Representation Theory Seminar: Tina Kanstrup
Title: Link homologies and Hilbert schemes via representation theory
Speaker: Tina Kanstrup.
Abstract: 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 cohomology of shaves on Hilbert schemes. In an attempt to prove this conjecture Oblomkov and Rozansky constructed a link invariant in terms of matrix factorizations and later proved that it computes Khovanov-Rozansky homology. Using previous work of Arkhipov and Kanstrup we show that the categories involved in their construction are equivalent to one of the main categories studied in geometric representation theory. Moreover, we explain why their construction is natural from the point of view of representation theory.