Scattering diagrams from stability conditions
Presenter
March 30, 2016
Keywords:
- quivers
- quiver representations
- algebraic combinatorics
- representation theory
- category theory
- Jacobi algebra
MSC:
- 18E30
- 18E35
- 16G60
- 16G20
- 16Gxx
- 13F60
Abstract
Stability conditions on triangulated categories allow us to define moduli spaces of objects in the category which undergo wall-crossing as the stability condition varies. We will consider certain Calabi-Yau-3 triangulated categories whose space of stability conditions has a wall-and-chamber structure which "categorifies" mutation in a corresponding cluster algebra. Following a recent article of Bridgeland I will show how to enhance this wall-and-chamber structure to a scattering diagram which in certain cases coincides with the scattering diagram associated to the cluster algebra by Gross-Hacking-Keel-Kontsevich.