Fukaya categories of symmetric products of disks

Abstract: Motivated by classical results and conjectures in representation theory of algebras, around 2004, Iyama introduced what nowadays is called higher Auslander–Reiten theory. On the other hand, motivated by the bordered Heegaard Floer homology of Lipshitz, Ozsváth and Thurston, around 2010, Auroux introduced what nowadays are called partially wrapped Fukaya categories associated to symmetric products of Riemann surfaces. In this talk, I will explain how these two subjects relate to each other in the simplest possible instance of each: the higher Auslander algebras of type A on the one hand, and symmetric products of disks on the other hand. This is a report of joint work with Dyckerhoff and Lekili.

Mathematics

Audience: researchers in the topic

Summer Research School: Topological Fukaya categories of surfaces with stops via gentle algebras

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