Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: Hilbert schemes and link homology

Seminar | February 11 | 3:45-4:45 p.m. | 939 Evans Hall

 Eugene Gorsky, UC Davis

 Department of Mathematics

Khovanov and Rozansky defined a link homology theory using Soergel bimodules. This invariant has a lot of interesting properties, but it is notoriously hard to compute. I will define it in terms of discuss recent progress in understanding Khovanov-Rozansky homology and its surprising relation to algebraic geometry of the Hilbert scheme of points on the plane. In particular, I will compute this invariant for all positive powers of the full twist and match it to the family of ideals appearing in Haiman's description of the isospectral Hilbert scheme. All notions will be introduced in the talk, no preliminary knowledge is required. The talk is based on joint works with Matt Hogancamp, Andrei Negut and Jacob Rasmussen.