Ralph Cohen : Calabi-Yau categories, string topology, and the Floer field theory of the cotangent bundle.

Abstract: I will describe joint work with Sheel Ganatra, in which we prove an equivalence between two chain complex valued topological field theories: the String Topology of a manifold M, and the Floer field theory of its cotangent bundle. This expands upon results of Viterbo, Abbondandolo and Schwarz, Abouzaid, and others. We use recent work of Kontsevich and Vlassopolous which describes two duality conditions among A-\infty-algebras and categories and show how they give rise to topological field theories. These "Calabi-Yau" conditions are related to the two dimensional cobordism hypothesis viewpoint of Lurie. We use this perspective to prove the equivalence of the theories above. We then show how Koszul duality affects the Calabi-Yau condition, and how it gives rise to a duality relationship between field theories.