SPEAKER: Dmitry Vaintrob
TITLE: Hochschild cohomology of group algebras, string topology and the Goldman Lie algebra.
ABSTRACT Chas and Sullivan discovered that the homology of the space of free loops (string topology) of a closed oriented smooth manifold has a structure of a Batalin-Vilkovisky (BV) algebra. We study the string topology BV algebra of aspherical manifolds. We prove that in this case it is isomorphic to the BV algebra of the Hochschild cohomology HH^*(A) of the group algebra A of the fundamental group. In particular, for a closed oriented surface X of genus g>1 we obtain a complete description of the BV algebra operations on H_*(LX) and HH^*(A) in terms of the Goldman bracket of loops on X. The only manifolds for which the BV algebra structure on H(LX) was known before were spheres.