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
Lecturer
Date
19th September ~ 5th December, 2025
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Friday | 13:30 - 16:55 | Shuangqing-B627 | ZOOM 13 | 637 734 0280 | BIMSA |
Prerequisite
The course should be accessible for an advance undergraduate student.
Audience
Undergraduate
, Graduate
, Postdoc
, Researcher
Video Public
No
Notes Public
No
Language
English
Lecturer Intro
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.