From Deformation to Quantization

Nowadays deformation theory of algebraic structures is a well developed, but still central, topic in different research areas of mathematics like algebraic topology, mathematical physics, algebraic geometry... The first example of this kind of deformations were infinitesimal and formal deformations of associative algebras, introduced by Gerstenhaber in the sixties. The aim of this talk is to give an introduction to this example and to the principal tool used in deformation theory, the Hochschild cohomology, and to show a modern application: deformation quantization of Poisson manifolds (Kontsevich, 1997).

http://math.univ-lille1.fr/~cesaro/