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Khovanov-Rozansky homology and Hilbert schemes of points.

Algebraic Geometry

Speaker: Eugene Gorsky, UC Davis
Location: 2112 MSB
Start time: Wed, Jan 17 2018, 11:00AM

Khovanov and Rozansky introduced a link homology theory which categorifies the HOMFLY polynomial. This invariant has a lot of interesting properties, but it is notoriously hard to compute. I will introduce HOMFLY homology and discuss its conjectural relation to algebraic geometry of the Hilbert scheme of points on the plane. In particular, I will compute this invariant for all positive powers of the full twist and match it to the family of ideals appearing in Haiman's description of the isospectral Hilbert scheme. The talk is based on joint works with Matt Hogancamp, Andrei Negut and Jacob Rasmussen.