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.
Member Seminar Intro
The BIMSA member seminar is a weekly event during which researchers engage in discussions about their extensive research interests, addressing a diverse audience that includes fellow researchers and all postdoctoral scholars within the institute. This forum provides a unique privilege and an invaluable opportunity for each research faculty member, serving as a speaker, to introduce their research field, promote the subject within the institute, and ignite the potential for future collaborations with other research groups within the institute.
The lecture format consists of a 30-minute colloquium-style presentation, thoughtfully tailored to be accessible to postdoctoral scholars and researchers from diverse disciplines within the institute. Following the presentation, a 15-minute discussion session is anticipated, involving active participation from postdocs representing various fields.
It is mandatory for all postdocs at the institute to actively participate in this event. The enthusiastic involvement of faculty members is greatly valued and will prove mutually beneficial for both the speaker and the junior audience.
