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Current trends in mathematics: algebra, geometry, differential equations, numerical analysis, applications to biology

Final Activity Report Summary - CURRENT MATH (Current trends in mathematics: algebra, geometry, differential equations, numerical analysis, applications to biology)

We organised a series of five events in pure and applied mathematics. The main objective was to give the younger generation of scientists on the one hand a broad education and on the other hand specialised training on specific topics which lie at the cutting edge of mathematical research. All proposed events have been selected by an International Scientific Committee with this viewpoint in mind, taking into account the scientific quality and relevance of the topics to current mathematical interests and achievements in Europe. The keynote speakers were leading scientists, the majority of them from European institutions. We had a total number of 305 participants from 42 countries. We used EU funds in order to support 214 eligible researchers of Groups 1,2,3. All actions foreseen by the contract have been carried out completely and successfully. Specifically, the following conferences have been held (Events 1, 2 and 3 in year 1 and events 4 and 5 in year 2):

Event 1. Conference: "Non linear dispersive wave phenomena"
Dates: July 9-15, 2005
Organisers: J.L. Bona (Illinois), V.A. Dougalis (Athens), J.- C. Saut (Paris).
Key-note speakers: J.L. Bona (U. Illinois at Chicago, USA), M. Chen (Purdue U., U.S.A.) V. Dougalis (U. Athens, Greece), A.S. Fokas (Cambridge U., UK), F. Merle (U. of Cergy-Pontoise, France), J-C. Saut (U. Paris-Sud, France), C. Sulem (U. Toronto, Canada).

event 2. Conference: "Number fields and curves over finite fields"
Dates: July 23-29, 2005
Organisers: R. Schoof (Rome), G. van der Geer (Amsterdam).
Key-note speakers: G. van der Geer (U. of Amsterdam, Holland), R. de Jong (U. Leiden, Holland), R. Schoof, (U. Rome - Tor Vergata, Italy), M.Tsfasman (U. Marseille, France).

Event 3. Conference: "Algebraic and geometric combinatorics"
Dates: August 20-26, 2005
Organisers: V. Batyrev (Tubingen), M. Henk (Magdeburg), F. Santos (Cantabria).
Key-note speakers: V. Batyrev, (U. of Tuebingen, Germany), L. Billera (Cornell U., USA), E-M Feichtner (ETH Zurich, Swicherland), M. Henk, (U. Magdeburg, Germany), P. McMullen, (U. College London, UK), F. Santos (U. of Cantabria, Spain), V. Welker (U. Marburg, Germany), G. Ziegler (TU of Berlin, Germany).

Event 4. Conference: "Discontinuous change in behavior issues in partial differential equations"
Dates: June 10-16, 2006
Organisers: I. Athanasopoulos (Crete), L. A. Caffarelli (Texas).
Key-note Speakers: L.A. Caffarelli (U. of Texas, USA). D. Christodoulou (ETH, Switzerland), I. Gamba (U. of Texas, USA), R. Nochetto (U. of Maryland, USA), S. Salsa (Politecnico di Milano, Italy), M. Soner (Koc University, Turkey), P. Souganidis (U. of Texas, USA).

Event 5. Conference: "Which mathematics for biology?"
Dates: July 9-15, 2006
Organisers: A. Deutsch (Dresden), D. Manoussaki (Vanderbilt), B. Perthame (Paris).
Key-note Speakers: A. Deutsch (TU Dresden, Germany), Y. Kevrekidis (Princeton Univ., USA), P. Maini (U. Oxford, UK), H. Metz (U. Leiden, Netherlands), C. J. Weijer (U. Dundee, UK).