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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-Î´ 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