Combinatorics Seminar: Combinatorial recursions for Khovanov-Rozansky homology, Mikhail Mazin, Kansas State University

Wednesday, September 11, 2024 3:30pm

 Khovanov-Rozansky homology is a powerful knot and link invariant categorifying the HOMFLY-PT polynomial. Matt Hogancamp and Anton Mellit, based on a previous work of Hogancamp and Elias, introduced a recursive algorithm for computing Khovanov-Rozansky homology, and applied it to torus links. Together with Carmen Caprau, Nicolle Gonzalez, and Matt Hogancamp, we generalized the work of Hogancamp and Mellit to include a new family of knots, the monotone knots of triangular partitions. We also related the resulting Poincare polynomials to combinatorics of generalized Dyck paths and Shuffle Theorem under any line.

In this talk, I will introduce Hogancamp-Mellit's recursions and monotone knots, and explain how one can apply this recursion to compute the Khovanov-Rozansky homology of monotone knots of triangular partitions.

 

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