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### Jucys-Murphy elements, affine braids and Hilb-knot homology

Algebra & Discrete Mathematics

 Speaker: Alexei Oblomkov Location: 2112 Start time: Mon, Mar 6 2017, 4:10PM

Talk is based on the recent joint preprints with Lev Rozansky. In the talk I will explain an interpretation of the HOMFLY knot homology as space of derived sections of quasi-coherent sheaf on the Hilbert scheme of points on the plane. In particular, the new geometric construction of the finite Hecke category will be explained. The construction allow us relate the knot homology of the closure of a braid and of the closure of the same braid but twisted by Jucys-Murphy element of the braid group. As one of the corollary we get an explicit formula for the knot homology of the torus links confirming earlier conjecture by Gorsky, Negut, Oblomkov, Shende and Rasmussen.