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Recursive computations for Khovanov-Rozansky homology
Algebra & Discrete Mathematics| Speaker: | Misha Mazin, KSU |
| Related Webpage: | https://www.math.ksu.edu/~mmazin/ |
| Location: | 1147 MSB |
| Start time: | Wed, Jan 28 2026, 1:10PM |
Description
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 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 show how a similar approach can be used for certain families of monotone knots of non-triangular partitions. I will also explore the limitations of the approach and the connections to EHA and Bqt actions.
This talk is based on our joint paper with Carmen Caprau, Nicolle Gonzalez, and Matt Hogancamp, as well as more recent developments conceived in discussions with Nicolle Gonzalez and Eugene Gorsky during the semester program at ICERM in Fall 2025.
Misha will be around Davis and MSB all week, especially MWF, so make a plan to chat w/ him. This talk was postponed from Monday at 11am