GT seminar: "The Hilb-vs-Quot conjecture"

Abstract:  The Oblomkov-Rasmussen-Shende conjecture relates the a, q, t-graded Khovanov-Rozansky homology of the link of a plane curve singularity to the topology of its punctual Hilbert schemes. While the t=-1 limit is a theorem of Maulik, and much is understood in the q=1 limit, almost no examples incorporating all three gradings exist. In work with Trinh, we introduce a different kind of Quot scheme and show that an analogous conjecture for these Quot schemes does hold for torus knots and (n, nk)-torus links. This motivates a surprising conjecture about how two kinds of Quot scheme on the same curve are related by a motivic substitution of variables, without reference to links or link homology.

This is a seminar in our Geometry and Topology seminar series.