Speaker: Ralph Kaufmann (UConn)
Title: Operads, Strings and Deligne's conjecture
Abstract: Motivated by ideas in string topology, D-branes and Deligne's conjecture, we study cell level actions of moduli spaces. For this we construct operadic models for certain moduli spaces of curves with extra structure and then find natural algebras over them. Using a combinatorial description of moduli space, we first show how to obtain cell level operads and then describe how these operate on Hochschild cochains of various algebras. This allows us to recover Deligne's conjecture and prove several generalizations of it.