**2022년 4월 QSMS Monthly Seminar**

**Date:**22 April Fri PM 2:00 ~ 5:00**Place:**129-101 (SNU)**Speaker:**Sylvaine Carpentier (14:00 ~ 15:00)

**Title:** Quantization of integrable differential difference equations

**Abstract:** We present a new approach to the problem of quantizing integrable systems of differential-difference equations. The main idea is to lift these systems to systems defined on free associative algebras and look for the ideals there that are stabilized by the new dynamics. In a reasonable class of candidate ideals, there are typically very few that are invariant for the first equation in the hierarchy. Once these ideals are picked the challenge is to prove that the whole hierarchy of equations stabilizes them. We will discuss these ideas using as a key example the hierarchy of the Bogoyavlensky equation. This is a joint work with A. Mikhailov (Leeds) and J. P. Wang (U. of Kent) that we put on arXiv last week (2204.03095).

**Speaker:** 강정수 Jungsoo Kang (16:00 ~ 17:00) Zoom

**Title:** Gysin sequence and Floer homology

**Abstract:** The Gysin sequence is a long exact sequence relating the homology of the total space of a circle bundle and that of the base space. After describing an interpretation of the Gysin sequence in Morse theory, I will discuss a counterpart in Floer theory.