Stability conditions and cluster varieties
Institución: University of British Columbia
Tipo de Evento: Investigación
Cuándo |
10/11/2020 de 10:00 a 11:00 |
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Dónde | https://paginas.matem.unam.mx/ocas/ |
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Stability conditions and cluster varieties
In the first part of the talk, I will describe a construction in low-dimensional topology that takes a holomorphic quadratic differential on a surface and produces a PGL(2)-local system. This construction provides a local homeomorphism from the moduli space of quadratic differentials to the moduli space of local systems. In the second part of the talk, I will propose a categorical generalization of this construction. In this generalization, the space of quadratic differentials is replaced by a complex manifold parametrizing Bridgeland stability conditions on a certain 3-Calabi-Yau triangulated category, while the space of local systems is replaced by a cluster variety. I will describe a local homeomorphism from the space of stability conditions to the cluster variety in a large class of examples and explain how it preserves the structures of these two spaces.
Nota: Esta charla es parte del Online Cluster Algebra Seminar organizado por Anna Felikson, Michael Gekhtman, Daniel Labardini-Fragoso, Kyungyong Lee, Pierre-Guy Plamondon, Ralf Schiffler y Khrystyna Serhiyenko.