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SUMMARY:Khovanov-Rozansky homology counts solutions to PDE
DTSTART:20260324T090000Z
DTEND:20260324T100000Z
DTSTAMP:20260501T113800Z
UID:indico-event-5784@agenda.irmp.ucl.ac.be
DESCRIPTION:Speakers: Maxime Weytens (Université Libre de Bruxelles)\n\nG
 iven a knot K in S^3\, seen as the boundary of hyperbolic 4-space\, the co
 unts n_{g\,d}(K) of minimal surfaces filling K of genus g and « twistor d
 egree » d are knot invariants. J. Fine conjectured that they may be assem
 bled to recover the HOMFLYPT polynomial.\n\nFollowing ideas of Donaldson a
 nd Thomas\, we conjecture a way to categorify this count. This is done via
  Floer homology techniques\, where the complex is generated by those minim
 al surfaces and the boundary map is constructed out of a count of a specia
 l type of submanifolds called « associative ».\n\n\nIt is natural to bel
 ieve that these homology knot invariants coincide with Khovanov-Rozansky h
 omology. If so\, knowledge of KR homology would give an existence result f
 or solutions of non-linear PDEs!\n\n\nhttps://agenda.irmp.ucl.ac.be/event/
 5784/
LOCATION:B/2nd floor-B.203 - Seminar room (Marc de Hemptinne (chemin du Cy
 clotron\, 2\, Louvain-la-Neuve))
URL:https://agenda.irmp.ucl.ac.be/event/5784/
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