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Khovanov-Rozansky homology and q,t Catalan numbers

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HTLW03 - Physics and knot homologies

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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