## Oliver Club

Christian GaetzCornell University
Web bases and plabic graphs
Thursday, March 23, 2023 - 4:00pm
Malott 532 (Lounge)

The $SL(3)$ web basis is a special diagrammatic basis of certain spaces of tensor invariants developed in the late 90's by Khovanov and Kuperberg as a tool for computing quantum link invariants. Since then, this basis has found further connections and applications to cluster algebras, canonical bases, dimer models, and tableau combinatorics. The main open problem has remained: how to find a basis replicating the desirable properties of this basis for $SL(4)$ and beyond? I will describe joint work with Oliver Pechenik, Stephan Pfannerer, Jessica Striker, and Josh Swanson in which we construct such a basis for $SL(4)$. Modified versions of plabic graphs and the six-vertex model and new tableau combinatorics will appear along the way. I will explain what all of these words mean, with lots of pictures.

Refreshments will be served at 3:30 PM.