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Khovanov-Rozansky homology and q,t Catalan numbers

Presented by: 
Matthew Hogancamp University of Southern California
Tuesday 11th April 2017 - 11:30 to 12:30
INI Seminar Room 1
I will discuss a recent proof of the Gorsky-Oblomkov-Rasmussen-Shende conjecture for (n,nm+1) torus knots, which generally expresses the Khovanov-Rozansky homology of torus knots in terms of representations of rational DAHA.  The proof is based off of a computational technique introduced by myself and Ben Elias, using complexes of Soergel bimodules which categorify certain Young symmetrizers.  We will summarize this technique and indicate how it results in a remarkably simple recursion which computes the knot homologies in question.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons