**Title: A new look at quantum knot invariants**

**Abstract:**

The Reshetikhin-Turaev construction associated knot

invariants to the data of a simple Lie algebra and a choice of

irreducible representation. The Jones polynomial is the most famous

example coming from the Lie algebra sl(2) and its two-dimensional

representation. In this talk we will explain

Cautis-Kamnitzer-Morrison’s novel approach to studying RT

invariants associated to the Lie algebra sl(n). Rather than delving

into a morass of representation theory, we will show how two

relatively simple Lie theoretic ingredients can be combined with a

powerful duality (skew Howe) to give an elementary and diagrammatic

construction of these invariants. We will explain how this new

framework solved an important open problem in representation theory,

proves the existence of an (a,q)-super polynomial conjectured by

physicists (joint with Garoufalidis and Lê), and leads to a new

elementary approach to Khovanov homology and its sl(n) analogs (joint

with Queffelec and Rose).

Wednesday, November 30, 4:30 – 5:30 p.m.

Mathematics 520

Tea will be served at 4:00 p.m.