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.

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