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Topological vertex, colored knot invariants and plane curve singularities.

QMAP Seminar

Speaker: Alexei Oblomkov, University of Massachusetts
Location: 2112 MSB
Start time: Thu, Jan 30 2014, 4:10PM

In my talk I will discuss the recent conjectures due to Shende, Rasmussen and myself that relate the topology of the Hilbert scheme of points on the singular curve to the knot invariants of the link of the singularity. I will explain how these conjectures generalize well-known topological vertex construction due to Aganagic-Klemm-Marino-Vafa. In particular, I will look at the case of the singularities $\{ x^n=y^m\}$ which have the torus knot $T_{n,m}$ as the link. In this case it is also possible to connect our conjecture with the recent results of Aganagic-Shakirov on Khovanov-Rozansky homology of the torus knots.

Joint meeting with Geometry/Topology seminar