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SUMMARY:Minh-Tâm Trinh (MIT)
DTSTART:20221006T185000Z
DTEND:20221006T195000Z
DTSTAMP:20260423T010012Z
UID:GPRTatNU/56
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GPRTatNU/56/
 ">Catalan combinatorics versus nonabelian Hodge theory</a>\nby Minh-Tâm T
 rinh (MIT) as part of Geometry\, Physics\, and Representation Theory Semin
 ar\n\n\nAbstract\nThe Oblomkov–Rasmussen–Shende conjecture relates the
  homologies of the Hilbert schemes of a plane curve singularity to the tri
 ply-graded Khovanov–Rozansky (i.e.\, HOMFLYPT) homology of its link\, vi
 a an identity in variables a\, q\, t. Two major cases are known: (1) the t
  = -1 limit\, settled a decade ago by Maulik\; (2) the lowest-a-degree\, q
  = 1 limit of the "torus link" case\, settled jointly by Elias–Hogancamp
 \, Mellit\, and Gorsky–Mazin\, using (q\, t)-Catalan combinatorics as an
  essential bridge. An unpublished research statement of Shende speculated 
 that the ORS conjecture could be proved in a third\, totally different way
 \, via a wild analogue of the P = W phenomenon in nonabelian Hodge theory.
  He and his coauthors carried out most of this approach for the "torus-kno
 t" subcase of case (1). We extend their work\, and also refine it enough t
 o handle the (more difficult) torus-knot subcase of case (2). The key is o
 ur new geometric model for Khovanov–Rozansky homology\, which realizes t
 he t variable as cohomological degree. If there is time\, we will explain 
 how this flavor of nonabelian Hodge theory is related to the noncrossing-n
 onnesting dichotomy in Catalan combinatorics.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/56/
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