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CATEGORIES:Differential Geometry and Topology Seminar
SUMMARY:The cohomological McKay correspondence via Floer t
heory - Alexander Ritter\, Oxford
DTSTART;TZID=Europe/London:20170222T160000
DTEND;TZID=Europe/London:20170222T170000
UID:TALK69761AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/69761
DESCRIPTION:The goal of my talk is to present work in progress
\, jointly with Mark\nMcLean (Stony Brook\, NY)\,
which proves the cohomological McKay\ncorresponden
ce using symplectic topology techniques. This\ncor
respondence states that given a crepant resolution
Y of the\nsingularity \\C^n / G\, where G is a fi
nite subgroup of SL(n\,\\C)\, the\nconjugacy class
es of G are in 1-1 correspondence with generators
of\nthe cohomology of Y. This statement was proved
by Batyrev (1999) and\nDenef-Loeser (2002) using
algebraic geometry techniques. We instead\nconstru
ct a certain symplectic cohomology group of Y whos
e generators\nare Hamiltonian orbits in Y to which
one can naturally associate a\nconjugacy class in
G. We then show that this symplectic cohomology\n
recovers the classical cohomology of Y. This work
is part of a\nlarge-scale project which aims to s
tudy the symplectic topology of\nresolutions of si
ngularities also outside of the Calabi-Yau setup.
LOCATION:MR13
CONTACT:Ivan Smith
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