## EVENT DETAILS AND ABSTRACT

**Geometry/Physics Seminar**
**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.

**Date:** Friday, May 19, 2006

**Time:** 3:00pm

**Where:** Lunt 107

**Contact Person:** Prof. Chiu-Chu Melissa Liu

**Contact email:** ccliu@math.northwestern.edu

**Contact Phone:** 847-467-1874

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