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# David Rose : Quantum knot invariants and Howe dualities

We'll review the quantum sl_n knot invariants and their description via MOY calculus, as well as work of Cautis-Kamnitzer-Licata-Morrison showing how these invariants arise naturally from a duality between sl_n and sl_m called skew Howe duality. We'll then discuss work (joint with Aaron Lauda and Hoel Queffelec) categorifying this result to give elementary constructions of Khovanov and Khovanov-Rozansky knot homology. Time permitting, we'll also discuss work (joint with Daniel Tubbenhauer) relating symmetric Howe duality to the colored Jones polynomial, and giving a new diagrammatic method for computing this invariant.

**Category**: Geometry and Topology**Duration**: 01:34:50**Date**: April 7, 2015 at 4:25 PM**Views**: 119-
**Tags:**seminar, Geometry/topology Seminar

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