Session S10 - Categorification, Higher Representation Theory, and Homological Knot Invariants

Tuesday, July 20, 17:30 ~ 18:05 UTC-3

Link homologies and Hilbert schemes via representation theory

Tina Kanstrup

University of Massachusetts Amherst, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The aim of this joint work in progress with Roman Bezrukavnikov is to unite different approaches to Khovanov-Rozansky triply graded link homology. The original definition is completely algebraic in terms of Soergel bimodules. It has been conjectured by Gorsky, Negut and Rasmussen that it can also be calculated geometrically in terms of cohomolgy of sheaves on Hilbert schemes. Motivated by string theory Oblomkov and Rozansky constructed a link invariant in terms of matrix factorizations on related spaces and later proved that it coincides with Khovanov-Rozansky homology. In this talk I'll discuss a direct relation between the different constructions and how one might invent these spaces starting directly from definitions.

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