Friday, November 13, 2020
Time  Items 

All day 

1:00pm 
11/13/2020  1:00pm Braverman, Finkelberg, and Nakajima define the $K$theoretic Coulomb branch of a 3$d$ $\mathcal{N}=4$ SUSY gauge theory as the affine variety $\mathcal{M}_{G,N}$ arising as the equivariant $K$theory of certain moduli space $\mathcal{R}_{G,N}$, labelled by the complex reductive group $G$ and its complex representation $N$. It was conjectured by Gaiotto, that (quantized) $K$theoretic Coulomb branches bear the structure of (quantum) cluster varieties. I will outline a proof of this conjecture for quiver gauge theories, and show how the cluster structure allows to count the BPS states (aka DTinvariants) of the theory. Time permitting, I will also show how the above cluster structure relates to positive and GelfandTsetlin representations of quantum groups. This talk is based on joint works with Gus Schrader. Location: 