1. HARMONIC AND COMPLEX ANALYSIS AND APPLICATIONS ESF Research Networking Programme 2007-2012 Mid-term report Alexander Vasiliev (University of Bergen, Norway) ESF Research Networking Programme 2007-2012 Mid-term report Alexander Vasiliev (University of Bergen, Norway)

2. 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 Research Council (EPSRC) 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 Research Council (EPSRC)

3. Steering Committee Austria- Hans Georg Feichtinger (Vienna) Austria- Hans Georg Feichtinger (Vienna) Finland- Ilkka Holopainen (Helsinki) Finland- Ilkka Holopainen (Helsinki) Germany- Dierk Schleicher (Bremen) Germany- Dierk Schleicher (Bremen) Ireland- Stephen Gardiner (Dublin) Ireland- Stephen Gardiner (Dublin) Israel- Lawrence Zalcman (Ramat Gan) Israel- Lawrence Zalcman (Ramat Gan) Luxembourg- Martin Schlichenmayer (Luxembourg) Luxembourg- Martin Schlichenmayer (Luxembourg) Norway- Alexander Vasiliev (chair) (Bergen) Norway- Alexander Vasiliev (chair) (Bergen) Spain- Fernando Pérez-González (Tenerife) Spain- Fernando Pérez-González (Tenerife) Sweden- Björn Gustafsson (Stockholm) Sweden- Björn Gustafsson (Stockholm) Switzerland- Zoltan Balogh (Bern) Switzerland- Zoltan Balogh (Bern) UK- John King (Nottingham) UK- John King (Nottingham) Austria- Hans Georg Feichtinger (Vienna) Austria- Hans Georg Feichtinger (Vienna) Finland- Ilkka Holopainen (Helsinki) Finland- Ilkka Holopainen (Helsinki) Germany- Dierk Schleicher (Bremen) Germany- Dierk Schleicher (Bremen) Ireland- Stephen Gardiner (Dublin) Ireland- Stephen Gardiner (Dublin) Israel- Lawrence Zalcman (Ramat Gan) Israel- Lawrence Zalcman (Ramat Gan) Luxembourg- Martin Schlichenmayer (Luxembourg) Luxembourg- Martin Schlichenmayer (Luxembourg) Norway- Alexander Vasiliev (chair) (Bergen) Norway- Alexander Vasiliev (chair) (Bergen) Spain- Fernando Pérez-González (Tenerife) Spain- Fernando Pérez-González (Tenerife) Sweden- Björn Gustafsson (Stockholm) Sweden- Björn Gustafsson (Stockholm) Switzerland- Zoltan Balogh (Bern) Switzerland- Zoltan Balogh (Bern) UK- John King (Nottingham) UK- John King (Nottingham)

4. Activities Conferences Workshops Summer/winter schools Exchange visits (> 15 days) Short visits (≤ 15 days) WEB activities Publications Conferences Workshops Summer/winter schools Exchange visits (> 15 days) Short visits (≤ 15 days) WEB activities Publications

5. General Scheme of Interaction Physical and Engineering Sciences Math. Physics Fluid Mechanics Signal Processing Medical Sciences Engineering Sci. Mathematical Sciences Harmonic Analysis Conformal and Quasiconformal Analysis Complex Analysis and Operator Theory Potential Analysis

6. Motivating model Contour dynamics

7. Motivating model Hele-Shaw cell, Saffman-Taylor instabilities

8. Motivating model For example, enhanced oil recovery

9. 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;

10. 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; 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;

11. 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; 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;

12. 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; 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;

13. 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. 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.

14. 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 non- European community (Russia, USA, Canada, Taiwan) New journal “Analysis and Mathematical Physics” Mittag-Leffler research semester. 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 non- European community (Russia, USA, Canada, Taiwan) New journal “Analysis and Mathematical Physics” Mittag-Leffler research semester.

15. Events and collaboration 3 main Programme conferences; 2007-2009 HCAA supported: 20 science meetings; 12 short visits; 4 exchange (long) visits; 3 main Programme conferences; 2007-2009 HCAA supported: 20 science meetings; 12 short visits; 4 exchange (long) visits;

16. 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”. 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”.

17. 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. 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.

18. Web Activities http://org.uib.no/hcaa Web-site available from June 2007 http://org.uib.no/hcaa Web-site available from June 2007

19. Web Activities http://org.uib.no/hcaa/preprints.html Preprints http://org.uib.no/hcaa/preprints.html Job listings within networkhttp://org.uib.no/hcaa/jobs.html Current and forthcoming eventshttp://org.uib.no/hcaa/events.html http://org.uib.no/hcaa/preprints.html Preprints http://org.uib.no/hcaa/preprints.html Job listings within networkhttp://org.uib.no/hcaa/jobs.html Current and forthcoming eventshttp://org.uib.no/hcaa/events.html

20. HCAA Brochure

21. 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 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

22. 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); 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);

23. 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 e- mail; Usually some funds are left for the next year (preparation to Mittag-Leffler research semester) 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 e- mail; Usually some funds are left for the next year (preparation to Mittag-Leffler research semester)

24. 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. 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.

25. End