Geometry of Integrable Systems
In this course, I will explain how quantum and classical integrable systems arise from algebrogeometric constructions. In particular, I will discuss space of opers and their deformations on the projective line and how this space leads to both quantum spin chains (XXX, XXZ, XYZ) and classical many-body systems (Calogero, Ruijsenaars, etc). The two types of systems are related to each other via so-called quantum/classical duality which is an integrable systems avatar of the Geometric Langlands correspondence.
The topics will include
1. (q-)Opers on the projective line
2. QQ-systems, Bethe Ansatz
3. The ODE/IM Correspondence
4. Quantum/Classical duality
5. Elliptic integrable systems
6. Enumerative algebraic geometry with connections to integrability
The topics will include
1. (q-)Opers on the projective line
2. QQ-systems, Bethe Ansatz
3. The ODE/IM Correspondence
4. Quantum/Classical duality
5. Elliptic integrable systems
6. Enumerative algebraic geometry with connections to integrability
讲师
日期
2025年09月19日 至 12月05日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周五 | 13:30 - 16:55 | Shuangqing-B627 | ZOOM 13 | 637 734 0280 | BIMSA |
修课要求
The course should be accessible for an advance undergraduate student.
听众
Undergraduate
, Graduate
, 博士后
, Researcher
视频公开
不公开
笔记公开
不公开
语言
英文
讲师介绍
My education begain in Russia where I learned math and physics at Moscow Insitute of Physics and Technology. I started my research career as a theoretical physicist after moving to the United States and obtaining my PhD from University of Minnesota in 2012. At first, my research focus was drawn to various aspects of supersymmetric gauge theories and string theory. However, I have always been fascinated by pure abstract mathematics since my student days. Since around 2017 I have been a full time mathematician.
My current research is focused on the interaction between enumerative algebraic geometry, geometric representation theory and integrable systems. In general I work on physical mathematics which nowadays represents a large part of modern math. A significant amount of problems that are studied by mathematicians comes from string/gauge theory. More recently I began to study number theory and how it is connected to other branches of mathematics.
If you are postdoc or a graduate student in Beijing area and you are interested in working with me contact me via email.
My current research is focused on the interaction between enumerative algebraic geometry, geometric representation theory and integrable systems. In general I work on physical mathematics which nowadays represents a large part of modern math. A significant amount of problems that are studied by mathematicians comes from string/gauge theory. More recently I began to study number theory and how it is connected to other branches of mathematics.
If you are postdoc or a graduate student in Beijing area and you are interested in working with me contact me via email.