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SUMMARY:Tomoyuki Arakawa (RIMS\, Kyoto University)
DTSTART:20231005T090000Z
DTEND:20231005T100000Z
DTSTAMP:20260423T035625Z
UID:EQuAL/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/EQuAL/13/">H
 ilbert Schemes of the points in the plane and quasi-lisse vertex superalge
 bras</a>\nby Tomoyuki Arakawa (RIMS\, Kyoto University) as part of Europea
 n Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\nFor each complex reflect
 ion group $\\Gamma$ one can attach a canonical symplectic singularity $\\m
 athcal{M}_{\\Gamma}$.  Motivated by the 4D/2D duality discovered by Beem e
 t at.\, Bonetti\, Menegheli and Rastelli conjectured the existence of a su
 persymmetric vertex operator algebra $\\mathbf{W}_{\\Gamma}$ whose associa
 ted variety is isomorphic to $\\mathcal{M}_{\\Gamma}$.  We prove this conj
 ecture when the complex reflection group $\\Gamma$ is the symmetric group 
 $S_N$\, by constructing a sheaf of $\\hbar$-adic vertex algebras on the Hi
 lbert schemes of $N$-points in the plane.  In physical terms\,  the vertex
  operator algebra  $\\mathbf{W}_{S_N}$ corresponds\,  by the 4D/2D duality
 \, to the $4$-dimensional $\\mathcal{N}=4$ super Yang-Mills theory with ga
 uge group $SL_N$.\nThis is a joint work with Toshiro Kuwabara and Sven Mol
 ler.\n
LOCATION:https://researchseminars.org/talk/EQuAL/13/
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