Scattering diagrams from stability conditions
Hot Topics: Cluster algebras and wall-crossing March 28, 2016 - April 01, 2016
Location: SLMath: Eisenbud Auditorium
quivers
algebraic combinatorics
quiver representations
Representation theory
category theory
Jacobi algebra
18D15 - Closed categories (closed monoidal and Cartesian closed categories, etc.)
18D20 - Enriched categories (over closed or monoidal categories)
16E50 - von Neumann regular rings and generalizations (associative algebraic aspects)
16E40 - (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.)
13P10 - Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
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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14484
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