Geometry/Topology Seminar

"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.