题目一：KdV equation: History and Recent Progress
内容简介：In 1834 Russel found an interesting phenomenon of shallow water waves, which is now called as solitons. Later in 1895 the equation describing this phenomenon was discovered by Korteweg-de Vries. In 1965 a computer simulation for this equation stimulated mathematical world, and in 1967 4 mathematicians found a close relationship between the equation and 1-D Schrödinger operators. In the talk I mention briefly the conventional methods of solving the equation by which one can treat mainly decaying or periodic initial data. Recent progresses also are presented, by which one can now solve the KdV equation starting from almost-periodic initial conditions.
报告人：Shinichi Kotani 教授（Osaka University）
题目二：Analytic local rigidity of isometries on compact real analytic Riemannian manifolds
内容简介：Rigidity theory for diffeomorphisms of compact manifolds is an area of prime importance in dynamical systems. In the most general form, it may be formulated in the following way: to find a condition which ensures that if two maps are topologically conjugated then they are also smoothly or analytically conjugated. There are many famous results on linearization of smooth circle diffeomorphisms with certain rotation numbers by Arnold, Herman, Yoccoz, Moser, Fayad, Khanin, etc. However, the rigidity in the higher-dimensional case is far from well-known. It was conjectured by K. Khanin at ICM 2018 that the rigidity also holds in a more general situation. In a joint work with Stolovitch, we show the local rigidity of the action of analytic isometries of compact real analytic Riemannian manifolds: if the action of diffeomorphisms is formally conjugated to an action of isometries of the manifold, then under certain Diophantine-like condition related to the isometries, this conjugation is indeed analytic. The proof is based on a Kolmogorov-Arnold-Moser (KAM) scheme.
报告人：Zhiyan Zhao 副教授（University Côte d’ Azur）
时 间：2023年11月16日（周四）下午14：30开始
地 点：暨南大学石牌校区教学楼A518
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信息科学技术学院
2023年11月10日