Feb 02 at 17:30 in 507

Title:  Residue construction of quantized Coulomb branches and the sphere trace

Abstract: Let A be a quantized Coulomb branch algebra associated to a reductive group G and its representation N. A possible way to understand A is to use the localization map in equivariant homology (called "abelianization map" in physics). I will describe the image of A under the localization map. The answer is a certain condition on zeroes and poles of the coefficients, similar to the Ginzburg---Kapranov---Vasserot description of the double affine Hecke algebra.

In the second part of the talk, based on an ongoing work with Vasily Krylov, I will talk about twisted traces on quantized Coulomb branches. Any Verma module over a quantized Coulomb branch gives rise to a twisted trace. 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.