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.
Fall Semester Schedule of 2021/2022:
Time: Tuesday 14:45 – 16:10
First lecture: September 7
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
Organizations
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region Steklov International Mathematical Center |