## Kontsevich formality theorem and applications to Lie theory and complex geometry

**Speaker(s): ** Professor Ping Xu (Penn State University)

**Time: **December 18 - December 23, 2013

**Venue: ** Room 29 at Quan Zhai, BICMR

Time: Wednesday Dec. 18, Thursday Dec. 19, Monday Dec. 23, 9:30-11:30 am.

Speaker: Professor Ping Xu (Penn State University)

Venue: Room 29 at Quan Zhai, BICMR

Abstract: In 1997, Kontsevich proved his famous formality theorem, which implies the existence of deformation quantization for a general Poisson manifold. However, Kontsevich formality theorem has many deep applications beyond Poisson geometry. One example is an alternative proof of the Duflo theorem in Lie theory. Another is in complex geometry. For a complex manifold $X$, Kontsevich described the relation between the Gerstenhaber algebra structure on $H^*(X, \wedge^* T_X)$ and the one on the Hochschild cohomology group $HH^*(X)$. In these lectures, I will give an overview of Kontsevich formality theorem.