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

Registration: https://www.wjx.top/vm/wsExuN1.aspx#