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SUMMARY:Non-perturbative hyperkahler manifolds - Boalch\, P (Universit Par
 is-Sud)
DTSTART:20150727T133000Z
DTEND:20150727T143000Z
UID:TALK60212@talks.cam.ac.uk
CONTACT:42080
DESCRIPTION:Following Kronheimer's construction of the ALE spaces from the
  ADE affine Dynkin graphs\, and Kronheimer-Nakajima's subsequent extension
  of the ADHM construction\, a large class of hyperkahler manifolds attache
 d to graphs emerged\, known as "quiver varieties". Nakajima has shown they
  play a central role in representation theory. If the underlying graph is 
 of a special type it turns out that the corresponding quiver varieties hav
 e natural partial compactifications\, which also admit complete hyperkahle
 r metrics. They arise as spaces of solutions to Hitchin's equations on Rie
 mann surfaces\, with wild boundary conditions. (They were constructed in w
 ork with Biquard published in 2004). The class of graphs for which this wo
 rks are known as "supernova" graphs and includes all the complete multipar
 tite graphs. In particular the square and the triangle are supernova graph
 s\, and so some gravitational instantons arise in this way. In this talk I
  will review this story focussing on specific examples and recent developm
 ents such as the algebraic construction of the underlying holomorphic symp
 lectic manifolds (the "wild character varieties").\n
LOCATION:Seminar Room 1\, Newton Institute
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