Introduction to Integrable Systems February 1–December 13, 2022, Steklov Mathematical Institute, Room 430 (8 Gubkina) + Zoom, 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.
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. 075-15-2022-265).
Fall Semester Schedule of 2022/2023:
Time: Tuesday 10:00 – 11:25
First lecture: September 13
Lecturers
Matushko Mariya Georgievna
Zotov Andrei Vladimirovich
Institutions
Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region Steklov Mathematical Institute of Russian Academy of Sciences, Moscow Steklov International Mathematical Center |
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Introduction to Integrable Systems, Moscow, February 1–December 13, 2022 |
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December 13, 2022 (Tue) |
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Lecture 11. Introduction to Integrable Systems II M. G. Matushko December 13, 2022 10:00, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina) + Zoom
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December 6, 2022 (Tue) |
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Lecture 10. Introduction to Integrable Systems II M. G. Matushko December 6, 2022 10:00, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina) + Zoom
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November 29, 2022 (Tue) |
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Lecture 9. Introduction to Integrable Systems II M. G. Matushko November 29, 2022 10:00, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina) + Zoom
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November 22, 2022 (Tue) |
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Lecture 8. Introduction to Integrable Systems II M. G. Matushko November 22, 2022 10:00, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina) + Zoom
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November 15, 2022 (Tue) |
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Lecture 7. Introduction to Integrable Systems II M. G. Matushko November 15, 2022 10:00, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina) + Zoom
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October 25, 2022 (Tue) |
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Lecture 6. Introduction to Integrable Systems II M. G. Matushko October 25, 2022 10:00, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina) + Zoom
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October 18, 2022 (Tue) |
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Lecture 5. Introduction to Integrable Systems II M. G. Matushko October 18, 2022 10:00, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina) + Zoom
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October 11, 2022 (Tue) |
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Lecture 4. Introduction to Integrable Systems II M. G. Matushko October 11, 2022 10:00, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina) + Zoom
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October 4, 2022 (Tue) |
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Lecture 3. Introduction to Integrable Systems II M. G. Matushko October 4, 2022 10:00, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina) + Zoom
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September 27, 2022 (Tue) |
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Lecture 2. Introduction to Integrable Systems II M. G. Matushko September 27, 2022 10:00, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina) + Zoom
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September 20, 2022 (Tue) |
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Lecture 1. Introduction to Integrable Systems II M. G. Matushko September 20, 2022 10:00, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina) + Zoom
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April 26, 2022 (Tue) |
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Lecture 12. Introduction to Integrable Systems A. V. Zotov April 26, 2022 13:10, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina) + Zoom
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April 19, 2022 (Tue) |
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Lecture 11. Introduction to Integrable Systems A. V. Zotov April 19, 2022 13:10, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina) + Zoom
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April 12, 2022 (Tue) |
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Lecture 10. Introduction to Integrable Systems A. V. Zotov April 12, 2022 13:10, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina) + Zoom
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April 5, 2022 (Tue) |
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Lecture 9. Introduction to Integrable Systems A. V. Zotov April 5, 2022 13:10, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina) + Zoom
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March 22, 2022 (Tue) |
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Lecture 8. Introduction to Integrable Systems A. V. Zotov March 22, 2022 13:10, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina) + Zoom
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March 15, 2022 (Tue) |
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Lecture 7. Introduction to Integrable Systems A. V. Zotov March 15, 2022 13:10, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina) + Zoom
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March 1, 2022 (Tue) |
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Lecture 5. Introduction to Integrable Systems A. V. Zotov March 1, 2022 13:10, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina) + Zoom
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Lecture 6. Introduction to Integrable Systems A. V. Zotov March 1, 2022 14:10, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina) + Zoom
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February 22, 2022 (Tue) |
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Lecture 4. Introduction to Integrable Systems A. V. Zotov February 22, 2022 13:10, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina) + Zoom
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February 15, 2022 (Tue) |
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Lecture 3. Introduction to Integrable Systems A. V. Zotov February 15, 2022 13:10, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina) + Zoom
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February 8, 2022 (Tue) |
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Lecture 2. Introduction to Integrable Systems A. V. Zotov February 8, 2022 13:10, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina) + Zoom
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February 1, 2022 (Tue) |
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Lecture 1. Introduction to Integrable Systems A. V. Zotov February 1, 2022 13:10, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina) + Zoom
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