Selected topics in representation theory: Hochschild (co)homology

Description

The goal of the course is to give an introduction to Hochschild (co)homology, focussing on its applications in deformation theory of algebras (and schemes), and the role of the Hochschild–Kostant–Rosenberg decomposition in all this. There will be three parts:

  1. Hochschild (co)homology for algebras
  2. Hochschild (co)homology and derived categories
  3. The Hochschild–Kostant–Rosenberg decomposition for schemes

The lecture notes of a previous installation of this course are available. All comments are welcome! They give a preview of what might be covered (which is not determined yet).

There will be 1 lecture per week.

Preliminaries

For the first part some basic knowledge of homological algebra is required, e.g. on the level of the first chapters of Weibel. For the second and third part we will need standard algebraic geometry, e.g. on the level of Hartshorne. Familiarity with derived categories will be helpful, and might be required even.