BIMSA > Methods of classical integrable systems
Methods of classical integrable systems
We consider integrable tops, the Toda chain, the Calogero-Moser model, and its spin generalization.
In the first part of the course, we will consider the theoretical group approach to integrable systems(such constructions as the Lax pair, the classical r-matrix, the momentum map)
In the second part, we will study algebro-geometric ways of solving integrable systems (spectral curve, compact Riemann surfaces, higher theta functions).
Professor Lars Aake Andersson
讲师
安德烈·利亚希克
日期
2024年10月08日 至 12月10日
位置
Weekday Time Venue Online ID Password
周四 15:20 - 17:50 A3-1a-205 ZOOM 11 435 529 7909 BIMSA
周二 13:30 - 16:05 A3-1-103 ZOOM 11 435 529 7909 BIMSA
修课要求
Hamiltonian mechanics; Analysis on manifolds (vector fields, differential forms, etc.); Basics of group theory and Lie algebras (tangent algebra of a group, action of a group on a manifold, compact Lie groups); Basics of Riemann Surfaces.
参考资料
A. Babelon, D. Bernard, M. Talon. "Introduction to classical integrable systems"
B. I. Arnold "Mathematical methods of classical mechanics"
C. M. Perelomov. "Integrable Systems of Classical Mechanics and Lie Algebras"
D. Olshanetsky and A. Perelomov. "Classical integrable finite-dimensional systems related to Lie algebras"
B. A. Dubrovin, I. M. Krichever, S. P. Novikov "Integrable Systems"
听众
Advanced Undergraduate , Graduate , 博士后
视频公开
公开
笔记公开
公开
语言
英文
讲师介绍
Andrii Liashyk的研究领域是可积系统，主要研究量子系统。他于2020年获得了Skoltech高等研究中心的博士学位。2022年，他加入BIMSA担任助理教授。