EVENT DETAILS AND ABSTRACT

Title: Formality of the homotopy Gerstenhaber algebra of Hochschild cochains of a regular algebra
Speaker: Professor Vasiliy Dolgushev
Speaker Info: Northwestern Unversity
Brief Description:
Special Note:
Abstract:

I will speak about my joint paper math.KT/0605141 with Dmitry Tamarkin and Boris Tsygan. The main slogan of this paper is the following: ``No more Fedosov resolutions, no more jets!'' We do NOT need all this in order to prove Kontsevich's formality theorem and even a more general result for an arbitrary smooth variety. I am actually going to explain the idea of the proof in my talk. Let me explain the words in the title. Gerstenhaber algebra is a graded vector with a commutative product and Lie bracket of degree -1. Of course these operations are assumed to be compatible. You can easily add the word ``homotopy'' to ``Gerstenhaber algebra'' if you know the idea of going from associative algebras to A-infinity algebras. A DG algebra is formal if it is quasi-isomorphic to its cohomology. So we will need a chain of quasi-isomorphisms. In order to understand the construction of the terms in this chain you will only need to know the bar and cobar constructions for (co)associative (co)algebras.