## String-Math Seminar: Monodromic deformation of Khovanov-Rozansky homology and Hilbert schemes

Seminar | October 15 | 2-3 p.m. | 402 LeConte Hall

Matthew Hogancamp, University of Southern California

Department of Mathematics

A conjecture of Gorsky-Negut-Rasmussen asserts the existence of a pair of adjoint functors relating the Hecke category for symmetric groups and the Hilbert scheme of points in the plane. One topological consequence of this conjecture is the prediction of a deformation of the triply graded Khovanov-Rozansky link homology which restores the missing $q\rightarrow tq^{-1}$ symmetry of KR homology for links. In this talk I will discuss a candidate for such a deformation, constructed in joint work with Eugene Gorsky, which indeed facilitates connections with Hilbert schemes. For instance our main result explicitly computes the homologies (both deformed and undeformed) of the $(n,nk)$ torus links, summed over all $n\geq 0$, as a graded algebra. Combining with work of Haiman this gives a functor from the Hecke category to sheaves on the relevant Hilbert scheme.

artamonov@berkeley.edu