https://mp.weixin.qq.com/s/IjmvnrfQJkpG8bZ-WZTMEg2023年秋季学期俄罗斯专家线上课程介绍
中俄数学中心 SRMC 2023-08-24 16:11 发表于北京
01
Geometry and topology of integrable Hamiltonian systems
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Prof. Elena Kudryavtseva
Moscow State University
Abstract: The course focuses on three main problems: to study topology, singularities (structurally stable singularities), and symplectic invariants of such singular Lagrangian fibrations. Using topological invariants of such fibrations makes it possible to effectively analyze the stability of equilibrium points and periodic solutions, and describe different dynamical regimes and passages between them without cumbersome calculations. It turns out that any integrable Hamiltonian system (for a wide class of systems arising in mechanics) can be assigned with a combinatorial object — an n-dimensional complex equipped with labels, that depends only on the topology of the foliation (i.e., it is a topological invariant). We will describe this topological invariant in the simplest cases — for integrable Hamiltonian systems on 2- and 4-manifolds. For such systems, this topological invariant completely characterizes the topology of the foliation.
Time：
The course starts on September 11, 2023 (Monday)
Mondays 18:40-19:30 19:40-20:30
Wednesdays 15:10-16:00 16:10-17:00
注：
该课程在选课系统中的名称：
00102933 拓扑学专题（研究生）
00137230 算术代数几何选讲（本科生）
助教联系方式：1321088183@qq.com
Tencent Meeting MONDAYS
https://meeting.tencent.com/dm/M6xRbDKyDplJ
Meeting ID: 177-807-310; Password: 1123
Tencent Meeting WEDNESDAYS
https://meeting.tencent.com/dm/1oeeP4waxg93
Meeting ID: 666-2395-5174; Password: 1123
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