Scattering diagrams from stability conditions
Hot Topics: Cluster algebras and wall-crossing March 28, 2016 - April 01, 2016
Location: MSRI: Simons Auditorium
quivers
algebraic combinatorics
quiver representations
Representation theory
category theory
Jacobi algebra
14484
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
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