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The cohomological McKay correspondence via Floer theory
If you have a question about this talk, please contact Ivan Smith.
The goal of my talk is to present work in progress, jointly with Mark McLean (Stony Brook, NY), which proves the cohomological McKay correspondence using symplectic topology techniques. This correspondence states that given a crepant resolution Y of the singularity \C^n / G, where G is a finite subgroup of SL(n,\C), the conjugacy classes of G are in 1-1 correspondence with generators of the cohomology of Y. This statement was proved by Batyrev (1999) and Denef-Loeser (2002) using algebraic geometry techniques. We instead construct a certain symplectic cohomology group of Y whose generators are Hamiltonian orbits in Y to which one can naturally associate a conjugacy class in G. We then show that this symplectic cohomology recovers the classical cohomology of Y. This work is part of a large-scale project which aims to study the symplectic topology of resolutions of singularities also outside of the Calabi-Yau setup.
This talk is part of the Differential Geometry and Topology Seminar series.
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