UNAM

Stability conditions and cluster varieties

Ponente: Dylan Allegretti
Institución: University of British Columbia
Tipo de Evento: Investigación

Cuándo 10/11/2020
de 10:00 a 11:00
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.

NotaEsta 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.