Abstract:

I will explain how to generalize the usual deformation theory to the non-commutative (more precisely, not necessarily commutative) case. I will consider the case where the fiber of the deformation is non-commutative, and also the case where the base is non-commutative.

Lecture 1: Hochschild cohomology and infinitesimal deformations.

Lecture 2: Deformation of an abelian category as a non-commutative variety.

Lecture 3: Multi-pointed non-commutative deformations of sheaves.