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Soergel bimodules and sheaves on the Hilbert scheme of points on plane
Algebraic Geometry and Number Theory| Speaker: | Alexei Oblomkov, University of Massachusetts |
| Related Webpage: | https://people.math.umass.edu/~oblomkov/ |
| Location: | zoom |
| Start time: | Tue, Apr 20 2021, 11:00AM |
Based on joint work with Rozansky. In my talk I outline a construction that produces a $\mathbb{C}^*\times\mathbb{C}^*$
-equivariant complex of
sheaves $S_b$ on $Hilb_n(\mathbb{C}^2)$ such that the space of global sections $H^*(S_b)$
of the complex are the Khovanov-Rozansky homology of the closure of the braid $b$.
The construction is functorial with respect to adding a full twist to the braid. Thus we prove a weak version of the conjecture by Gorsky-Negut-Rasmussen.
In the heart of our construction is a fully faithful functor from the category of Soergel bimodules to a particular category of matrix factorizations.
I will keep the matrix factorization part minimal and concentrate on the main idea of the construction as well as key properties of the categories that we use.
Notes: Notes from the talk