Finite Dimensional Integrable Systems 2013

国际会议“FDIS 2013：有限维可积系统”将于2013年7月15日至19日在法国马赛的国际数学会议中心举行，会议将重点关注有限维可积系统的最新进展，并提出新的研究方向。有限自由度可积系统是可积系统理论中最经典的部分。由于Kolmogorov，Arnold，Moser和许多其他人的开创性贡献，这个主题正在经历复兴。最近，基于数学和物理学不同分支之间的深刻相互作用，已经开发了新的强大的方法来处理可积系统：复分析，辛几何，李理论，表示论，簇代数理论，离散微分几何和计算机代数。非线性常微分方程和偏微分方程描述了大量的物理现象，从力学、流体力学、光学、磁学到广义相对论，它们都是由非线性常微分方程和偏微分方程组成的。以及许多自然的、有趣的几何问题。处理它们的最有效的方法之一是与所谓的可积系统有关，粗略地说，这是一系列方法的集合，用于找到某些系统的精确解，或者在不显式地知道它们的情况下分析它们的解的行为。会议将由领先的专家进行约20场演讲，并将为初级研究人员提供一个网络，与高级研究人员互动并促进新的合作的场所。

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.