**2023년 11월 QSMS Monthly Seminar**

**Date:**Nov. 10th (Fri) 14:00 ~ 17:00**Place:**27-220 (SNU)**Contents:**

**Speaker: **김유식 (부산대)

**Title: **Cluster structures on polygon spaces

**Abstract**: I will talk about polygon spaces, completely integrable systems, and their cluster structures.

**Speaker: **Sylvain Carpentier (서울대)

**Title: **From classical to quantum integrability

**Abstract**: Integrable models are non-generic systems with a large group of symmetries, conservation laws and can often be exactly solved. Integrable systems in infinite dimension lie at the crossroads of combinatorics, number theory, Lie theory, representations of non-commutative algebras, and geometry, to name a few. The goal of this lecture is to discuss the various algebraic structures that lie behind these systems and are responsible for their high level of symmetry. First, we will explain how classical integrable systems of PDEs or differential-difference equations can be cast in a Hamiltonian formalism and review the concepts of Lax pairs and recursion operators. In a second time we will look at the so-called quantum spin chains systems through the scope of R matrices and describe their connections with quantum groups. Finally we will present advances made in our new scheme of quantization, which proposes a systematic way of constructing a quantum system from a classical integrable system.