Alexei Oblomkov (UMass Amherst) HOMFLY-PT cohomology of torus links as sheaf homology


The talk is based on the joint work with Lev Rozansky. I will overview our joint work where provide a catogification of HOMFLY-PT polynomial. The construction provide an interpretation of the knot homology as homology of coherent sheaves on the nested Hilbert scheme of points on the plane. In the second part of my talk I show how one can compute these homology explicitly for the large class of knots that includes in particular torus knots T_{n,1+kn}.