Description:

 Title:  Twisted and positive traces on abelian Coulomb branches

Abstract:  For a noncommutative algebra $A$ and an antilinear automorphism $\rho$ of $A$ there is a notion of positive trace. On the physics side, positive traces are related to superconformal field theories. On the mathematical side, positive traces are connected to spherical unitary representations of complex Lie groups. 

We consider the case when $A$ is a quantized abelian Coulomb branch, also known as hypertoric enveloping algebra. I will talk about the classification of positive traces and related objects in this case. I will also discuss how these results fit into the symplectic duality program.