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.