On the HOMFLY invariant of algebraic knots

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• Vivek Shende, Princeton
• Tuesday 26 January 2010, 16:00-17:00
• MR 4.

If you have a question about this talk, please contact Jake Rasmussen.

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A complex plane curve singularity determines, by taking the boundary of a small neighborhood, an iterated torus link in the three-sphere. The algebraic geometry of the singularity and the topology of the link are intimately related; for instance, Zariski showed that the series of blowups needed to resolve the singularity carries data equivalent to the isotopy class of the link. More recently, Campillo, Delgado, and Gusein-Zade gave a formula equating the Alexander polynomial of the link to a generating series populated by Euler characteristics of spaces of functions defined at the singularity. I will state a conjectural generalization of their formula: the HOMFLY invariant of the link of a plane curve singularity is a generating function of Euler characteristics of moduli spaces of schemes supported at the singularity. I will discuss the evidence for the conjecture, and show that it holds for torus knots. The talk presents joint work with Alexei Oblomkov.

This talk is part of the Differential Geometry and Topology Seminar series.

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