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The Oblomkov-Rozansky link invariant and the Gorsky-Negut-Rasmussen conjecture.
Algebraic Geometry and Number Theory| Speaker: | Tina Kanstrup, University of Bonn |
| Related Webpage: | http://www.math.uni-bonn.de/people/kanstrup/ |
| Location: | 2112 MSB |
| Start time: | Thu, Oct 11 2018, 1:00PM |
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 complexed 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.