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Colloquium - Aaron Lauda

Aaron Lauda
February 20, 2020
4:15 pm - 5:15 pm
Cockins Hall 240

Title: A new look at quantum knot invariants

Speaker:  Aaron Lauda - University of Southern California

Abstract: In this talk we will explain how Lie theory leads to interesting families of invariants for knots and links that can all be defined in an elementary diagrammatic fashion. 
 
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 (Howe duality) 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 q-holonomic conjecture in knot theory (joint with Garoufalidis and Lê), and leads to a new elementary approach to 'categorifying' these knots invariants to link homology theories.
 

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