String Math: Alexei Oblomkov (UMass Amherst) “Kapustin-Rozanksy-Witten (KRS) theory path to knot homology”

Seminar Organizer

Event Details

My talk is based on the joint project with Lev Rozansky.  I will explain how we rigorously construct 3D TQFT, which is a KRS theory with targets Hilbert scheme of points on a plane.
Defects in the last theory encode a knot in the three-space and we rediscover the HOMFLY-PT homology of a link as  a part of the TQFT.

The construction is very flexible and allows us to construct the annular $gl_n$-homology as well as a categofified quantum super-group $gl(m|n)$ link invariant. If time permits,  I will  explain how one can use Elliptic Hall Algebra (that acts on coherent sheaves on the Hilbert scheme) to compute knot homology  a large class of knots.