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SCGP Weekly Talk: Ralph Cohen, Standford

Title: Calabi-Yau categories, string topology, and the Floer field theory of the cotangent bundle
Speaker: Ralph Cohen, Stanford
Date: Tuesday, November 11, 2014
Time: 01:00pm – 02:00pm
Place: Lecture Hall 102, Simons Center

 

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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. We use recent work of Kontsevich, Lurie, and and others which describe duality conditions (the “Calabi-Yau” conditions) among algebras and categories and show how they give rise to topological field theories. 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.