Videos

Recursive computations for Khovanov-Rozansky homology

Presenter
October 22, 2025
Abstract
Khovanov-Rozansky homology of torus knots and links were computed recursively using categorified Young symmetrizers of Elias and Hogancamp in a series of papers by different combinations of Ben Elias, Matt Hogancamp, and Anton Mellit. In our joint paper with Carmen Caprau, Nicolle Gonzalez, and Matt Hogancamp, we showed that the same recursion also computes KR homology of the monotone knots of triangular partitions. Can these methods be applied to other families of knots? A natural class of knots to explore are the monotone knots of concave partitions. In this talk I will review the recursion that computes the KR homology of torus knots and monotone knots of triangular partitions, and then explore on examples how similar methods can be applied to other knots and, perhaps, what are the limitations. This talk is based on our joint paper with Carmen Caprau, Nicolle Gonzalez, and Matt Hogancamp, as well as recent discussions with Nicolle Gonzalez and Eugene Gorsky.
Supplementary Materials