Vivek Shende Simons Postdoctoral Fellow ( CV ) Office : 2-248 Email : vivek@math.mit.edu

I study plane curves. My present work focuses on a conjecture relating the homology of their Hilbert schemes of points with the Khovanov-Rozansky homology of the links of the singularities. Here is a talk I gave about this conjecture. I am also interested in the cohomology of compactified Jacobians, and in counting holomorphic curves on complex manifolds.

I am currently in Cambridge, MA.

Articles

		On the Göttsche Threshold with Steven Kleiman.
		The Hilbert scheme of a plane curve singularity and the HOMFLY homology of its link with Alexei Oblomkov and Jacob Rasmussen; and with an appendix by Eugene Gorsky.
		Large N duality, lagrangian cycles, and algebraic knots with Duiliu Emanuel Diaconescu and Cumrun Vafa. to appear in Comm. Math. Phys.
		A support theorem for Hilbert schemes of planar curves with Luca Migliorini. To appear in J. Eur. Math. Soc.
		A short proof of the Göttsche conjecture with Martijn Kool and Richard Thomas. Geometry and Topology 15, pp. 397-406, (2011).
		Hilbert schemes of points on a locally planar curve and the Severi strata of its versal deformation Compositio Mathematica 148.2, pp. 531-547, (2012).
		The Hilbert scheme of a plane curve singularity and the HOMFLY polynomial of its link (corrected version, not on arxiv) with Alexei Oblomkov To appear in Duke Math J.