Introduction to Donaldson–Thomas invariants

Abstract

These notes represent three lectures given at the International Conference on Representations of Algebras (ICRA) held at Bielefeld in August 2012. The goal of the lectures was to introduce refined Donaldson–Thomas invariants for the categories of modules over Jacobian algebras associated to quivers with potentials. We define refined Donaldson–Thomas invariants and compute them in some simple cases and then discuss their basic properties, including integrality, positivity, and wall-crossing phenomena.