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SUMMARY:Tudor Dimofte (UC Davis)
DTSTART:20201026T180000Z
DTEND:20201026T190000Z
DTSTAMP:20260423T004641Z
UID:UMassRep/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UMassRep/12/
 ">3d mirror symmetry and HOMFLY-PT homology</a>\nby Tudor Dimofte (UC Davi
 s) as part of UMass Amherst Representation theory seminar\n\n\nAbstract\nS
 ince the original physical prediction of triply-graded HOMFLY-PT link homo
 logy by Gukov-Schwarz-Vafa\, and its mathematical definition by Khovanov-R
 ozansky\, many other (conjectural) constructions of HOMFLY-PT link homolog
 y have appeared --- with different algebraic and geometric origins\, and m
 anifesting different properties. One recent proposal of Oblomkov-Rozansky 
 (closely related to work of Gorsky-Neguț-Rasmussen) associated to a link 
 L a coherent sheaf E_L on a Hilbert scheme\, whose cohomology reproduces H
 OMFLY-PT homology. Another proposal\, by Gorsky-Oblomkov-Rasmussen-Shende\
 , computes HOMFLY-PT homology of algebraic knots via Borel-Moore homology 
 of affine Springer fibers. I will explain how the first (Hilbert scheme) c
 onstruction is realized in the "B" twist of a 3d supersymmetric gauge theo
 ry\, and then carefully apply 3d mirror symmetry to discover a variant of 
 the second (Springer fiber) construction. I will also indicate how both 3d
  gauge theory setups are related to the original work of Gukov-Schwarz-Vaf
 a based using M-theory on the resolved conifold. (Preprint soon to appear\
 , with N. Garner\, J. Hilburn\, A. Oblomkov\, and L. Rozansky).\n
LOCATION:https://researchseminars.org/talk/UMassRep/12/
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