**2022년 4월 QSMS Monthly Seminar**

**Date:**27 May Fri PM 2:00 ~ 5:00**Place:**27-220 (SNU)**Speaker: Myungho Kim**

**Title: Yokonuma Hecke algebras and invariants of framed links**

**Abstract: **

Yokonuma-Hecke algebra (of rank n) is a finite-dimensional quotient of the group algebra of the framed braid group $F_n$, which is a semidirect product of $Z^n$ with the braid group $B_n$. Yokonuma-Hecke algebras provide a polynomial invariant for framed links along the similar line as the Iwahori-Hekce algebras of type A provide the HOMFLYPT polynomials. We will review the construction of the invariants in this talk.

**Speaker: Hanwool Bae**

**Title: Calabi-Yau cluster structures on Rabinowitz Fukaya categories**

**Abstract: **

In this talk, I will consider the plumbing of the cotangent bundles of (d+1)-dimensional spheres along a tree T. I will discuss that its (derived) wrapped Fukaya category W, its (derived) compact Fukaya category F, and a certain generator L of W form a (d+1)-Calabi-Yau triple, where L is given by the direct sum of cocore disks. This implies that the quotient category W/F carries a d-Calabi-Yau cluster structure. Recently, by Ganatra-Gao-Venkatesh, the quotient category W/F was shown to be quasi-equivalent to the Rabinowitz Fukaya category if F is a Koszul dual subcategory of W. Using this result, in the case the tree T is given by a Dynkin diagram of type A,D or E, I will discuss how to show that the Lagrangian Rabinowitz Floer homology of L and itself is isomorphic to the path algebra of a certain quiver as a ring .

This talk is based on a joint work with Wonbo Jeong and Jongmyeong Kim.