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Completely Integrable Systems and Applications - ESF-EMS-ERCOM Conference
03 July 2011 — 08 July 2011
European Science Foundation
The scope of the conference includes Completely Integrable Systems (mostly PDEs and systems of ODEs) and related subjects such as Random Matrices, Whitham and Seiberg-Witten theory, Orthogonal Polynomials, Processes in Combinatorial Probability that are asymptotically described by Integrable Systems and Exactly Solvable Interacting Particle Systems modeling nonequilibrium phenomena. We will particularly stress questions of “universality” appearing in both random matrices and semiclassical limits of integrable systems and “non-self-adjoint” problems. We will also address the newly evolving area of boundary problems for integrable PDEs.
Random Matrices have been a subject of central importance in mathematics and physics in the last decade. Although several conferences have been held worldwide in this subject, one main novelty is proposed: that is the focus on nonself-adjoint random matrices (and also integrable systems with non-self-adjoint Lax operator). This is related to new interesting results in the theory of the semiclassical nonlinear Schrödinger equation, elliptic Whitham equations and the theory of Laplacian growth and Hele-Show flows, which we expect to be presented. We are also asking some physicists to talk about the relation between string theory and Seiberg-Witten equations on one hand and Whitham equations on the other. We feel that this is a connection that is worth more attention from mathematicians, in particular experts in semiclassical theory of integrable equations. Second, although universality results have been well publicized in the theory of random matrices there are deep new results on universality phenomena appearing in the semiclassical limits of integrable systems (Trieste school) the dissemination of which is expected to benefit the integrable systems community.
Third, there are some exciting open problems in the theory of boundary problems for integrable PDEs (asymptotic behavior for large times) to which the combined attention of invited researchers from Western Europe as well as the Kharkov school of Ukraine should greatly contribute. Some (few) collaborations already exist but a meeting of (essentially) all the experts in this field will provide an important impetus to the theory of IBVP. Fourthly, exactly solvable Interacting Particle Systems have been shown in the last decade to be helpful in the study of (generally important) nonequilibrium phenomena. We expect that the meeting of experts in that field and experts in orthogonal polynomials, integrable systems and Riemann-Hilbert methods to be very fruitful.
Invited speakers will include:
- Jerry Bona - University of Illinois at Chicago, US
- Anne Boutet de Monvel - Paris 7 University, FR
- Adrian Constantin - University of Vienna, AT - On the Camassa-Holm equation: physical relevance and mathematical properties
- Ira Egorova - Institute for Low Temperature Physics, UA - Asymptotical solitons for the Toda lattice with steplike initial data
- Athanassios S. Fokas - Cambridge University, UK
- Fritz Gesztesy - UMC Columbia, US - Burchnall-Chaundy theory, integrable systems, and spectral theory
- Tamara Grava - SISSA Trieste, IT - Hamiltonian PDEs and Painleve' equations
- Helge Holden - NTNU Trondheim, NO
- Vladimir Kotlyarov - Institute for Low Temperature Physics, UA - Matrix Riemann-Hilbert problems: long-time asymptotic behavior of solutions of completely integrable equations with step-like initial data on the line and periodic in time boundary conditions on the half-line
- Igor Kriechever - Columbia University, US
- Arno Kuijlaars - UCL Louvain, BE - Multiple orthogonal polynomials in the normal matrix model
- Jonatan Lenells - Baylor University, US - Boundary value problems for theErnst equation
- Leonid Pastur - Institute for Low Temperature Physics, UA
- Dmitry Shepelsky - Institute for Low Temperature Physics, UA - The short-wave model for the Camassa-Holm equation: the Riemann-Hilbert approach
- Pierre Van Moerbeke - UCL Louvain, BE - Non-intersecting Brownian motions and integrable systems
- Stephanos Venakides - Duke University, US - Steepest descent for integrable systems
The conference is open to scientists world-wide, whether from academia or industry. Attendance is possible only after successful application. A certain number of grants will be available for students, postdocs and early stage researchers to cover the conference fee and, possibly, part of the travel costs. Grant requests should be made by ticking appropriate field(s) in the paragraph "Grant application" of the application form.