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HARMONIC AND COMPLEX ANALYSIS AND APPLICATIONS

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

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HARMONIC AND COMPLEX ANALYSIS AND APPLICATIONS

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  1. HARMONIC AND COMPLEX ANALYSIS AND APPLICATIONS 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)

  3. 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)

  4. Activities • 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;

  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;

  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;

  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.

  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.

  15. Events and collaboration • 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”.

  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.

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

  19. Web Activities • Preprintshttp://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

  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

  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);

  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)

  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.

  25. End

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