School and Workshop on Algebraic Geometry and Physics 2017

Relating stability conditions and cluster varieties

Jun 20, 2017, 12:10 PM

1h

Room D (basement) (SISSA)

Speaker

Dylan Allegretti (University of Sheffield, UK)

Abstract

I will describe the relationship between two spaces associated to a quiver with potential. The first is a complex manifold parametrizing Bridgeland stability conditions on a certain triangulated category, and the second is a cluster variety with a natural Poisson structure. For quivers of type $A_n$, I will describe a local biholomorphism from the space of stability conditions to the cluster variety. This result is a special case of work in progress with Tom Bridgeland.