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SUMMARY:Dylan Allegretti (University of British Columbia)
DTSTART:20201110T160000Z
DTEND:20201110T170000Z
DTSTAMP:20260423T021138Z
UID:OCAS/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OCAS/11/">St
 ability conditions and cluster varieties</a>\nby Dylan Allegretti (Univers
 ity of British Columbia) as part of Online Cluster Algebra Seminar (OCAS)\
 n\n\nAbstract\nIn the first part of the talk\, I will describe a construct
 ion in low-dimensional topology that takes a holomorphic quadratic differe
 ntial on a surface and produces a $PGL(2)$-local system. This\nconstructio
 n provides a local homeomorphism from the moduli space of quadratic differ
 entials to the moduli space of local systems. In the second part of the ta
 lk\, I will propose a categorical\ngeneralization of this construction. In
  this generalization\, the space of quadratic differentials is replaced by
  a complex manifold parametrizing Bridgeland stability conditions on a cer
 tain\n3-Calabi-Yau triangulated category\, while the space of local system
 s is replaced by a cluster variety. I will describe a local homeomorphism 
 from the space of stability conditions to the cluster\nvariety in a large 
 class of examples and explain how it preserves the structures of these two
  spaces.\n
LOCATION:https://researchseminars.org/talk/OCAS/11/
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