manuscript on the application
of the Generalized Master Equation (GME) to
describe the transport of electrons through a finite
quantum wire weakly coupled to semi-infinite
leads. The manuscript has been published in the
New Journal of Physics [1]. We use the nonMarkovian GME to describe the time-dependent
transport of electrons in the transient regime and
as the system approaches a steady state.
Time-dependent transport of interacting
electrons in a magnetic field
In the summer months of 2009 we had already
discovered that our GME could be modified to
include the Coulomb interaction between the
electrons in the finite wire. We used the fall
months of 2009 to implement this
computationally. We use the so called "exact
diagonalization", or the "configuration
interaction" method to calculate all the interacting
many-electron Fock sector for 0 to N electrons,
and apply a unitary transformation on the GME to
rewrite it in the new interacting many-electron
basis. The first publication with these results,
where we demonstrate the expected Coulomb
blocking and other more subtle correlation effects
has appeared recently in Physical Review B [2].
The effects of the Coulomb blocking on the
current in the right lead of the system can be seen
in Figure 2.
Figure 1: A schematic view of the finite quantum wire (S)
coupled to the semi-infinite left (L) and right (R) lead.
The green shaded area indicates the contact area.
The lower panel shows the parabolic confinement of
the system and the leads with an embedded
subsystem in the finite wire.
By carefully restricting the number of states of
the finite wire used in the GME around the bias
window imposed by the leads we were able to
observe geometrical effects in the current through
the system using a many-electron formalism,
effects that are commonly only seen in transport
calculations built on scattering formalism for
single-electrons. In addition, the coupling to the
Figure 2: The current in the right lead as a function of the bias
and the time.
In addition, we used the fall to calculate the
transport properties of a more complex embedded
subsystem seen in Figure 3. In an external
magnetic field the system has single-electron
197 ‹‹- Research Activities of Individuals
Figure 3: A quantum ring embedded in a short quantum wire,
aw is the effective magnetic length.
states that can be localized either in the contact
area or away from it in the ring. We find that the
charging of the system depends strongly on the
presence or absence of the Coulomb interaction.
For a system empty at t=0 when the leads are
coupled we find that the Coulomb interaction
enhances the charging by imposing a correlation
between the leads states and the ring states that is
not present in the absence of the interaction. In
high magnetic field the these effects lead to
correlation oscillations long after the coupling of
the leads to the system, instead of a steady state.
The oscillations are shown in Figure 4 for 4
instances of time.
These results have been accepted for
publication in Physical Review B [3]. With a
student of mine in Iceland, Cosmin M. Gainar, we
been working on a description of a quantum
turnstile within the GME formalism. We have
submitted a manuscript about this project to
Physical Review B [4].
In December we presented our GME model to
the CCP-2009 conference of computational
physics held in Kaohsiung focusing on the effects
of the width and the bandstructure of the leads on
the transport. The slides of the talk are on the web
[7], but the contribution will be published in
Computer Physics Communications [5].
Figure 4: The induced density in the system at 4 close points in
time.
Research Activities of Individuals -›› 198
Presently, I am refining for publication a short
manuscript on the dynamic Coulomb correlations
between two parallel short 1D wires together with
Dr. Valeriu Moldoveanu and Prof. Andrei
Manolescu [6]. Together with Prof. Chi-Shung
Tang and a student of mine in Iceland, Nzar Rauf
Abdullah, we are calculating the time-dependent
properties of the transport through two parallel
finite quasi-2D quantum wires. The electrons in
the wires not only communicate through the
Coulomb interaction, but also by tunneling
through the finite barrier between them, and
through a perturbation potential in the form of a
window between the wires. The results of this
project will be compared to our earlier
calculations of the transport properties of a double
quantum wire within the single-electron
Lippmann-Schwinger scattering formalism.
In the spring of 2010 I have been working on
an extension of the GME formalism to include a
quantized electromagnetic field (EM). It is
interesting to remember that the GME formalism
was developed within quantum optics, but we are
not aware of any effort to use it to describe the
transport of electrons through a finite open central
system in an external electromagnetic field. We
have known for some time that, an extension of
the GME to include time-dependent Hamiltonian
for the central system is exceedingly difficult due
to the complex structure of the kernel of the
integro-differential equation representing the
GME. This was one of the reasons why we did not
try to include the mutual Coulomb interaction of
the electrons via a DFT mean-field approach, but
our experience form using the exact
diagonalization has helped us to understand that it
is possible to include a quantized EM-field in the
model. We have already completed most of the
analytical preparation and are now wrestling with
the immense computational problem at hand. To
master that we will accomplish the task in steps.
In the first one we shall build a model of the
isolated Coulomb interacting electrons in an
external constant classical magnetic field
interacting with a single mode quantized
EM-field, we already have a program ready for
this step we are testing now. In the next step we
open up the system to the leads, and the third step
will include an external EM multi-mode field
acting as a reservoir to the EM-field. It is clear
that we will be working on this model in the next
months and years. I have presented my work on
the transport of Coulomb interacting electrons in a
talk at the NCTS, the slides are on my web server
in Iceland [8].
Cooperation
Here in Taiwan I have been cooperating with
Prof. Chi-Shung Tang from the NUU in MiaoLi.
We have been discussing cooperation with
Prof. Shun-Jen Cheng at the NCTU. In the fall I
met weekly with students of Prof. Chi-Shung Tang
from the NUU discussing the application of open
software. In the spring I have met weekly with
two students from the group of Prof. Shun-Jen
Cheng from the NCTU that Prof. Chi-Shung Tang
i s s u p e r v i s i n g . We h a v e b e e n d i s c u s s i n g
computational methods and software for parallel
calculations using FORTRAN, and transport
described by the Lippmann-Schwinger scattering
approach.
Me and Prof. Chi-Shung Tang have been
working on a proposal for a Memorandum of
Understanding (MOU) between the three
universities, NUU, NCTU in Taiwan, and UI in
Iceland. We have met a goodwill in all of the
universities and hope to have a contract for
graduate students and academics before the fall of
2010. The Office of International Affairs of the
NTHU has also approached me for a discussion
about a similar agreement between the NHTU and
UI. This will now be decided upon by the two
universities in the next weeks. It is our hope that
these agreements can establish a framework for
exchange of graduate students and cooperation
b e t w e e n r e s e a r c h g r o u p s i n t h e d i ff e r e n t
universities.
Once again, I have experienced the highly
professional work of the office staff, the
organizers, and the directors of the NCTS. I am
amazed by the hospitality of the Taiwanese people
I have met everywhere and I am very thankful for
the opportunity to renew and deepen the relation
with my friends in Taiwan.
199 ‹‹- Research Activities of Individuals
Publications
[1] T
ime-dependent transport via the generalized
master equation through a finite quantum wire
w i t h a n e m b e d d e d s u b s y s t e m , Vi d a r
Gudmundsson, Cosmin Gainar, Chi-Shung
Tang, Valeriu Moldoveanu, and Andrei
Manolescu, New Journal of Physics 11,
113007 (2009), (arXiv:0903.3491).
[2] Coulomb interaction and transient charging of
excited states in open nanosystems, Valeriu
Moldoveanu, Andrei Manolescu, Chi-Shung
Tang, and Vidar Gudmundsson, Phys. Rev.
B 81, 155442 (2010), (arXiv:1001.0047).
[3] Correlated time-dependent transport through a
2D quantum structure, Vidar Gudmundsson,
Chi-Shung Tang, Olafur Jonasson, Valeriu
Moldoveanu, and Andrei Manolescu, Phys.
Rev. B 81, 205319 (2010), (arXiv:1002.1556).
[4] T i m e - d e p e n d e n t m a g n e t o t r a n s p o r t i n
semiconductor nanostructures via the
g e n e r a l i z e d m a s t e r e q u a t i o n , Vi d a r
Gudmundsson, Chi-Shung Tang, Cosmin
Mihai Gainar, Valeriu Moldoveanu, and
Andr ei Manolescu, Computer Physics
Communications , submitted (2010),
(arXiv:1002.1579).
[5] Turnstile pumping through an open quantum
w i r e , C o s m i n M i h a i G a i n a r, Va l e r i u
Moldoveanu, Andrei Manolescu, and Vidar
Gudmundsson, Phys. Rev. B , submitted
(2010), (arXiv:1004.4052).
Research Activities of Individuals -›› 200
[6] D
ynamic Coulomb correlations in a double
nanosystem, Valeriu Moldoveanu, Andrei
Manolescu, and Vidar Gudmundsson, Phys.
R e v. L e t t e r s , s u b m i t t e d ( 2 0 1 0 ) ,
(arXiv:1005.3860).
Lectures
[7] T
ime-dependent transport through quantum
nanostructures, NCTS, HsinChu, Taiwan,
September (2009). (http://hartree.raunvis.
hi.is/~vidar/Rann/Fyrirlestrar/NCTS_09.pdf).
[8] T i m e - d e p e n d e n t m a g n e t o t r a n s p o r t i n
semiconductor nanostructures via the
generalized master equation, CCP-2009,
KaoHsiung, Taiwan, December 16 (2009).
(http://hartree.raunvis.hi.is/~vidar/Rann/
Fyrirlestrar/CCP-2009-VG.pdf).
Research Activities on String Theory
Takayuki Hirayama (Masukawa Institute at Kyoto Sanyo University, email: [email protected])
Postdoctoral researcher, 2007/9/1~2010/8/31
have been working on non perturbative
effects of gauge theory and quantum
gravity. I have published two papers with my
collaborators in the academic year of 2009.
In the paper [1], I have studied quark mass
dependence of hadrons using a holographic dual
gravitational description of QCD (Quantum
Chromo Dynamics). QCD is a gauge theory which
describes the interactions between quarks and
gluons. Since the interaction becomes very strong
in the low energy, it is difficult to analyze. In the
low energy, the chiral symmetry is dynamically
broken by the quark condensate, and quarks make
composites, i.e. mesons and baryons. These
dynamics cannot be computed from the
perturbative QCD approach. Therefore it is
important to find another approach. In string
theory, there is a conjecture which claims the
equivalence between a string theory or
supergravity on a curved space and a quantum
field theory without gravity like QCD. The
example which have been studied intensively is
the duality between Type IIB string theory in a
space of 5 dimensional Anti-de Sitter space times
5 dimensional sphere and the four dimensional
N=4 supersymmetric Yang-Mills theory. This
duality is a weak-strong duality in a sense that a
weak string coupling region of Type IIB string
theory is dual to a strong gauge coupling region of
Yang-Mills theory. Therefore this AdS/CFT
correspondence offers a quite powerful tool of
computing a strongly coupled gauge theory from a
weakly coupled gravity theory. I have been
challenging to construct the gravity dual
description of QCD. One successful model was
constructed by Sakai and Sugimoto which is based
on D-branes in string theory. Though their model
is successful, the pion, which is associated with
the chiral symmetry breaking, is massless
although the pion has a mass about 140 Mev. I and
my collaborators studied how to introduce the
pion mass, i.e. the quark mass in the academic
year 2007. In the paper [1], we then studied how
much the masses of mesons and baryons are
shifted by the presence of quark masses. We gave
the formulae to compute their values and
compared the results with the data from lattice
calculations. We found that our values are
consistent with lattice results and thus our model
is a good candidate for the holographic dual of
QCD. Since the model is known to have many
other unsuccessful points, it is important to
improve our model.
In the paper [2], we studied the Unruh effect in
terms of AdS/CFT correspondence. Einstein’s
general relativity is based on gravitational
equivalence principle. That is, the gravitational
force as experienced locally while standing on a
massive body (such as the Earth) is actually the
same as the pseudo-force experienced by an
observer in a non-inertial (accelerated) frame of
reference. This principle implies an interesting
consequence in quantum gravity. As Hawking
discovered, a black hole radiates the Hawking
radiation with temperature T. Then with the
equivalence principle, we can conclude that an
accelerating observer will see the black body
radiation with temperature T which is proportional
to the value of acceleration. This effect is called
the Unruh effect. However this effect is often
dispute since it has not been observed and it is
difficult to accept. Therefore we study the Unruh
effect on QCD using AdS/CFT correspondence. If
the Unruh effect exists, the chiral condensate will
be resolved when the Unruh temperature becomes
above a critical temperature. We realize the
accelerating observer by considering an
accelerating string in AdS space and study the
chiral condensate of supersymmetric QCD from
the dual gravitational description. We then showed
that the chiral symmetry breaking will be restored
and the meson will not be composed above a
201 ‹‹- Research Activities of Individuals
critical temperature. Our study shows that the
Unruh effect really exists and can be treated in
terms of AdS/CFT correspondence.
References
[1] Q
uark Mass Dependence of Hadron Spectrum
in Holographic QCD. Koji Hashimoto,
Takayuki Hirayama, Deog Ki Hong. Phys.
Rev.D81:045016, 2010
[2] U nruh effect and Holography. Takayuki
Hirayama, Pei-Wen Kao, Shoichi Kawamoto,
Feng-Li Lin, 27pp. e-Print: arXiv:1001.1289
[hep-th]
Research Activities of Individuals -›› 202
Research Activities on Particle Physics
Jae Sik Lee (email:[email protected])
Assistant research scholar, 2008/7/1~present
et me begin with our efforts to go beyond
the Minimal Supersymmetric extension
of the Standard Model (MSSM). The MSSM has a
weak point known as the mu problem. For a
supersymmetric model to be phenomenologically
viable, the size of the mu parameter should be
a r o u n d t h e s c a l e o f 1 Te V. T h e m i n i m a l
supersymmetric model to achieve this goal is the
Next-to-Minimal Supersymmetric Standard Model
(NMSSM) which adds one more gauge singlet to
the MSSM. Furthermore, it is well known that the
strongfirst-order phase transition, which is needed
for the mechanism of the electro-weak
baryogenesis to explain the matter-dominance of
our Universe, can be realized in the NMSSM
more comfortably.
We have made a team for the NMSS M
phenomenology with explicit CP violation. The
team consists of Prof. Kingman Cheung, Dr. TieJiun Hou, Dr. Eibun Senaha, and myself. We have
done the calculation of the Higgs mass spectrum
and the mixing by including the higher-order
corrections beyond the one-loop level [1].Now we
are working on the constraints from the nonobservation of the electric dipole moments on the
CP phases in the NMSSM, the electro-weak phase
transition, relevant B- and K-meson observables
with high tan(beta) values, etc.
We believe that Top-quark Physics will be one
of the most important topics in the LHC era and it
is likely for any New Physics to show through the
productions and decays of the top quarks.
Motivated by a possible anomaly in the forwardbackward asymmetry of top quark observed at the
Tevatron, we perform a model independent
analysis using an effective Lagrangian with dim-6
four-quark operators [2]. We derive necessary
conditions on new physics structures and the
couplings that are consistent with the top-quark
pair production cross section and the forwardbackward asymmetry measured at the Tevatron,
and discuss possible new physics scenarios that
could generate such dim-6 operators. We are
extending our study to include the top-quark pair
invariant mass and rapidity-gap distributions,
resonance productions of new particle(s) at the
LHC, top-quark polarizations in general, and
impacts on the low-energy flavour observables.
We emphasize the importance of the LHC as a
top-quark factory as well as a New-Physics
discovery machine.
On the other hand, with my UK colleagues, we
present a new geometric approach to the flavour
decomposition of an arbitrary soft
supersymmetry-breaking sector in the MSSM [3].
Our approach is based on the geometry that results
from the quark and lepton Yukawa couplings, and
enables us to derive the necessary and sufficient
conditions for a linearly-independent basis of
matrices related to the completeness of the
internal [SU(3) x U(1)]^5 flavour space. In a
second step, we calculate the effective Yukawa
couplings that are enhanced at large values of
tan(beta) for general soft supersymmetry-breaking
mass parameters. We highlight the contributions
due to non-universal terms in the flavour
decompositions of the sfermion mass matrices. We
present numerical examples illustrating how such
terms are induced by renormalization-group
evolution starting from universal input boundary
conditions, and demonstrate their importance for
the flavour-violating effective Yukawa couplings
of quarks.
We also analyze the constraints imposed by
experimental upper limits on electric dipole
moments within the Maximally CP- and
Minimally Flavour-Violating version of the
MSSM [4]. Since the MCPMFV scenario has 6
non-standard CP-violating phases, in addition to
the CP-odd QCD vacuum phase \theta_QCD,
cancellations may occur among the CP-violating
contributions to the three measured EDMs, those
of the Thallium, neutron and Mercury, leaving
open the possibility of relatively large values of
the other CP-violating observables. We develop a
novel geometric method that uses the small-phase
203 ‹‹- Research Activities of Individuals
approximation as a starting point, takes the
existing EDM constraints into account, and
enables us to find maximal values of other
CP-violating observables, such as the EDMs of
the Deuteron and muon, the CP-violating
asymmetry in b -> s \gamma decay, and the B_s
mixing phase. We apply this geometric method to
provide upper limits on these observables within
specific benchmark supersymmetric scenarios,
including extensions that allow for a non-zero \
theta_QCD.
At the time of writing this Annual Report, we
have two preprints. The first one [5] is a sequel to
the paper published previous year. In the paper,
we provide a comparative study of the Higgs
boson mass measurements based on two
approaches to the dileptonic decay of W-bosons
produced by the Higgs boson decay, one using the
kinematic variable M_T^true and the other using
the M_T2-assisted on-shell reconstruction of the
invisible neutrino momenta. We found that these
two approaches can determine the Higgs boson
mass with a similar accuracy for both of the two
main production mechanisms of the SM Higgs
boson at the LHC, i.e. the gluon-gluon fusion and
the weak vector boson fusion. It is noticed also
that the efficiency of both approaches might be
improved with an appropriate M_T2-cut. The
second preprint [6] is a Mathematical note related
to our geometric approach to CP Violation [4].
The note presents an analytic construction of the
optimal unit-norm direction that maximizes or
minimizes the objective linear expression which is
under a system of linear constraints. We have
submitted it to the mathematical journal of "Linear
Algebra and Its Applications" and are waiting for
a constructive referee report.
Lastly, I report our invited contribution to
Summary document Pre-SUSY 2009 has been
published as in Ref.[7]. I am closing my Annual
report by accounting that the preprints mentioned
in my contribution to the 2009 Annual Report
have been published as Refs.[8,9]. The first one
[8] is on a possibility of dimension-five operators
with strong couplings in the superpotential as an
alternative origin of the particle masses. And the
second one [9] is on the exotically decaying
MSSM Higgs bosons at hadron colliders.
Research Activities of Individuals -›› 204
References
[1] K
ingman Cheung, Tie-Jiun Hou, Jae Sik Lee,
Eibun Senaha, The Higgs Boson Sector of the
Next-to-MSSM with CP Violation, To appear
in Phys. Rev. D, arXiv:1006.1458 [hep-ph]
[2] D ong-Won Jung, P. Ko, Jae Sik Lee, Soohyeon Nam, Model independent analysis of
the forward-backward asymmetry of top
quark production at the Tevatron, Phys. Lett.
B691, 238-242 (2010)
[3] J ohn Ellis, Robert N. Hodgkinson, Jae Sik
Lee, Apostolos Pilaftsis, Flavour Geometry
and Effective Yukawa Couplings in the
MSSM, JHEP 1002:016 (2010)
[4] John Ellis, Jae Sik Lee, Apostolos Pilaftsis, A
G e o m e t r i c A p p r o a c h t o C P Vi o l a t i o n :
Applications to the MCPMFV SUSY Model,
To appear in JHEP, arXiv:1006.3087 [hep-ph]
[5] Kiwoon Choi, Jae Sik Lee, Chan Beom Park,
Measuring the Higgs boson mass with
transverse mass variables, arXiv:1008.2690
[hep-ph]
[6] John Ellis, Jae Sik Lee, Apostolos Pilaftsis,
Note on a Differential-Geometrical
Construction of Optimal Directions in
Linearly-Constrained Systems,
arXiv:1009.1151 [math.OC]
[7] P. Nath et al., The Hunt for New Physics at
the Large Hadron Collider, Nucl. Phys. Proc.
Suppl. 200-202, 185-417 (2010)
[8] D ong-Won Jung, Otto C.W. Kong, Jae Sik
Lee, Holomorphic Supersymmetric NambuJona-Lasinio Model, Phys. Rev. D81, 031701
(2010)
[9] J . S . L e e , Y. P e t e r s , A . P i l a f t s i s , C .
Schwanenberger, Strangephilic Higgs Bosons
in the MSSM, Eur. Phys. J. C66, 261-269
(2010)
Research Activity on Plasma Science
Chia-Hsien Lin (Institute of Space Science, National Central University, email: [email protected])
Postdoctoral researcher, 2010/1/1~7/31
Research Plans and Objectives
he subject of my latest research interest is
the coronal mass ejections (CMEs),
which I began to study while being a postdoc in
Dr. Peter Gallagher's Astrophysics Research
Group at Trinity College Dublin (TCD).
Solar corona is the outermost and hottest layer
in the solar atmosphere, and coronal mass
ejections (CMEs) are the most violent events in
this layer. They eject large amount of coronal
mass and magnetic flux from the Sun to as far as
the boundary of the solar system. They can
damage our space station and satellites, and
disrupt the wireless communications on Earth.
The aim of my study on the CMEs has been to
understand what kind of condition(s) and
mechanism(s) would trigger such eruption and
allow it to propagate away from the Sun, in the
hope that the results would lead to better spaceweather forecasts and more accurate predictions of
CME occurrence and magnitude.
While working at TCD, I had examined two
CMEs using 2-D extreme ultraviolet (EUV)
images and white-light coronagraphs, along with
hard X-ray (HXR) and soft X-ray (SXR) data. My
current work has been to implement a statistically
significant study on the CMEs, utilizing the data
from different observation tools, including soft
X - r a y, h a r d X - r a y, u l t r a v i o l e t c o r o n a l
spectrometer, coronagraph and imagers. The
purpose of utilizing multi-wavelength, multiinstrument observational data is to be able to
study the CMEs from different aspects.
The project will consist of two main phases,
the first one is the data collection and processing,
and the second one is the analysis and
interpretation of the processed data. During the
first phase, the objective is to build a large
database containing the processed data of the
CME events that have been observed by different
instruments. Since the data processing procedures
of different instruments are different, the main
task in this phase will be to install and become
fluent with these different procedures. Such
comprehensive database will be useful for many
other future studies on CMEs and CME-related
events.
In the second phase, I plan to first develop a
robust and reliable procedure that can be applied
to many events to extract all the correct
information from CMEs in a consistent and
efficient manner, and then apply the procedure to
the CME data collected in the first phase. My
examination strategy is to compare, both
quantitatively and qualitatively, the observations
and various CME models. The theory most
consistent with observations can be used to infer
the physics of the observed CMEs, while any
discrepancies between the observations and
theories can indicate how to improve the existing
theories.
Research Progress
During the first several months as a postdoc at
the National Center for Theoretical Sciences, I
worked at the National Tsing-Hua University, and
my main work was to install and run the softwares
for processing the data from UltraViolet Coronal
Spectrometer (UVCS). Such data and analysis
would allow us to study the jets and/or wave
propagations associated with the CMEs.
In the early December 2009, I attended the
Hinode III meeting in Tokyo to present my work
on CMEs. During the meeting, I met Dr. Angelos
Vourlidas, from the Naval Research Lab, who
expressed his interest for a collaboration utilizing
the data from the Solar TErrestial Relation
Observatory (STEREO). STEREO is a space
observatory designed to observe the Sun from two
205 ‹‹- Research Activities of Individuals
viewpoints, and its data can be used to reconstruct
the 3D view of the observed objects, including
CMEs.
Since 2010 March, I was relocated to the
Plasma and Space Science Center at the National
Cheng-Kung University, in order to be able to
work closely with the solar physicists there,
specifically, Prof. C.-Z. Cheng and Dr. Ya-Hui
Yang. I began to implement the processing and
analysis procedures for STEREO data, with the
help from several solar physicists from various
institutes. I have so far processed the data and
constructed the 3D kinematics for the CME event
occurred on 2008 Jan. 2nd.
In addition to my CME project, I also joined
Prof. Cheng and Dr. Yang to begin a study on the
radio emissions caused by the magnetic
reconnections during CME/solar flare events. This
has been a preparation for a project to use the
radio data from ALMA.
In June, during the West Pacific Geophysics
Meeting (WPGM) in Taipei and the International
Space Plasma Symposium in NCKU, I met Dr.
Vourlidas again, as well as two CME modellers,
Dr. Jun Lin and Dr. James Chen. This gave me a
rare opportunity to have long and very
constructive discussions with the three CME
scientists. These discussions have greatly
enhanced my understanding about the CMEs,
from both theoretical and observational point of
view.
In the early July, I attended the Asia Oceania
Geophysics Society (AOGS) meeting in
Research Activities of Individuals -›› 206
Hyderabad, India. I was granted an oral
presentation opportunity to present my work. The
solar sessions of this meeting covered various
topics of the solar physics, from wave
propagations to magnetic reconnections to coronal
mass ejections and solar winds. Since the solar
sessions were relatively small, it was easy to meet
and discuss with fellow participants about
different aspects of the Sun and their connections.
These discussions, as well as the talks, were very
helpful in stirring up new ideas.
Future
I have been offered an assistant professor
position by the Institute of Space Science at the
National Central University. The position will
commence on August 1st 2010. At the new
position, I will continue my work on CMEs, and
cultivate students' interest in the solar physics,
which, hopefully, will lead to a prosperous future
for solar research in Taiwan.
Research Activities on Lattice Gauge Theory in Physics of the Large Hadron Collider
Chi-Jen David Lin (Institute of Physics, National Chiao Tung University; email: [email protected])
Center Scientist, 2009/2/1/~2012/1/31
Introduction
ince I joined the NCTS in 2007, I have
been working on projects in physics
related to the Large Hadron Collider using largescale numerical simulations in Lattice Gauge
Theory. This is reflected in two main research
avenues that I am pursuing. First, I am studying
the scenario of electroweak symmetry breaking
via strongly-coupled gauge theories at TeV scale.
Second, I am performing calculations for decay
amplitude of baryons containing a b quark, which
is the main subject of the LHC-b experimental
project. Finally, I am computing the spectrum and
vacuum propertiesof the Higgs-Yukawa systems at
the presence of large Yukawa coupling.
Hardware
The start-up equipment fund for my position
was granted in the summer of 2007, from the
National Science Council and Faculty of Sience,
National Chiao-Tung University. From August
2007 to December 2007, I played the main role in
the purchase of a PC cluster using this start-up
fund. The cluster was delivered between January
and April 2008. Now it contains twenty-six
computing nodes. Each node has two quad-code
CPUs and sixteen gigabites of memory (with error
checking). Twenty-two of these nodes are
connected via a Double-Data-Rate (up to 20
gigabits per second) infiniband switch. The other
four are on a gigabit network. In addition to the
computing nodes, we have a six-terabite disc array
for storage.
Recently, I started to set up facilities for highperformance computing using GPU. I already
have six such computing nodes, and will expand
to have eight soon.
Dynamical Electroweak Symmetry
Breaking
Walking technicolour is one of the candidates
that generate electroweak symmetry breaking at
TeV scale without the need for the Higgs particles.
It is a strongly-coupled gauge theory, hence lattice
gauge theory can play an important role in this
research avenue. In the walking-technicolour
scenario, the coupling constant in the gauge
theory increases over a range of scale when the
energy is decreased, then it becomes "frozen". At
the very low energy regime, it starts increasing
again, such that conformal symmetry and chiral
symmetry are broken dynamically. The system
then develops an energy gap which generates the
spectrum.
The reason why such a scenario is required is
due to the need to dynamically suppress the
flavour-changing neutral currents (FCNC) in
physics beyond the Standard Model. A walking
theory is likely to produce large anomalous
dimensions for the operators that generate the
Standard Model fermion masses. This can then lift
the scale at which flavour emerges, hence
suppress the FCNC. It is not easy even just to find
a theory which has the "walking" feature and
dynamical symmetry breaking at low energy.
Exploratory result using the step-scaling method
was reported by Appelquist and collaborators
recently [1].These authors calculated the coupling
constant in the so-called Schroedinger functional
scheme for QCD-like theories with large numbers
of flavours. They discovered that the coupling
constant would stop running for a range of scale in
some of these theories. However, the coupling
constant not physical, hence depends on the
renormalisation scheme in which it is calculated.
Therefore it is important to check the claim by
Appelquist et al. in at least another scheme.
207 ‹‹- Research Activities of Individuals
I have formed a collaboration with physicists
in Professor Tetsuya Onogi's group at Osaka
University. We are studying the scale dependence
of the coupling constant in these theories iusing
the Creutz-ratio scheme, as well as the TwistedPolyakov-line (TPL) scheme. In the Creutz-ratio
scheme, we fix the scheme by keeping constant
the ratio between the Wilson-loop size and the
lattice size. This specifies the scheme. We then
perform calculations at various lattice sizes and
extrapolate to the continuum limit at each step.
The lattice size is the renormalisation scale in this
procedure. Since this is a new scheme, we have
performed exploratory numerical study of the
coupling constant in the quenched prroximation
for QCD and found that it worked well [2], since
it could reproduce the perturbative results in the
region where perturbation theory would apply.
Figure 1 shows the result of this calculation,
where the x-axis is the scale and the y-axis is the
coupling constant.
2 shows the quenched feasility study of the TPL
scheme. Figure 3 exhibits the data in the case of
12 flavours, where x-axis is the lattice spacing
(left-hand size is coarser), y-axis is proportional to
the coupling constant and different symbols
correspond to various lattice sizes. Figure 4 shows
the beta function obtained from our data. From
this plot, it is evident that the running of the
coupling constant does slow down, but it is not
possible to conclude that the theory contains an IR
fixed point.
Physics of the B-Baryon
For the simulations with 12 flavours, we go for
the TPL scheme, since the required lattice size is
smaller in this scheme, compared to the Creutzratio scheme. From our preliminary result [3],
there is evidence that the theory flows into an
infrared fixed point in this scheme as well. Figure
Research Activities of Individuals -›› 208
A b-baryon is composed of three valence
quarks, namely, a b-quark and two light quarks.
The rare decay channels in which a non-stranged
b-baryon decays into a stranged baryon plus a
photon or a lepton pair are sensitive to new
physics effects involving the mixing of quarks via
right-handed coupling structure that is absent in
the Standard Model. This structure cannot be
probed by existing experiments performed with
the B mesons which do not carry spin. With
William Detmold and Matthew Wingate, I have
set up a programme to pin down the relevant
matrix elements in the above decay channel as our
final goal.
In our programme, we use the dynamical
gauge configurations generated and kindly lent to
us by the RBC Collaboration. The lattice size is
24-cube times 64, with lattice spacing around 0.1
fm. The 2+1 flavours of dynamical quarks in
these RBC configurations are domain wall
fermions. We also use the same fermions for our
valence light quarks. For the heavy quark, we use
the static approximation where the heavy-quark
mass is infinite. The most time-consuming step in
this programme is to generate light-quark
propagators. We have accumulated many such
propagators using my PC cluster and other
computing resources in the USA.
As the first step towards the calculation of rare
decay matrix elements of b-baryons, we have
studied the spectrum of these baryons. In
particular, we are investigating the light-quark
mass dependence of the spectrum. There have
been very few lattice calculations for the b-baryon
spectrum, and the parameters (quark mass, lattice
volume, etc.) in our work are the closest to the
physical values. Figure 5 collects our results for
this spectrum calculation. It is shown that our
results are largely compatible with experiments.
This calculation has been published in Ref. [4].
We are also performing the same calculation using
a different heavy-quark formulation. The result
has been reported in Ref. [5]. At the same time,
we are proceeding with calculations of various
matrix elements. We have accumulated data for
measuring the coupling amongst a vector B
meson, a pseudoscalar B meson and a pion.
Physics of large Yukawa Coupling
The understanding of the Higgs-Yukawa model
at large Yukawa coupling is phenomenologically
relevant due to the search for extra generation of
fermions. It is plausible that the large Yukawa
coupling may induce condensation involving
fermions to break electrowek symmetry.It is also
an interesting field-theoretical topic to investigate
the symmetry breaking pattern and the spectrum
of such scenario.
To study such a system, we have to scan a
large parameter space to determine the phase
transition lines and work out bare parameters
wchich correspond to a constant (high) cut-off
scale. This is because the cut-off cannot be
removed in this field theory. Based on the existing
work in the literature, there are two disconnected
phases where the scalar field has a vanishing
vacuum expectation value (vev) in the bare
parameter space. One of these two phases is in the
small bare Yukawa coupling regime, the other is in
the large bare Yukawa coupling regime. Physics
in or near the second regime has not been well
studied and it is our goal to probe this are in the
parameter space. We plan to calculate the scalar
and fermion mass spectrum, as well as the mass of
the bound state composed of the scalar and the
fermion.
I am now working on this research topic, in
collaboration with Professor George Hou at
National Taiwan University under an Academic
Summit Programme funded the National Science
Council. We have also established collaboration
with Professor Karl Jansen's group in DESY
Zeuthen.
In this project, we have the scalar and fermion
fields on the lattice and couple them vis the
Yukawa coupling. The fermions are discretised
using the overlap formalism which preserves
exact chiral symmetry on the lattice. Right now,
we already have the computer program ready and
is performing the scanning of the parameter space.
Figure 6 shows one of such runs. In this figure,
we plot the scalar vev in lattice units against the
bare Yukawa coupling at constant bare scalar mass
and bare scalar quartic coupling. It is evident that
a vev is developed when the Yukawa coupling
grows stronger, and then it disappears again when
the coupling is further increased. This signals the
possibility of having two disconnected phases in
209 ‹‹- Research Activities of Individuals
which the scalar vev vanishes. This can also be
used to determine the cut-off scale.
References
[1] T
. Appelquist, G. Fleming and E. Neil,
"Lattice Study of Conformal Behavior in
SU(3) Yang-Mills Theories", Phys.Rev.
D79:076010, 2009
[2] E . Bilgici, A. Flachi, E. Itou, M. Kurachi,
C.-J.D. Lin, H. Matsufuru, H. Ohki, T. Onogi
and T. Yamazaki, "A New scheme for the
running coupling constant in gauge theories
using Wilson loops", Phys.Rev.D80:034507,
2009
Research Activities of Individuals -›› 210
[3] E
. Bilgici, A. Flachi, E. Itou, M. Kurachi,
C.-J.D. Lin, H. Matsufuru, H. Ohki, T. Onogi,
E. Shintani and T. Yamazaki, "Search for the
IR fixed point in the twisted Polyakov loop
scheme", arXiv:0910.4196 [hep-lat] (Lattice
2009 proceedings)
[4] W. Detmold, C.-J.D. Lin and M. Wingate,
"Bottom hadron mass splittings in the static
limit from 2+1 flavour lattice QCD", Nucl.
Phys.B818:17-27, 2009
[5] S. Meinel, W. Detmold, C.-J.D. Lin and M.
Wingate, "Bottom hadrons from lattice QCD
with domain wall and NRQCD fermions",
arXiv:0909.3837 [hep-lat] (Lattice 2009
proceedings)
Research Activities on Condensed Matter Physics
Pei-Jen Fareh Lin (National High Magnetic Field Laboratory, Applied Superconductivity Center; email: [email protected])
Postdoctoral researcher, 2008/12/1~2010/9/13
uperconducting materials are candidates
for small and fast electronic device
becauses of their low power loss and fast
response; the electrodynamic response of
superconductor attracts special interest for both
practical and fundamental reasons. The essential
issue for applications is the ability to control and
extract a response signal. However, in spite of the
fact that it can be a perfect conductor and perfect
diamagnet in the absence of external
electrodynamic field, physical properties of
superconducting material can change dramatically
in the presence of external fields; the advantages
of superconducting materials are reduced by a
mechanism which is not yet clearly understood.
equation [1]. The driving electric field is
introduced into the system through covariant
derivatives. The solution is steady-state, and work
done by the input signal is dissipated through
vortex cores, mainly by scattering with phonons.
The solution shows nonlinear response. The
existence of well-defined parameters to control
nonlinear effects is important for any practical
application in electronics, and a normalised
distance from the normal-superconducting phasetransition boundary is found to be a parameter to
which the response is sensitive. Beyond linear
response, our predictions are put forward
regarding the suppression of heating and also the
lattice configuration at high frequency [1].
I study the electrodynamic properties of
superconductors, particularly the response theory
of the type-II superconductor using GinzburgLandau (GL) types of theories and Maxwell
equations. In the presence of a strong enough
magnetic field, the magnetic field will penetrate
into a sample in a form of quantized flux tube.
The center of the flux tube is in the normal state
and it is surrounded by circulating supercurrent,
which is a vortex. Such a vortex is a topological
defect; it is stable under perturbations. When a
vortex moves, energy dissipates. The response and
dynamics of vortices can dominate the physical
properties of superconductor.
The applied-field response can be thought of as
analogous to thermal fluctuations, in the sense that
they both result in vibration of the vortex lattice.
The influence of the electromagnetic fluctuation is
stronger at the nucleation region of
superconductivity than deep inside the
superconducting phase. Since at high frequency
the motion of vortices is limited, the influence
from electric field is suppressed, as is the Hall
effect.
The GL theory has a microscopic base; it can
be derived from BSC theory under certain
assumptions, even though it has also been shown
to be a useful tool beyond its microscopic limit.
Nevertheless, to study using microscopic theory
the response of a dense vortex region where
vortices form a lattice is a sophisticated and
seemingly intractable problem.
The dynamical response of the vortex lattice in
the presence of an oscillating driving field is
calculated by constructing an analytical solution
of the Time-Dependent Ginzburg-Landau (TDGL)
Even with the simplified model of the GL
theory, the set of equations is still difficult to
solve. To provide a simple formula for wider
application, we studied the forces acting on
vortices in the linear response region [2].
Consideration of the balance of forces on
superconducting condensate at low frequencies
leads to the well-known Josephson Relation.
Using the GL expression for the current, an
expression relating the electric field to the vortex
velocity via the magnetic field is obtained. This
expression is the Josephson Relation,
supplemented by a term accounting for the inertia
of charge carriers. We call this the Inertial
Josephson Relation (IJR); it may be viewed as the
Josephson Relation extended to the case of sub-
211 ‹‹- Research Activities of Individuals
gap high-frequency response. When applied to
vortex dynamics the IJR yields the same
conductivity as exact solution of the GinzburgLandau theory. Favourable comparison with NbN
experimental data in the optical region is made.
We would like to point out here that widely used
model [3] base on JR is not applicable in high
frequency.
This comparison with experiment of the real
part of conductivity is not as good as in the case of
the imaginary part. The reason comes from the
fact that the normal-part contribution should be
accounted for [4]. To understand the real part of
conducti vity, the dissipative par t , I h a v e
collaborated with P.Lipavsky on proposing a
modified TDGL theory, with the assumption of
local equilibrium made in the reference frame
floating with normal electrons. This theory with
floating nucleation kernel is applied to the far
infrared conductivity in a vortex lattice. It yields
better agreement with recent experimental data
than the TDGL theory. This new approach does
not generally introduce significant additional
c o m p l e x i t y, i t m a y b e p r o m i s i n g i n t h e
consideration of systems farther from equilibrium
than is usually amenable to analysis via standard
TDGL theory. Following the new approach, we
study the force acting on the system and we obtain
a simplified model for the set of TDGL equations
[5].
Another project on paraconductivity, the
pretransitional rise in the conductivity typical for
high-Tc superconductor, is studied with an
experimental group in NCTU. The experimental
group can efficiently tune the hole-dopping rate
on oxygen deficient Y0.7Ca0.3Ba2Cu3O7-δ film
by doping with Ca. Conductivity as function of
temperature are measured on various samples,
from overdoped to underdoped region. In such
YBCO system, the distance between
superconducting layers, which are CO-planes, are
tuned, this influencing also their physical
properties. A dome-like curve in Tc vs Ca doping
rate, with corresponding slope changing rate of
paraconductivity in temperature are observed.
Research Activities of Individuals -›› 212
Base on Lawrence-Doniach theory, a tool for the
study of layered materials, we found that the
paraconductivity for samples beyond optimized
doping level is dominated by thermal fluctuations.
In particular for a quasi-two-dimensional sample
the fluctuation effects are stronger than in a threedimensional sample. For very under-doped
samples, the theory based on thermal fluctuations
has qualitative comparison with experimental
results, but not quantitative; we expect the
existence of other mechanisms [6].
S uperconductors have a w ide range of
application, from nanoscale electronic device to
resonator cavity of particle accelerator. Present
studies focus on the homogeneous system where
vortices can move freely. Further study on pinning
effects is desirable, as pinning is used to decrease
the mobility of vortices, in turn reducing the
dissipation of input signal.
References
[1] F
. P. -J. Lin, P. Matlock, "High-frequency
dynamical response of Abrikosov vortex
lattice in flux-flow region", Phys. Rev. B
(2010)
[2] F. P. -J. Lin, P. Lipavsky, P. Matlock, "Inertial
Josephson Relation for FIR frequencies",
submitted to Phys. Rev. Lett. (2010)
[3] J.~I.~Gittleman, B.~Rosenblum, Phys. Rev.
Lett. 16, 734 (1966)
[4] P.-J. Lin, P. Lipavsky, " Time-dependent
Ginzburg-Landau theory with floating
nucleation kernel: Far-infrared conductivity in
the Abrikosov vortex lattice state of a type-II
superconductor", Phys.Rev.B 80, 212506
(2009)
[5] P.-J. Lin, P. Lipavsky, in preparation.
[6] Y.-J. Chen, P.-J. Lin, J.-Y. Lin, K. H.Wu, B.
Rosenstein, C. W. Luo, J. Y. Juang, T. M. Uen,
"The phase diagram of cuprates from the
analysis of electric transport properties"
Research activities on Higgs Physics at Zero and Nonzero Temperatures
Eibun Senaha (email:[email protected])
Postdoctoral researcher, 2009/08/01~present
n [1], Cheng-Wei Chiang and I have
conducted the comprehensive studies of
the electroweak phase transition (EWPT) in the
secluded U(1)’-extended-minimal supersymmetric
standard model (sMSSM).
In the sMSSM, since there are the singlet
contributions in the Higgs potential, the stability
of the Higgs potential is not manifest at all. The
possibility of the metastable vacuum, however,
had been often neglected in the previous works. In
our analysis, we required that the prescribed
electroweak vacuum should be a global minimum,
and the minimum search was done by a numerical
method. We found that such a vacuum condition
cannot be neglected and makes the allowed region
much smaller.
To investigate the properties of the EWPT, we
used the one-loop effective potential at zero and
nonzero temperatures taking the contributions
from the Z and W bosons, the third generation of
quarks and squarks into account. Under the
theoretical and experimental constraints, we
exclusively searched for the non-MSSM-like
EWPT by scanning the relevant parameters and
worked out the upper limits of the Higgs boson
masses which are consistent with the strong firstorder EWPT. We obtained the lower bounds, 160
GeV and 250 GeV for the lightest CP-even and
-odd Higgs bosons, respectively, where the
perturbativity of the Yukawa couplings were not
imposed.
We also considered the light stop scenario in
which the light stop is lighter than the top quark.
Although such a light stop can make the firstorder EWPT stronger up to 60%, the upper bound
of the CP-even Higgs boson mass is virtually
unchanged due to the smallness of the soft SUSYbreaking mass of the right-handed stop.
In the sMSSM, owing to the soft SUSYbreaking mass terms, it is possible to realize both
explicit and spontaneous CP violation at the tree
level. The effect of such a CP-violating phase on
the Higgs mass spectrum and the strength of the
first-order EWPT were also investigated. In
g e n e r a l , t h e r e a r e 1 0 o r d e r p a r a m e t e rs i f
spontaneous CP violation exists. Since it is highly
a non-trivial task to investigate the EWPT such a
case thoroughly, and the numerical calculation is
extremely time-consuming, we focused
exclusively on both the CP-conserving case and
the explicit CP-violating case in which the number
of order parameters is reduced to 6. It is observed
that such a CP-violating effect does not spoil the
strong first-order EWPT for the typical parameter
sets.
Our numerical study suggests that to have nonMSSM-like EWPT, the vacuum expectation
values (VEVs) of the singlet Higgs bosons,
particularly of that which couples to the doublet
Higgs bosons, in the broken phase and the
symmetric phase must be significantly different
from each other. For the typical parameter sets,
the VEV difference must be larger than 100 GeV,
which is almost temperature-independent. In
principle, such a VEV difference can be derived
provided that the soft SUSY-breaking masses are
known, or more precisely, once the global
structure of the Higgs potential is completely
determined. Therefore, the detection of a sizable
VEV difference from collider experiments may be
evidence of strong first-order EWPT in the
singlet-extended MSSM.
In [2], Cheung, Hou, Lee and I have studied
the Higgs sector of the next-to-minimal
supersymmetric standard model (NMSSM) with/
without CP violation. Although there have been a
lot of studies on this direction in the NMSSM, the
calculation was done up to the one-loop level. In
[2], we improved it by using the renormalization
group (RG) equations and investigated their
effects on the Higgs boson masses and couplings.
213 ‹‹- Research Activities of Individuals
In our analysis, we imposed the global minimum
condition, the positivity of the Higgs squared
masses and the experimental constraints such as
the LEP data. We demonstrated the three
representative scenarios: (S1) Typical (tan beta =
3, vS = 750 GeV), (S2) LEP-allowed (tan beta =
10, vS = 600 GeV), (S3) electroweak
baryogenesis-motivated (tan beta = 5, vS = 200
GeV), where the tan beta is defined by the ratio of
the VEVs of the two Higgs doublets and the vS
denotes the VEV of the Higgs singlet.
S1 without both the CP violation and RG
improvement had been investigated in the
literature, and it was found that the region for the
moderate values of lambda and kappa couplings
(The lambda is the coupling between the Higgs
doublet and the singlet Higgs and the kappa is the
cubic coupling of the singlet Higgs) can be
allowed. In contrast to this, we observed that after
including the RG effects on the top and bottom
Yukawa couplings, the SM-like Higgs boson mass
can be reduced to up to about 10 GeV, shrinking
to the allowed region significantly. Moreover, the
CP-violating phase can change the allowed region
drastically. In the maximal CP violation, the Higgs
mass spectrum and the couplings were found to be
inconsistent with the LEP data. In S2 and S3, the
shrink of the allowed region by the RG
improvement and CP violation was also observed.
In contrast to S1, however, we found the allowed
region in the maximal CP-violating case. Such a
l a rg e C P v i o l a t i o n m a y b e u s e f u l f o r t h e
successful electroweak baryogenesis in the
NMSSM.
Research Activities of Individuals -›› 214
What we have not investigated in [2] are (i) the
electric dipole moment constraints (ii) the detailed
calculation of electroweak baryogenesis (iii) the
collider signatures, which will be given elsewhere.
References
[1] E
lectroweak phase transitions in the secluded
U(1)-prime-extended MSSM, Cheng-Wei
Chiang and Eibun Senaha JHEP 1006, 030
(2010) [arXiv:0912.5069 [hep-ph]]
[2] T he Higgs Boson Sector of the Next-toMSSM with CP Violation', Kingman Cheung,
Tie-Jiun Hou, Jae Sik Lee and Eibun Senaha
[arXiv:1006.1458 [hep-ph]], accepted for
publication in Phys. Rev. D.
Research Activities on String Theory
Dan Tomino (email: [email protected])
Assistant research scholar, 2008/8/1~present
uring 2009-2010, I have researched a
Yang-Mills type matrix model and gauge
theories based on Lie 3-algebra.
be consistent with the strict bound of the torsions
in present universe which is observed by
measurements.
Yang-Mills type matrix model
Gauge theories based on Lie 3-algebra.
A proposal of non-perturbative definition of
super string theory has been formulated using a
Yang-Mills type matrix model, called as IKKT
model. In the IKKT model, the spacetime picture
dose not exist at its formulation, and this is
expected to be an emergent phenomenon in
various large N limit (N is the size of matrices) of
the matrix model. This is a remarkable feature as a
formulation of the quantum gravity. Therefore it is
an important issue to realize gravity by large N
matrix in the IKKT model. Recently it has been
r e c o g n i z e d t h a t l a rg e N m a t r i c e s c a n b e
understood as differential operators in a curved
manifold. Using this idea, it was shown that
equations of motion of the IKKT matrix model
describe just an extension of the Einstein gravity
with extra degrees of freedom, namely, torsion
and infinitely many kinds of higher spin fields.
The Lie 3-algebra is an extension of the
ordinary Lie (2-) algebra. There has been much
attention on this algebraic structure in study of
M-theory recently. The M-theory is the strong
coupling limit of type II A superstring. It is known
that the M-theory includes the eleven-dimensional
supergravity in its classical limit. And the strong
coupling limit of strings in superstring becomes
M-theory membranes (M2-branes). The
3-algebraic structure appeared in construction of a
low energy effective model of multiple M2-brane
with desirable symmetries. One can also construct
reduced models in 0-dimension with the Lie
3-algebraic structure. This is naturally related with
Green Schwarz-type supermembrane in 2+2 or
3+2 dimensional Minkowski spacetime, through a
regularization of the membrane world volume.
Therefore this can be regarded as a toy model of
quantized M2-brane.
To clarify the feature of the gravity which
comes from the IKKT model, I studied the
classical solution of the gravity equation with
torsion degrees of freedom. This study was done
with Dr. H. Isono (NTU). We considered time
dependent equation of a homogeneous and
isotropic spacetime with torsion degrees of
freedom. Under a simple ansatz of torsions, we
found an analytic solution which describes an
accelerating universe. It is expected that we can
find more interesting solution that describe the
inflation or the dark matter problem in future
works. We also studied static solution with
spherical symmetry. We found analytic and
numerical solutions which have event horizon.
But all solutions which we found were not
asymptotically flat solution. This result seems to
As a first step to study quantum aspect of these
reduced models, I calculated 1-loop determinants
of such a reduced model under several choices of
3-algebras. To calculate the 1-loop determinant, it
is necessary to consider the reduced model
expanded around a background. This background
provides a (fuzzy) spacetime, and the 1-loop
determinant around this background are
interpreted to the 1-loop correction of the vacuum
energy associated with the (fuzzy) spacetime. As a
future work, one can study stabilities between
various (fuzzy) spacetime, including the higher
loop correction. These studies will be used to
discuss dynamical generation of spacetime in
reduced models with 3-algebra.
215 ‹‹- Research Activities of Individuals
Ongoing project
Finally I briefly report on an ongoing project
with Dr. S. Kawamoto (NTNU) and Dr. T. Takimi
(NTU). Non-Abelian generalization of (2.0) tensor
multiplet in six-dimension have been a long
standing problem. Recently, using the Lie
3-algebraic structure, a supersymmetric algebra of
the non-Abelian tensor multiplet was written
down together with its equations of motion. On
the other hand, this (2.0) tensor multiplet appears
as the low energy effective theory of M-theory
5-brane (M5-brane). To describe multiple
M5-branes, we need a non-Abelian generalization
of the (2.0) tensor multiplet. Now we are studying
the equations of motion associated with the new
super algebra to investigate on low-energy
multiple M5-branes.
Research Activities of Individuals -›› 216
References
[1] " Classical Solutions of a Torsion Gravity from
a Large N Matrix model", Hiroshi Isono and
Dan Tomino, Phys.Rev.D.81, 084049 (2010)
[artXIv: 0911.1769]
[2] "Quantum Correction of (Fuzzy) Spacetimes
from a supersymmetric reduced model with
Filippov 3-algebra", Dan Tomino [arXiv:
1007.3090]
Research Activities on String Theory
Yi Yang (Department of Electrophysics, National Chiao Tung University; email: [email protected])
Center scientist, 2009/8/1~2010/7/31
uring the year 2009/8/1~2010/7/31, I
have continued to work on the following
two projects. One of them is to study the
relationship between the high energy behavior of
string scattering amplitudes and the hidden
symmetry in string theory. The other is to study
the low energy QCD by using the AdS/CFT
duality.
Project I
There are two fundamental regimes of high
energy string scattering amplitudes. These are the
fixed angle regime or Gross regime (GR), and the
fixed momentum transfer regime or Regge regime
(RR). These two regimes represent two different
high energy perturbation expansions of the
scattering amplitudes, and contain complementary
information of the theory. The UV behavior of
high energy string scatterings in the GR is well
known to be very soft exponential fall-off, while
that of RR is hard power-law. The high energy
string scattering amplitudes in the GR were
recently intensively reinvestigated for massive
string states at arbitrary mass levels. An infinite
number of linear relations, or stringy symmetries,
among string scattering amplitudes of different
string states were obtained. Moreover, these linear
relations can be solved for each fixed mass level,
and ratios among the amplitudes can be obtained.
An important new ingredient of these calculations
is the decoupling of zero-norm states (ZNS) in the
old covariant first quantized (OCFQ) string
spectrum. It is interesting to note that the
calculation is valid only for four-tachyon
amplitude, but not for all other amplitudes of
excited string states. This was pointed out and the
calculation was corrected by two independent
groups with two different approaches. Since there
does not exist any algebraic structure (or group
structure) of this high energy 26D spacetime
symmetry, mathematically the meaning of these
infinite number of ratios remains mysterious.
Another fundamental regime of high energy
string scattering amplitudes is the RR. Since the
decoupling of ZNS applies to all kinematic
regimes, one expects some implication of this
decoupling in the RR. Moreover, it is conceivable
that there exists some link between the patterns of
the high energy scattering amplitudes of GR and
RR. With this in mind, in this paper, we give a
detail calculation of high energy string scattering
amplitudes in the RR. We will find that the
number of high energy scattering amplitudes for
each fixed mass level in the RR is much more
numerous than that of GR calculated previously.
On the other hand, it seems that both the saddlepoint method and the method of decoupling of
high energy ZNS adopted in the calculation of GR
do not apply to the case of RR. However the
calculation is still manageable, and the general
formula for the high energy scattering amplitudes
for each fixed mass level in the RR can be written
down explicitly.
In contrast to the case of scatterings in the GR,
we will see that there is no linear relation among
scatterings in the RR. Moreover, we discover that
the leading order amplitudes at each fixed mass
level in the RR can be expressed in terms of the
Kummer function of the second kind. More
surprisingly, for those leading order high energy
amplitudes in the RR with the, we can extract
from them the ratios in the GR by using this
Kummer function. Mathematically, the proof of
217 ‹‹- Research Activities of Individuals
this result turns out to be highly nontrivial and is
based on a summation algorithm for Stirling
number identity derived by Mkauers in 2007. It is
very interesting to see that there is an identity in
suggested by string theory calculation can be
rigorously proved by a totally different but
sophisticated mathematical method. The
derivation of these physical ratios from Kummer
function through Stirling number identities seems
to suggest another interpretation of these infinite
number ratios mathematically. At last, as an
application of our results, we show that the well
known power-law behavior of the four tachyon
string scattering amplitude in the RR can be
extended to all high energy massive string
scattering amplitudes.
an octet with largely unbroken SU(3) symmetry
and a fairly good singlet which is f0(1370). The
other left scalar meson f0(1710) is identified as an
almost pure scalar glueball with a ∼ 10% mixture
of ¯qq, which is supported from lattice calculation
and experimental observation of the copious
f0(1710) production in radiative J/ψ decays.
Project II
The string description of realistic QCD has not
been successfully formulated yet. By using AdS/
CFT correspondence to study non-conformal field
theory like QCD, the usual way of breaking
conformal symmetry is by introducing a hard
infrared (IR) cut-off, i.e. the hard-wall AdS5
model or introducing a smooth cut-off through a
dilaton background field, i.e. the soft-wall AdS5
model. One can extend the AdS/CFT
correspondence to a more general case, and expect
the realistic QCD is dual to a non-conformal Dp
brane system, like the D4 − D8/¯D8 system, i.e.
the Sakai-Sugimoto model. We have investigated
the general embedding Dp − Dq systems, where
the Nc background Dp-brane describes the effects
of pure QCD theory, while the Nf probe Dq-brane
is to accommodate the fundamental flavors.
The glueball spectrum has attracted much
attention more than three decades. Study particles
like glueballs where the gauge field plays a more
important dynamical role than in the standard
hadrons, offers a good opportunity of
understanding the nonperturbative aspects of
QCD. The complexity of determing the glueball
states lies in that gluonic bound states always mix
with ¯qq states. For example, one has to
distinguish the lightest scalar glueball state among
other scalar mesons observed in the energy range
below 2GeV. Though the pseudoscalar, vector and
axial-vector, and tensor mesons with light quarks
have been reasonably well known in terms of their
SU(3) classification and quark content, the scalar
meson sector, on the other hand, is much less
understood in this regard. There are 19 states
which are more than twice the usual ¯qq nonet as
in other sectors.
Despite of extensive study from both
experimental side and theoretical side, no
conclusive answer has been obtained on scalar
mesons and scalar glueballs. One possible
scenario is: The lightest scalars σ, κ, f0, a0
below 1GeV make a full SU(3) flavor nonet. The
inversion of the κ and f0 or a0 mass ordering,
suggests that these mesons are not naive ¯qq
states, one natural explanation for this inverted
mass spectrum is that these mesons are diquark
and antidiquark bound states, or tetraquark states.
Above 1GeV, the nonet ¯qq mesons are made of
Research Activities of Individuals -›› 218
Recently, the discovery of the gravity/gauge
duality, or anti-de Sitter/conformal field theory
(AdS/CFT) correspondence provides a
revolutionary method to tackle the problem of
strongly coupled gauge theories. Many efforts
have been invested in examining meson spectra,
baryon spectra as well as in the glueball sector. It
is widely expected that this new analytical
approach can shed some light on our
understanding of the nonperturbative aspects of
QCD.
The motivation of our research is to investigate
the scalar meson and glueball spectra in the
general embedding Dp − Dq systems, and study
which Dp − Dq system is more close to the dual
theory of realistic QCD. Our finding is that in the
D4 − D6 and D4 − D8 hard wall models, the
predicted masses of the ¯qq scalar meson f0 and
the scalar glueball are consistent with their
experimental or lattice results, which indicates
that D4 − D6 and D4 − D8 hard-wall models are
favorite candidates of the realistic holographic
QCD model. We will study the mixing between
scalar mesons, tetraquark states and glueballs in
the future.
References
[1] S
.L. Ko, J.C. Lee, and Y.Y., "Stirling number
identities and High energy String
Scatterings", arXiv:0909.3894
[2] J .C. Lee, and Y.Y., "Regge Closed String
Scattering and its Implication on Fix Angle
Close String Scattering", arXiv:1001.4843,
Phys.Lett. B687:84-88, 2010
[3] S . He, J.C. Lee, K. Takahashi and Y.Y.,
"Massive Superstring Scattering in Regge
Regime", arXiv:1001.5392
219 ‹‹- Research Activities of Individuals
Introducing New Members
Dr. Chian-Shu Chen
Postdoctoral researcher (Ph.D. National Tsing Hua University, Taiwan)
email: [email protected]
am starting this summer 2010 as a new
postdoctor in the physics division of
NCTS after previously being a posdoctor at
National Cheng-Kung University under the
supervision of Professor Chung-Hsien Chou, and I
have been also at the Academia Sinica where I
worked with Professor T.C. Yuan and Dr. Y.H.
Ahn.
Currently my interests are in the study of the
basic properties of neutrinos through the interface
between collider physics and cosmology. In
collider physics, we proposed a scenario in which
the neutrino masses are generated at two-loop
level. The model has several features that provide
us to search the unique signals, and are able to
distinguish from other mechanisms in the market,
especially the so-called the type-II seesaw
mechanism. This year Professor C.Q. Gneg at
National Tsing-Hua University and I proposed a
method by using the branching ratios of same-sign
dilepton modes at the LHC, it is possible to
measure the absolute magnitude of neutrino
masses. So far there are only few experiments that
can give us the absolute magnitude of neutrinos
such as the tritium decays, the neutrinoless double
beta decays, and cosmological survey. The
mystery of matter-antimatter asymmetry of the
universe can be explained by the mechanism of
Introducing New Members -›› 220
leptogenesis which usually requires lepton number
violation and the breaking scale is related to the
light neutrino mass generation. I studied the topic
in different models which give the neutrino
masses. There are also several issues that could be
intimately related to neutrinos including the
puzzles of what is dark matter and dark energy.
The quest of the homogeneous and isotropic of
our universe as well as the initial condition of the
density perturbations of our structure formation
can be explained by the inflation theory. Recently
a postdoctor Chia-Min Lin at National Tasing-Hua
University and I proposed that the type-II seesaw
triplet scalar may play the role which drives the
inflation in the early universe. Furthermore, their
d e c a y s c a n c r e a t e t h e m a t t e r- a n t i m a t t e r
asymmetry of our universe. Other related topics
will be addressed in my future research.
References in 2010
[1] Y
. H . A h n a n d C . S . C h e n , P h y s . R e v.
D81,105013 (2010)
[2] C.S.Chen and C.Q.Geng, arXiv:1005.2817 (to
be published in PRD)
[3] C.S.Chen and C.M.Lin, aeXiv:1009.5727
Dr. Hong-Da Chen
Postdoctoral researcher (Ph.D., Department of Physics, National Center University, Taiwan)
email: [email protected]
am starting Sep. 2010 as a new
Postdoctoral fellow in the Physics
Division of NCTS, after previously being a
postdoctoral fellow at Graduate Institute of
Systems Biology and Bioinformatics in the
National Center University under the supervision
of Professor H.C. Paul Lee.
My area of research is Bioinformatics and
Systems Biology, including the genome evolution
of the mode of replication and mutation, network
systems and regulatory mechanisms of cancer.
In my recent work, I tried to study the
symmetry of the source of genomic, and gene
expression in different transcripts of the impact of
cancer.
Dr. Ming-Chiang Chung
Assistant research scholar (Ph.D., Freie Universitaet Berlin, Germany)
email: [email protected]
obtained my Ph.D. degree in the free
university Berlin and after my graduation
I worked for different institutes, Ames Lab in
Iowa USA, RWTH Aachen Germany, Max-Planck
Institute for the Physics of the Complex Systems,
Dresden Germany. In the last position I worked
for Prof. Sungkit Yip in Academia Sinica. In
February 2010, I started my position as an
assistant research scholar in the physics division
of NCTS.
My research interests can be divided to two
areas: quantum information applied in the
condensed matter physics and cold atoms,
especially applied to condensed matter too. For
the first part of my research, I focus on the
entanglement entropy for quantum systems,
especially for the physical systems at critical
points and the topological systems. We found that
investigating the so-called entanglement entropy
spectra can decipher the area law of the bi-partite
entanglement entropy and the edge states for the
topological systems. In order to find the
entanglement spectra, we use the "block Greenfunction matrices" which I found in Germany
several years ago. Using this method, we plan to
work on quench dynamics of the entanglement
and some other interesting properties, for
example, the area law for graphenes.
Another topic I am working on is the coldatom system. After the discovery of BEC in 1995,
cold-atom experiments have been developing into
a very important tool to investigate different
quantum systems. For a small atom-atom
interaction, the atoms are in the superfluid region,
while for a much larger interaction, the atoms lie
on the insulating regime. These two regimes
essentially separate the system into two parts:
macroscopic quantum phenomena and quantum
simulation for the condensed matter physics. For
the superfluid regime, I am interested in the
dynamics, for example, Bloch oscillations and
elementary damping (Landau and Beliaev
damping). I am also interested in solving Gross
Pitaevskii equations to study the density and
quantum excitations. While in the insulating
regime, I am more interested in the spinor Bose
gases. We study the spin-1 Bose gases in an
optical lattice. We found that there is a way to cool
the system into nematic states by adiabatically
increasing the atom-atom interaction. We also
found the phase diagrams for the spin-1 Bose
gases in an optical lattice under the influence of
Zeeman effects.
221 ‹‹- Introducing New Members
Dr. Shulin Sun
Postdoctoral researcher (Ph.D., Fudan University, China)
Email: [email protected]
joined the physics division of NCTS as a
postdoctoral fellow at National Taiwan
University under the supervision of Prof. GuangYu Guo in May 2010. I got my Ph.D. degree at
Fudan University guided by Prof. Lei Zhou in
2009.
Plasmonic metamaterials receive much
attention in recent years because of its
extraordinary physical properties and promising
application prospect. The development of
industrial technology can help people to design
nano-scale plasmonic metamaterials which can be
widely applied in microscopic imaging, biosensor, bio-detector and enhanced Raman effect,
etc. My interests focus on the theoretical and
simulation research of plasmonic metamaterials.
Introducing New Members -›› 222
My simulation tools mainly include the FiniteDifference-Time-Domain and Finite Element
Method methods. Besides theoretical research, I
will always try my best to design realistic
structures to demonstrate our ideas in
experiments. Recently we introduce a new
mechanism of converting propagating
electromagnetic waves to surface plasmon
polariton perfectly using gradient metamaterials.
Its conversion efficiency is much higher than
traditional methods. Our idea has been realized in
micro-wave experiments. Next my goal is to
design devices in optical region. Considering
excellent experimental condition in NTU, I hope I
can have a good interaction with the experimental
groups and provide my theoretical support.
December
2010
Annual Report
National Center for Theoretical Sciences
No. 101, Section 2, Kuang Fu Road, Hsinchu, Taiwan 30013
Mathematics Division
Tel: 886-3-5728263/5745253~5
Fax: 886-3-5728161
e-mail: [email protected]
http://www.math.cts.nthu.edu.twl
Physics Division
Tel: 886-3-5734969
Fax: 886-3-5735086
e-mail: [email protected]
http://www.phys.cts.nthu.edu.tw
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