QM Research Seminar: The complex geometry of Bridgeland stability conditions

Seminar by Ruadhaí Dervan (University of Glasgow)

Abstract:

Bridgeland stability conditions give a very general way of understanding the algebro-geometric notion of stability on a triangulated category. In the simplified, geometric situation of a holomorphic vector bundle, I will describe a conjectural counterpart to stability through the notion of a Z-critical connection. This is concretely a Hermitian metric on the vector bundle satisfying a geometric partial differential equation. The conjecture is motivated by the Hitchin-Kobayashi correspondence, which links the existence of Hermite-Einstein metrics to the notion of slope stability of a holomorphic vector bundle. This is joint work with John McCarthy and Lars Sektnan.