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Title:
Hilbert schemes of singular curves and Catalan numbers
Speaker:
Abstract:
A conjecture of Oblomkov and Shende, recently proven by Maulik, relates the Hilbert schemes of points on a plane curve singularity to the invariants of the corresponding knots. I will describe the homology of these Hilbert schemes for singularities {x^n=y^m} corresponding to torus knots, and relate it to the bigraded deformation of Catalan numbers introduced by Garsia and Haiman. The talk is based on a joint work with M. Mazin
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