Spaces of Bridgeland stability conditions in representation theory

Abstract

The space of Bridgeland stability conditions is a complex manifold that can be attached to a triangulated category, of which it encodes some homological properties. These notes are an introduction to this topic, with a focus on examples from representation theory, and review the example of the Bridgeland-Smith correspondence for some quiver categories from marked surfaces.

Survey article based on a mini-course held by the author in 2022 at the International Conference on Representation of Algebras. To appear in the Proceedings Volume of the 20th ICRA. v2: references updated