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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Non-perturbative hyperkahler manifolds - Boalch\,
P (Universit Paris-Sud)
DTSTART;TZID=Europe/London:20150727T143000
DTEND;TZID=Europe/London:20150727T153000
UID:TALK60212AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/60212
DESCRIPTION:Following Kronheimer's construction of the ALE spa
ces from the ADE affine Dynkin graphs\, and Kronhe
imer-Nakajima's subsequent extension of the ADHM c
onstruction\, a large class of hyperkahler manifol
ds attached to graphs emerged\, known as "quiver v
arieties". Nakajima has shown they play a central
role in representation theory. If the underlying g
raph is of a special type it turns out that the co
rresponding quiver varieties have natural partial
compactifications\, which also admit complete hype
rkahler metrics. They arise as spaces of solutions
to Hitchin's equations on Riemann surfaces\, with
wild boundary conditions. (They were constructed
in work with Biquard published in 2004). The class
of graphs for which this works are known as "supe
rnova" graphs and includes all the complete multip
artite graphs. In particular the square and the tr
iangle are supernova graphs\, and so some gravitat
ional instantons arise in this way. In this talk I
will review this story focussing on specific exam
ples and recent developments such as the algebraic
construction of the underlying holomorphic symple
ctic manifolds (the "wild character varieties").\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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