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 new
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).