Hilbert schemes, Torus Knots, and Khovanov Homology
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Mon, 10/10/2011 14:15 |
Jacob Rasmussen (Cambridge) |
Geometry and Analysis Seminar  |
L3 |
| Khovanov homology is an invariant of knots in S^3 which categorifies the Jones polynomial. Let C be a singular plane curve. I'll describe some conjectures relating the geometry of the Hilbert scheme of points on C to a variant of Khovanov homology which categorifies the HOMFLY-PT polynomial. These conjectures suggest a relation between HOMFLY-PT homology of torus knots and the representation theory of the rational Cherednik algebra. As a consequence, we get some easily testable predictions about the Khovanov homology of torus knots. | |||