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).
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).
Lecturer
Date
8th October ~ 8th December, 2024
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Thursday | 15:20 - 17:50 | A3-1a-205 | ZOOM 11 | 435 529 7909 | BIMSA |
| Tuesday | 13:30 - 16:05 | A3-1-103 | ZOOM 11 | 435 529 7909 | BIMSA |
Prerequisite
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.
Reference
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"
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"
Audience
Advanced Undergraduate
, Graduate
, Postdoc
Video Public
Yes
Notes Public
Yes
Language
English
Lecturer Intro
Andrii Liashyk is a researcher in the field of integrated systems, mainly quantum ones. He received his degree from the Center for Advanced Study at Skoltech in 2020. In 2022 he joined BIMSA as a Assistant Professor.