What is a Coulomb branch?

Abstract: As hinted at in their name, Coulomb branches come from physics: they are spaces which physicists associate to certain quantum field theories. But it so happens that many spaces of mathematical interest arise as Coulomb branches, which are especially important in representation theory and in the study of integrable systems. As with many constructions in quantum field theory, a precise mathematical definition of Coulomb branches was difficult to achieve. Fortunately for us this was accomplished in recent work of Braverman, Finkelberg and Nakajima (BFN), who provide a rigorous definition in a large family of cases. In this talk we will take a look at the BFN construction of Coulomb branches, making stops along the way to see some of the interesting spaces that arise.

algebraic geometrycombinatoricsdifferential geometrynumber theoryrepresentation theory

Audience: learners

What is ...? Seminar

Series comments: The ``What is ... ? Seminar'' (WiSe) is a weekly Zoom mathematics seminar. The goal is to explain interesting things to each other in a casual manner. The name is inspired by the What is ...? column of the Notices of the American Mathematical Society. See the website for more details. If you want to receive the zoom link for the talks please fill out the form linked on the website or contact Anna at a.puskas@uq.edu.au.