Ben Ward from Purdue University speaking about "Cyclic A_∞ Algebras and Deligne's Conjecture".

Abstract: First we describe a class of homotopy Frobenius algebras via cyclic operads which we call cyclic A_∞ algebras. We then define a suitable new combinatorial operad which acts on the Hochschild cochains of such an algebra in a manner which encodes the homotopy BV structure. Moreover we show that this operad is equivalent to the cellular chains of a certain topological (quasi)-operad of CW complexes whose constituent spaces form a homotopy associative version of the Cacti operad of Voronov. These cellular chains thus constitute a chain model for the framed little disks operad, proving a cyclic A_∞ version of Deligne's conjecture.