Tuesday, December 11, 14:00, 7.527

Tom Sutherland (Mainz), Scattering diagrams (after Bridgeland)

Abstract:
Scattering diagrams arise in the context of toric degenerations, encoding data which allows for a reconstruction of a variety from its degeneration and equipping it with a canonical basis of so-called theta functions. Applied to cluster varieties associated to a quiver, it encodes certain information of the cluster algebra as well as a new basis containing the cluster variables.
The aim of this talk is to give an overview of work of Bridgeland, who constructs a scattering diagram on a real slice of the space of stability conditions on a triangulated category. Applied to a certain 3-Calabi-Yau categorification of the cluster algebra this construction recovers the scattering diagram of the cluster variety, giving a representation theoretic interpretation to the canonical basis.
No prior knowledge of scattering diagrams or stability conditions will be assumed.