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Plane curve singularities, knot homology and Hilbert scheme of points on plane


Speaker: Alexei Oblomkov, University of Massachusetts
Location: 2112 MSB
Start time: Tue, Jan 28 2014, 4:10PM

I will present a conjectural formula for the Poincare polynomial of the Hilbert scheme of points on a planar curve (joint with Rasmussen and Shende). The formula is written in terms of the Khovanov-Rozansky invariants of the links of the singularities of the curve. In the case of toric curve $\{ x^m=y^n\}$ the Poincare polynomial also could be written in terms of equivariant Euler characteristic of some sheaf of some particular equivariant sheaf on $Hilb^n(\mathbb{C}^2)$ (joint with Yun). If time permits I will also discuss cohomology ring of the compactified Jacobian of the toric curve and the conjectural description of the ring for general curve singularity (joint with Yun).

There will be a dinner.