Speaker: Justin Thomas from University of Notre Dame

Title: Kontsevich's Swiss Cheese Conjecture

Abstract: We prove a conjecture of Kontsevich which states that if A is an Ed-1 algebra then the Hochschild cohomology object of A is the universal Ed algebra acting on A. The notion of an Ed algebra acting on an Ed-1 algebra was defined by Kontsevich using the swiss cheese operad of Voronov. We prove a homotopical property of the swiss cheese operad from which the conjecture follows.