Overall introduction:
This seminar is about integrable systems. In the first part, we are going to follow the book of Gleb Arutyunov, Elements of classical and quantum integrable systems, which includes the topics about Liouville Integrability, Integrability from Symmetries, Quantum-Mechanical Integrable Systems, Factorised Scattering Theory, Bethe ansatz and Integrable Thermodynamics. When we cover these topics, we plan to discuss some advanced topics related to quantum field theories. Listeners are welcome to suggest some interesting topics about integrable systems and give talks.
Upcoming talk:
Title: The integrable models of statistical physics
Speaker: Hao Wang (YMSC)
Time: 2023/06/08 (Thursday)；15:20-17:50pm
Venue：静斋304 (Jingzhai 304)
Abstract:
This time I will talk about the integral models of statistical physics, including the quantum spin models, Yang-Baxter realtions and the some algebraic relations related to quantum group.
Past talks:
Title: The Lax Method
Speaker: Hao Wang (YMSC)
Time: 2023/06/01 (Thursday)；15:20-17:50pm
Venue：静斋304 (Jingzhai 304)
Abstract:
This time I will talk about the Lax method which allows one to find an appropriate linear equation for a given nonlinear evolution equation. I will talk about its origin in Schordinger equation, the formal Lax theory and its specialization to KdV case.
Title: Inverse Scattering Method(II)
Speaker：Hao Wang (YMSC)
Time: 2023/05/18 (Thursday)；15:20-17:50pm
Venue：静斋304 (Jingzhai 304)
Abstract:
This time I will talk about general theory of inverse scattering method. First I will begin fromt he one-dimensional scattering problem and then give a description on the analytic behavior of scattering coefficients. Finally I will talk about the action-angle variables for KdV.
Title: Introduction to KdV equation(III) and Inverse Scattering Method(I)
Speaker：Hao Wang (YMSC)
Time: 2023/05/11 (Thursday)；15:20-17:50pm
Venue：静斋304 (Jingzhai 304)
Abstract:
This time I will talk about the initial value problem of KdV equation, including the scattering parameters in Schordinger equation. Then I will talk about an very important method in integrable system, i.e. inverse scattering method and show how it applies to KdV system.
Title: Introduction to KdV equation(II)
Speaker: Hao Wang (YMSC)
Time: 2023/04/27 (Thursday)；15:20-17:50pm
Venue：静斋304 (Jingzhai 304)
Abstract:
This time I will talk about the integrability properties of KdV equation, I will show that the KdV equation possess an infinite number of conserved quantites. These infinite conserved quantities are in involution to each other.
Title: Introduction to KdV equation(I)
Speaker：Hao Wang (YMSC)
Time: 2023/04/20 (Thursday)；15:20-17:50pm
Venue：静斋304 (Jingzhai 304)
Abstract:
This time I will give a basic introduction on KdV equation from the physical background of the equation and the mathematical properties of its soliton solutions. Also I will discuss the quantum mechanics of the soliton solutions of KdV equation. The talk will be two parts, next time I will introduce the integrability of KdV equation.
Title: Hamiltonian reduction and cotangent bundle of the Lie group(II)
Speaker：Hao Wang (YMSC)
Time: 2023/04/13 (Thursday)；15:20-17:50pm
Venue：静斋304 (Jingzhai 304)
Abstract:
This time I will continue to discuss the cotangent bundle of Lie group, including its symplectic form and Poisson bracket,symmetries and moment map.
Title: Hamiltonian reduction and cotangent bundle of the Lie group(I)
Speaker: Hao Wang (YMSC)
Time: 2023/04/06 (Thursday)；15:20-17:50pm
Venue：静斋304 (Jingzhai 304)
Abstract:
This time I will continue the discussion about the Hamiltonian reductio and introduce the concepts of the cotangent bundle of a Lie group.
Title: Phase Spaces with Symmetry(I)
Speaker：Hao Wang (YMSC)
Time: 2023/03/23 (Thursday)；15:20-17:50pm
Venue：静斋304 (Jingzhai 304)
Abstract:
This time I will discuss the topics about coadjoint orbits of the Lie group, Hamiltonian action of a Lie group and moment map of the hamiltonian action.
Title: Examples of Integrable system models, Lax representation and R-matrix
Speaker: Xiaoyue Sun (YMSC)
Time: 2023/03/16 (Thursday)；15:20-17:50pm
Venue：静斋304 (Jingzhai 304)
Abstract:
This time we will introduce some typical integrable systems, including Kepler Problems and multi-body problems. We will also discuss the cornerstone topics about the modern integrability theory, the Lax representaion and classical r-Matrix.
Title: Liouville integrability
Speaker: Xiaoyue Sun (YMSC)
Time: 2023/03/09 (Thursday)；15:20-17:50pm
Venue：近春园西楼第三会议室 (The Third Conference Room at Jinchunyuan West Building)
Abstract:
As the first lecture of this seminar, we will begin with an introduction of plan for this seminar and a rough historical remark of integrability. Next we'll talk about Liouville integrability, some integrable models, Lax pairs and classical r-matrix. The main reference for this lecture is the first chapter of the book of Gleb Arutyunov, Elements of Classical and Quantum Integrable Systems.
