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SUMMARY:Dan Kaplan (University of Birmingham\, UK)
DTSTART:20210128T120000Z
DTEND:20210128T130000Z
DTSTAMP:20260423T005749Z
UID:LAGOON/28
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LAGOON/28/">
 Multiplicative preprojective algebras in geometry and topology</a>\nby Dan
  Kaplan (University of Birmingham\, UK) as part of Longitudinal Algebra an
 d Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nIn 2006\, Crawley-B
 oevey and Shaw defined the multiplicative preprojective algebra (MPA) to s
 tudy certain character varieties. More recently\, MPAs appeared in work of
  Etgü--Lekili in the study of Fukaya categories of 4-manifolds. Nice prop
 erties of the (additive) preprojective algebra are expected to hold for MP
 As\, but most proof techniques are not available. In joint work with Travi
 s Schedler\, we define the strong free product property\, following older 
 work of Anick. Using this property\, we prove MPAs are 2-Calabi--Yau algeb
 ras for quivers containing a cycle. Moreover\, using a result of Bocklandt
 --Galluzzi--Vaccarino\, we prove the formal local structure of multiplicat
 ive quiver varieties is isomorphic to that of a (usual) quiver variety. In
  this talk\, I'll survey these ideas and illustrate them in small examples
 .\n
LOCATION:https://researchseminars.org/talk/LAGOON/28/
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