BIMSA

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).

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。