BIMSA > BIMSA Member Seminar Integrable systems and representation theory: between geometry, algebra and analysis
Integrable systems and representation theory: between geometry, algebra and analysis
Organizers
Yuval Peres , Artan Sheshmani , Mohammad Yavartanoo
Speaker
Nicolai Reshetikhin
Time
Monday, April 29, 2024 5:00 PM - 5:45 PM
Venue
A6-101
Online
Zoom 388 528 9728 (BIMSA)
Abstract
This talk is an overview of some of the research directions that I am currently interested in. We will start with basic notions. The notion of an integrable system is clearly defined in the Hamiltonian mechanics, it extends naturally to quantum systems and to models of statistical mechanics where the transfer matrix is considered as a quantum evolution. After this introduction, I will focus on some examples that clearly illustrate the relation between integrable systems and representation theory. If time permit, I will also mention another research direction which is very important for quantum field theory but is not a part of the "world of integrable systems". It is the quantization of gauge theories.
Speaker Intro
Professor Nicolai Reshetikhin was born in Leningrad, former Soviet Union, now St. Petersburg, Russia. In 1982, he graduated from Leningrad State University with a bachelor's degree and a master's degree. In 1984, he graduated from the Steklov Institute of Mathematics and obtained a PhD degree. He has taught at well-known universities such as Harvard University, the University of California, Berkeley and the University of Amsterdam. He was invited twice to give a talk at the ICM International Conference of Mathematicians, one of which was a plenary talk. Professor Reshetikhin's main research interests include quantum topology, quantum groups and their representations, classical and quantum integrable systems, and integrable models statistical mechanics. He is one of the founders of quantum group theory, one of the authors of Reshetikhin-Turaev invariant, has important results in the theory of quantum integrable system, in Poisson and symplectic geometry, in the theory of quantum Kac Moody algebra. In 2010, he was elected as a Foreign member of the Royal Danish Academy. In 2021, he became a Fellow of the American Mathematical Society.