Alexei Oblomkov - Dualisable link homology and 3D TQFT
This talk is based on the joint work with Lev Rozansky. It is elementary to see that the HOMFLYPT polynomial of a knot K $P_K(a,q)$ is palindromic: $P_K(a,q)=P_K(a,1/q)$. It was conjectured by Dunfield-Gukov-Rasmussen that the Poincare polynomial $\mathcal{P}_L(a,q,t)$ of the HOMFLYPT homology has similar property. In my talk I explain a proof of the conjecture that relies on the construction 3D TQFT that provides a mathematical model for 3D sigma model of Kapustin-Rozansky-Saulina. As by-product of our construction we find an interpretation of the knot homology as v space of sections of a particular sheaf on the Hilbert scheme of points on the plane as well as another explanation why the skein algebra of torus is an elliptic Hall algebra.