[QSMS Monthly Seminar] Yokonuma Hecke algebras and invariants of framed links

by qsms posted May 27, 2022


PrevPrev Article

NextNext Article


Larger Font Smaller Font Up Down Go comment Print
Extra Form
일정시작 2022-05-27
일정종료 2022-05-27
배경색상 #036eb7

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


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


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.





1 2 3 4 5 6 7 8