HARMONIC AND COMPLEX ANALYSIS
AND APPLICATIONS
ESF Research Networking Programme
2007-2012
Mid-term report
Alexander Vasiliev (University of Bergen, Norway)
Participating Agencies
Austria: The Austrian Science Research Fund (FWF)
Finland: Academy of Finland
Germany: Deutsche Forschungsgemeinschaft (DFG)
Ireland: Irish Research Council for Sciences, Engineering
and Technology (IRCSET)
Israel: Israel Academy of Sciences (from 2008)
Luxembourg: Fonds National de la Recherche
Norway: Research Council of Norway
Spain: Consejo Superior de Investigaciones Cientificas
(CSIC) and
Ministerio de Educacion y Ciencia (MEC)
Sweden: Swedish Research Council
Switzerland: Swiss National Science Foundation (SNF)
United Kingdom: Engineering and Physical Sciences
Steering Committee











Austria- Hans Georg Feichtinger (Vienna)
Finland- Ilkka Holopainen (Helsinki)
Germany- Dierk Schleicher (Bremen)
Ireland- Stephen Gardiner (Dublin)
Israel- Lawrence Zalcman (Ramat Gan)
Luxembourg- Martin Schlichenmayer (Luxembourg)
Norway- Alexander Vasiliev (chair) (Bergen)
Spain- Fernando Pérez-González (Tenerife)
Sweden- Björn Gustafsson (Stockholm)
Switzerland- Zoltan Balogh (Bern)
UK- John King (Nottingham)
Activities







Conferences
Workshops
Summer/winter schools
Exchange visits (> 15 days)
Short visits (≤ 15 days)
WEB activities
Publications
General Scheme of Interaction
Physical and
Engineering
Sciences
•Math. Physics
•Fluid Mechanics
•Signal Processing
Mathematical
Sciences
•Harmonic Analysis
•Conformal and
Quasiconformal Analysis
•Medical Sciences
•Complex Analysis and
Operator Theory
•Engineering Sci.
•Potential Analysis
Motivating model

Contour dynamics
Motivating model

Hele-Shaw cell, Saffman-Taylor instabilities
Motivating model

For example, enhanced oil recovery
Scientific achievements

Contour dynamics (Laplacian growth/Hele-Shaw, Loewner) is
reformulated in terms of Conformal Field Theory. Common
algebraic background is provided by Virasoro algebra;
Scientific achievements


Contour dynamics (Laplacian growth/Hele-Shaw, Loewner) is
reformulated in terms of Conformal Field Theory. Common
algebraic background is provided by Virasoro algebra;
Lax operator algebras, classification of central extensions;
Scientific achievements



Contour dynamics (Laplacian growth/Hele-Shaw, Loewner) is
reformulated in terms of Conformal Field Theory. Common
algebraic background is provided by Virasoro algebra;
Lax operator algebras, classification of central extensions;
Loewner theory is revised via semigroups/evolution families;
Scientific achievements




Contour dynamics (Laplacian growth/Hele-Shaw, Loewner) is
reformulated in terms of Conformal Field Theory. Common
algebraic background is provided by Virasoro algebra;
Lax operator algebras, classification of central extensions;
Loewner theory is revised via semigroups/evolution families;
Harmonic momenta in Laplacian growth are represented in the
language of transfinite functions. Quantum Hele-Shaw via random
matrix theory;
Scientific achievements







Contour dynamics (Laplacian growth/Hele-Shaw, Loewner) is
reformulated in terms of Conformal Field Theory. Common
algebraic background is provided by Virasoro algebra;
Lax operator algebras, classification of central extensions;
Loewner theory is revised via semigroups/evolution families;
Harmonic momenta in Laplacian growth are represented in the
language of transfinite functions. Quantum Hele-Shaw via random
matrix theory;
Schwarz-Christoffel formula for unbounded multiply connected
domains (applications to multiply connected Laplacian growth);
Non-holonomic systems (infinite and finite dimensional).
Foundations of sub-Lorentzian geometry;
Analysis on Banach spaces of analytic functions.
Scientific impact






Broad interaction between Analysis, Geometry,
Mathematical Physics;
Work groups of scientists with different scientific
background;
Training of young mathematicians within
interdisciplinary environment;
Collaboration (joint events, interchange) with nonEuropean community (Russia, USA, Canada, Taiwan)
New journal “Analysis and Mathematical Physics”
Mittag-Leffler research semester.
Events and collaboration

3 main Programme conferences;
2007-2009 HCAA supported:
 20 science meetings;
 12 short visits;
 4 exchange (long) visits;
Main Network Conferences
Past:
 2007, 7-12 May: Norway, Voss “New Trends in Complex
and Harmonic Analysis”;
Current:
 2010, 29 June-3July: Germany, Bremen “New Trends in
Complex and Harmonic Analysis”;
Plan:
 2012, February: Spain, Tenerife “New Trends in
Complex and Harmonic Analysis”.
Collaboration









ESF NRP “Global and Geometric Aspects of non-Linear PDE”
(GLOBAL);
ESF NRP “Interactions of Low-Dimensional Topology and
Geometry with Mathematical Physics” (ITGP);
FP6/7 Network “Conformal Structures and Dynamics” (CODY);
FP6/7 Network “Geometry, Mathematical Physics and
Applications” ENIGMA;
FP6/7 Network “Sub-Riemannian Geometric Analysis on Lie
Groups” GALA;
Nordic (NordForsk) Network “Analysis and Applications”;
Spanish platform Ingenio Mathematica I-MATH;
NSF (USA), CIMPA (UNESCO), NCTS (Taiwan), Steklov Institute
(Russia), CRM (Canada)
National grants.
Web Activities


http://org.uib.no/hcaa
Web-site available from June 2007
Web Activities

Preprints http://org.uib.no/hcaa/preprints.html

Job listings within network
http://org.uib.no/hcaa/jobs.html

Current and forthcoming events
http://org.uib.no/hcaa/events.html
HCAA Brochure
Publishing Activities









62 published papers mentioning HCAA support,
10 of which are direct collaboration within HCAA;
Journals include
Advances in Mathematics
Annales de l’Institut Fourier
Communications in Mathematical Physics
Duke Mathematical Journal
Inventiones Mathematicae
Journal of the American Mathematical Society
Physica D
Publishing activities





Preprint server (79 preprints 2007-2009),
research papers, books;
Special Birkhäuser volume “Analysis and
Mathematical Physics”- 2009;
Special Springer volume planned 2012;
Special issue in the journal “Complex Analysis
and Operator Theory”- 2010;
New journal “Analysis and Mathematical
Physics” in Birkhäuser (planned 2011);
Management







Annual budget 125 000 €;
Steering Committee meetings typically in January;
Road-map for events (average budget 80 000 €);
Much collaboration is within schools, workshops;
Reserve approx. 20 000 € for grants;
Executive Committee decides on short visits all over the year by email;
Usually some funds are left for the next year (preparation to
Mittag-Leffler research semester)
Future planning





Scientific excellence, further integration of
Analysis and Mathematical Physics
communities, applications;
Most important events:
2010, 2012 Porgramme conferences;
2011 Mittag-Leffler research semester;
Forward look: applications for EUROCORES
program, EU Framework Programs.
End