2025년 05월 QSMS  Monthly Seminar

 

• Date:   May 22th (Fri) 14:00 ~ 17:00
• Place:  27-220 (SNU)
• Contents:

 

Speaker:  조철현 (SNU)

Title:  Simple Lie algebras from simple curve singularities
Abstract:  We give a geometric construction of simple Lie algebras from the corresponding simple singularities. Milnor fibers of each simple singularities are rearranged to form, what we call, a Coxeter wheel, whose equivalence class of edges and diagonals can be identified with the corresponding root system of the Lie algebra. We give a geometric definition of Lie brackets using elementary operations in singularity theory. This is a joint work Wonbo Jeong with Beom-seok Kim

 

Speaker:  김종명 (SNU)

Title:   Constructing a new Fukaya category for a marked disk

Abstract:  $A_n$ Milnor fibers are often used as testing grounds for symplectic geometry. Although we have a good understanding of these spaces, many aspects still remain unclear. One of such aspects is the cluster structures on the Rabinowitz Fukaya categories of $A_n$ Milnor fibers. In order to understand these structures, we are attempting to construct a new Fukaya category for a marked disk by "unspecializing" the dimension of an $A_n$ Milnor fiber. This can be viewed as a symplectogeometric realization of the Calabi-Yau X-category introduced by Ikeda and Qiu, or as a categorification of the work of Khovanov and Seidel. In this talk, I will provide an overview and discuss the current state of our project. This is based on an ongoing work with Hanwool Bae and Wonbo Jeong.