Event time:

Monday, October 14, 2019 - 4:30pm

Speaker:

Alexei Oblomkov

Speaker affiliation:

UMass Amherst

Event description:

Talk is based on joint work with Lev Rozansky. I will explain a mathematical

construction of N=4 gauge 3D TQFT, known as Kapustin-Saulina-Rozansky theory.

The defects in this theory encode the braids and that allows us to categorify

Ocneanu-Jones trace and obtain a triply-graded knot homology. We show the

homology coincide with the Khovanov-Rozansky trace on the Rouquier complexes

on Soergel bimodules. Because of the geometric nature of our TQFT

construction we obtain an interpretation of the homology as space of global sections of a sheaf on the Hilbert scheme of point on the plane. I will also explain the relation between our result and the conjectures of Gorsky-Negut-Rasmussen.