15 Wed  14:00 - 15:00 Kyoungmo Kim, 1
        15:30 - 16:30 Cheol-Hyun Cho, 1

16 Thu  15:00 - 16:00 Kyoungmo Kim, 2
        16:30 - 17:30 Cheol-Hyun Cho, 2

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Speaker: Kyoungmo Kim (University of Cologne)

Title: Topological Fukaya categories and Semi-gentle algebras

Abstract: Topological Fukaya categories provide a combinatorial and geometric model for partially wrapped Fukaya categories of marked surfaces. Given a suitable arc system on a marked surface, the endomorphism algebra of a formal generator in the associated topological Fukaya category is a gentle algebra. In this way, gentle algebras, a distinguished class of finite-dimensional algebras with well-understood derived categories, naturally arise from surface geometry. In the first talk, we will review topological Fukaya categories of marked surfaces and explain how arc systems give rise to gentle algebras. We will then discuss skew-gentle algebras from the viewpoint of involutive surfaces and related orbifold models, which serves as a bridge from ordinary arc systems to tagged arc systems. In the second talk, we will introduce topological Fukaya categories associated with \mathbb{Z}/2\mathbb{Z}-orbifold surfaces with marked boundary and tagged arc systems. The endomorphism algebras of suitable formal generators give rise to semi-gentle algebras, a class of derived-tame algebras containing skew-gentle algebras. We will also discuss closedness properties of this class under derived equivalence. This talk is partially based on my thesis and on joint work with Severin Barmeier, Cheol-Hyun Cho, Sibylle Schroll, Kyungmin Rho, and Zhengfang Wang.


Speaker: Cheol-Hyun Cho (POSTECH)

Title:  Geometric models of simple Lie algebras via singularity theory I, II.

Abstract: It is well-known that ADE Dynkin diagrams classify both the simply-laced simple Lie algebras and simple singularities. We introduce a polygonal wheel in a plane for each case of ADE, called
the Coxeter wheel. We show that equivalence classes of edges and spokes of a Coxeter wheel form a geometric root system isomorphic to the classical root system of the corresponding type. This wheel is in fact derived from the Milnor fiber of corresponding simple singularities of two variables, and the bilinear form on the geometric root system is the negative of its symmetrized Seifert form. Furthermore, we give a completely geometric definition of simple Lie algebras using arcs, Seifert form and variation operator of the singularity theory. It is a joint work with Wonbo Jeong and Beom-Seok
Kim.