Koszul duality patterns in Floer theory

Princeton/IAS/Columbia Symplectic Geometry Seminar
Topic:Koszul duality patterns in Floer theory
Speaker:Yankı Lekili
Affiliation:University of Illinois, Chicago
Date:Friday, March 13
Time/Room:2:30pm - 3:30pm/Math 407, Columbia University

We study symplectic invariants of the open symplectic manifolds $X$ obtained by plumbing cotangent bundles of spheres according to a plumbing tree. We prove that certain models for the Fukaya category $\mathcal F(X)$ of closed exact Lagrangians in $X$ and the wrapped Fukaya category $\mathcal W(X)$ are related by Koszul duality. As an application, we give explicit computations of symplectic cohomology for the vast majority of these symplectic manifolds (including the case of $A_n$-Milnor fibres). This is joint work with Tolga Etgü.