Geometry of Integrable Systems

Time：Fri., 13:30-16:30, Sept. 19-Dec. 5, 2025

Venue：B627, Shuangqing Complex Building A

Organizer：/

Speaker：Peter Koroteev

Speaker

Peter Koroteev

Associate Professor of BIMSATime

Fri., 13:30-16:30, Sept. 19-Dec. 5, 2025

Venue

B627, Shuangqing Complex Building A

Online

Zoom Meeting ID: 6377340280

Passcode: BIMSA

Description

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

Prerequisite：

The course should be accessible for an advance undergraduate student.

Target Audience:

1.Undergraduate students/ Graduate students

2.Postdocs/Researchers

Teaching Language: English

DATESeptember 5, 2025

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