Finite Dimensional Integrable Systems 2013

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The international conference "FDIS 2013: Finite Dimensional Integrable Systems," to be held at the International Center of Mathematical Meetings in Marseille, France, July 15-19, 2013, will focus on recent advances in finite dimensional integrable systems and present new directions of research. Integrable systems with a finite number of degrees of freedom is the most classical part of the theory of integrable systems. Due to the seminal contributions of Kolmogorov, Arnold, Moser, and many others, this subject is experiencing a revival. Recently, new powerful method for working with integrable systems have been developed based on a deep interplay between different branches of mathematics and physics: complex analysis, symplectic geometry, Lie theory, representation theory, theory of cluster algebras, discrete differential geometry, and computer algebra. As a result, new integrable systems have been discovered, new applications of integrable systems in physics and geometry were unveiled, and many questions explicitly asked in the classical period have been answered.Non-linear ordinary and partial differential equations describe a large number of physical phenomena, ranging from mechanics, fluid mechanics, optics, magnetism to general relativity, and also many natural and interesting geometrical problems. One of the most effective methods to handle them is related to the so called integrable systems, which is, roughly speaking, a collection of methods for finding exact solutions of certain systems, or to analyze the behavior of their solutions without knowing them explicitly. The conference will feature about 20 talks by the leading experts and will provide a venue for junior researchers to network, to interact with senior researchers, and to foster new collaborations.