# 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:

- Hochschild (co)homology for algebras and deformation theory
- Hochschild (co)homology and derived categories
- The Hochschild–Kostant–Rosenberg decomposition for smooth varieties

The **lecture notes** of a previous installment of this course are available, and give you an idea of what will be covered (although there will be differences).

## 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.

## Schedule

Lectures are on **Thursday**, from **14:15 to 15:45**

The following dates are public holidays: May 13, May 27, June 3. There might be a replacement class for (some of) these days.

Bonn students can register for the course on eCampus.