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VERSION:2.0
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CALSCALE:GREGORIAN
BEGIN:VEVENT
UID:3a217cba-6a83-4c7c-be36-c45ee0677bc0@nexttoyou
DTSTAMP:20261106T175222Z
DTSTART:20261113T190000Z
DTEND:20261113T200000Z
SUMMARY:Algebra and Combinatorics Seminar
LOCATION:Founders Building (FO) 2.208\, 800 W. Campbell Road\, Richardson\
 , Texas 75080-3021
DESCRIPTION:Speaker: Michael Shapiro (Michigan State University)\n\nTitle:
  Symplectic groupoid and cluster structure on the Teichmueller space of c
 losed genus two surfaces.\n\nAbstract: The symplectic groupoid of unipote
 nt nxn upper-triangular matrices is formed by pairs (B\, A) where B is a 
 nondegenerate nxn matrix\, A is a unipotent upper-triangular nxn matrix\,
  and BAB^t is unipotent upper triangular. The symplectic groupoid is equi
 pped with the natural symplectic form defined by Bondal\, which induces a
  Poisson bracket on the space of upper triangular unipotent matrices stud
 ied by Bondal\, Dubrovin-Ugaglia\, and others.\nWe compute the cluster st
 ructure compatible with the Poisson structure and discuss its connection 
 with the Teichmueller space of genus g curves with one or two holes equip
 ped with a Goldman Poisson bracket.\nAs an unexpected byproduct\, we obta
 in a cluster structure on the Teichmueller space of closed genus two curv
 es unknown earlier. This is a joint project with L. Chekhov.\n\nhttp://ne
 xt-to-u.app/events/3a217cba-6a83-4c7c-be36-c45ee0677bc0
URL:http://next-to-u.app/events/3a217cba-6a83-4c7c-be36-c45ee0677bc0
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