Seminar

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Let A be the quantized Coulomb branch corresponding to a group G and its representation N. In order to compute the partition function of a 3d sphere in the corresponding TQFT, Gaiotto and Okazaki introduced a linear functional T on A, which we call "sphere trace". In the first part of the talk I will describe the image of A under the localization (abelianization) map under the mild technical assumption and use it to give a mathematical definition of the sphere trace for any quantized Coulomb branch.

The second part is based on joint work in progress with Merrick Cai, Vasily Krylov and Alan Yan. Let A be the truncated shifted Yangian that acts on a minuscule chamber module V. I will explain how to compute the q-character of V by using the sphere trace T.