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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Minimal models of symplectic quotient singularitie
s - Ulrich Thiel (University of Kaiserslautern)
DTSTART;TZID=Europe/London:20200130T134500
DTEND;TZID=Europe/London:20200130T143500
UID:TALK138184AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/138184
DESCRIPTION:Namikawa associated to any conic symplectic singul
arity a hyperplane arrangement which is deeply int
ertwined with its geometry. For example\, Bellamy
proved that for a symplectic quotient singularity
the cohomology of the complement of this arrangeme
nt encodes the number of minimal models of the sin
gularity. For the symplectic singularity associate
d to a complex reflection group we were able to pr
ove that the Namikawa arrangement coincides with t
he degenericity locus of the number of torus fixed
points of the corresponding Calogero-Moser deform
ation. This has a series of remarkable consequence
s\, especially it proves a conjecture by Bonnaf&ea
cute\; and Rouquier. Using representation theory a
nd sophisticated computer algebraic methods\, we c
ould compute this arrangement explicitly for sever
al exceptional complex reflection groups. The arra
ngements seem to be of a new kind\, and many more
are out there. This is joint work with Gwyn Bellam
y (Glasgow) and Travis Schedler (London)\, and wit
h Cé\;dric Bonnafé\; (Montpellier).
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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