Representation theory seminar: Link homology and Hilbert schemes
Seminar | October 16 | 10-11 a.m. | 939 Evans Hall
Tina Kanstrup, Aarhus
Khovanov and Rozansky defined a link invariant called triply graded homology. It is conjectured by Gorsky, Negut and Rasmussen that this invariant can be expressed geometrically by a functor from complexes of Soergel bimodules to the derived category of coherent sheaves on the dg flag Hilbert scheme followed by taking cohomology. A functor with similar properties has been constructed by Oblomkov and Rozansky using matrix factorizations and it is believed that this functor solves the conjecture. The aim of this joint work in progress with Roman Bezrukavnikov is to relate the two constructions using previous work of Arkhipov and Kanstrup.