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Introduction to Integrable Systems
February 9–May 25, 2021, MIPT - MI RAS, Moscow

The first part of a course is mainly devoted to classical integrable systems. Main algebraic structures will be described such as the Lax equations, the classical r-matrices and related Poisson structures on Lie (co)algebras, coadjoint orbits and Lie groups. We will review different kind of models including examples of many-body systems, integrable tops, the classical (spin) chains as well as their continuous limit leading to integrable field theories having soliton type solutions. The phenomenon of integrability is often related to existence of symmetries, generated by the action of groups, and generating the conservation laws. Using the moment map technique, we will see that integrable systems can be obtained by performing the Hamiltonian reduction starting from a free motion. In the end we come to the main idea of R-matrix quantization underlying the quantum inverse scattering method and the Bethe ansatz. We will explain how the quantum groups appear naturally in this way.

To connect via Zoom:
Zoom link
Zoom meeting ID: 976 0728 1275
password: 303200


Spring Semester Schedule of 2020/2021:

Time: Tuesday 13:35 – 15:00

First lecture: 9 February


Financial support. The course is supported by the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, Agreement no. 075-15-2019-1614).

RSS: Forthcoming seminars

Seminar organizer
Zotov Andrei Vladimirovich

Institutions
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
Steklov International Mathematical Center


Introduction to Integrable Systems, Moscow, February 9–May 25, 2021

April 6, 2021 (Tue)
1. Lecture 8. Introduction to Integrable Systems
A. V. Zotov
April 6, 2021 13:35, Moscow, MIPT - MI RAS

March 30, 2021 (Tue)
2. Lecture 7. Introduction to Integrable Systems
A. V. Zotov
March 30, 2021 13:35, Moscow, MIPT - MI RAS

March 23, 2021 (Tue)
3. Lecture 6. Introduction to Integrable Systems
A. V. Zotov
March 23, 2021 13:35, Moscow, MIPT - MI RAS

March 16, 2021 (Tue)
4. Lecture 5. Introduction to Integrable Systems
A. V. Zotov
March 16, 2021 13:35, Moscow, MIPT - MI RAS

March 9, 2021 (Tue)
5. Lecture 4. Introduction to Integrable Systems
A. V. Zotov
March 9, 2021 13:35, Moscow, MIPT - MI RAS

March 2, 2021 (Tue)
6. Lecture 3. Introduction to Integrable Systems
A. V. Zotov
March 2, 2021 13:35, Moscow, MIPT - MI RAS

February 16, 2021 (Tue)
7. Lecture 2. Introduction to Integrable Systems
A. V. Zotov
February 16, 2021 13:35, Moscow, MIPT - MI RAS

February 9, 2021 (Tue)
8. Lecture 1. Introduction to Integrable Systems
A. V. Zotov
February 9, 2021 13:35, Moscow, MIPT - MI RAS
 
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