Stability conditions and cluster varieties
Hot Topics: Cluster algebras and wall-crossing March 28, 2016 - April 01, 2016
Location: SLMath: Eisenbud Auditorium
quivers
quiver representations
algebraic combinatorics
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)
14493
We will study the geometry of cluster varieties from the perspective of stability conditions on the associated Calabi-Yau-3 triangulated category. I will focus on ideas introduced by Gaiotto-Moore-Neitzke which suggest how to produce cluster coordinates from stability conditions. In particular we will consider the class of examples associated to triangulations of marked bordered surfaces for which the cluster variety is a moduli space of rank 2 local systems and the space of stability conditions is a space of quadratic differentials with prescribed singularities on an associated closed surface
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14493
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