## EVENT DETAILS AND ABSTRACT

**Geometry/Physics Seminar**
**Title:** Khovanov-Rozansky invariants of knots, plane curve singularities and Cherednik algebras

**Speaker:** Alexei Oblomkov

**Speaker Info:** UMass Amherst

**Brief Description:**

**Special Note**:

**Abstract:**

In 1985, V. Jones discovered a new remarkable knot invariant which revolutionized the field of low-dimensional topology. Jones's invariant was interpreted as an Euler characteristic of a natural complex by M. Khovanov in 2000; the Poincare polynomial of the complex is now called the Khovanov invariant. Later Khovanov and Rozansky added to the picture a new invariant called the Khovanov-Rozansky invariant, it is related to the Khovanov invariant by means of the spectral sequence discovered by J. Rasmussen. Led by the recent discoveries in enumerative geometry, the speaker, together with V. Shende and J. Rasmussen, proposed a curious formula for the Khovanov-Rozansky invariant of the link of plane curve singularity as a generating function of some natural blow-ups of symmetric powers of the curves. In the case of curve x^p=y^q the corresponding knot is the torus knot and its Khovanov-Rozansky homology is expected to carry a natural action of the rational Cherednik algebra.

**Date:** Thursday, March 15, 2012

**Time:** 3:30pm

**Where:** Lunt 107

**Contact Person:** John Francis

**Contact email:** jnkf@northwestern.edu

**Contact Phone:**

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