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Coulomb branches for quiver gauge theories: geometry and representation theory
Algebraic Geometry and Number Theory| Speaker: | Vasily Krylov, Harvard University |
| Related Webpage: | https://people.math.harvard.edu/~vkrylov/Index.html |
| Location: | 2112 MSB |
| Start time: | Wed, Mar 4 2026, 12:10PM |
Description
Higgs and Coulomb branches of quiver gauge theories form two important families of Poisson varieties that are expected to be exchanged under so-called 3D mirror symmetry. The representation theory of quantized Coulomb branches is deeply connected with the enumerative geometry of Higgs branches. One important approach to studying modules over quantized Coulomb branches is by analyzing their graded traces. Graded traces generalize the notion of characters and are closely related to the q-characters introduced by Frenkel and Reshetikhin. Any graded trace defines a solution of the D-module of graded traces introduced by Kamnitzer, McBreen, and Proudfoot.
In this talk, I will discuss techniques that allow us to explicitly compute characters and graded traces of certain modules over quantized Coulomb branches. Time permitting, I will explain how some of these results naturally appear on the Higgs side, leading to an explicit description of the D-module of graded traces for a quantized Coulomb branch via the geometry of the Higgs branch. We prove these results for ADE quivers and formulate explicit conjectures in the general case. Talk is based on joint works with Dinkins, Karpov, Klyuev, and Lance.