Eugene Gorsky (UC Davis), Khovanov-Rozansky homology and the flag Hilbert scheme
The Jucys-Murphy elements are known to generate a maximal commutative subalgebra in the Hecke algebra. They can be categorified to a family of commuting complexes of Soergel bimodules. I will describe a relation between a category generated by these complexes and the category of sheaves on the flag Hilbert scheme of points on the plane, using the recent work of Elias and Hogancamp on categorical diagonalization. As an application, I will give an explicit conjectural description of the Khovanov-Rozansky homology of generalized torus links. The talk is based on a joint work with Andrei Neguț and Jacob Rasmussen.