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SUMMARY:The cohomological McKay correspondence via Floer theory - Alexande
 r Ritter\, Oxford
DTSTART:20170222T160000Z
DTEND:20170222T170000Z
UID:TALK69761@talks.cam.ac.uk
CONTACT:Ivan Smith
DESCRIPTION:The goal of my talk is to present work in progress\, jointly w
 ith Mark\nMcLean (Stony Brook\, NY)\, which proves the cohomological McKay
 \ncorrespondence using symplectic topology techniques. This\ncorrespondenc
 e states that given a crepant resolution Y of the\nsingularity \\C^n / G\,
  where G is a finite subgroup of SL(n\,\\C)\, the\nconjugacy classes of G 
 are in 1-1 correspondence with generators of\nthe cohomology of Y. This st
 atement was proved by Batyrev (1999) and\nDenef-Loeser (2002) using algebr
 aic geometry techniques. We instead\nconstruct a certain symplectic cohomo
 logy group of Y whose generators\nare Hamiltonian orbits in Y to which one
  can naturally associate a\nconjugacy class in G. We then show that this s
 ymplectic cohomology\nrecovers the classical cohomology of Y.  This work i
 s part of a\nlarge-scale project which aims to study the symplectic topolo
 gy of\nresolutions of singularities also outside of the Calabi-Yau setup.
LOCATION:MR13
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