Graded characters of Verma modules via the sphere trace

I will talk about twisted traces on quantized Coulomb branches. Any Verma module over a quantized Coulomb branch gives rise to a twisted trace. For conical Coulomb branches there is also a trace introduced by Gaiotto and Okazaki (“sphere trace”). I will show how the sphere trace allows us to compute the graded character of Verma modules in certain cases. Based on joint work in progress with Vasily Krylov.