University of Sydney Algebra Seminar

Alex Weekes (Perimeter Institute for Theoretical Physics)

Friday 17 February, 12-1pm, Place: Carslaw 375

An introduction to Coulomb branches.

This will be an introductory talk on the developing theory of Coulomb branches, as defined recently by Braverman, Finkelberg and Nakajima. These spaces are proposed as a mathematically rigorous definition of spaces coming from physics: the Coulomb branches of certain 3d N=4 supersymmetric gauge theories. They are defined in the language of algebraic geometry, by explicitly constructing their coordinate rings. Many varieties of interest in representation theory arise as Coulomb branches.
We will overview the definition of Coulomb branches, and discuss some examples. We will also describe their connection to representation theory, especially their expected role in symplectic duality.

In follow-up talks on Feb. 20 and 22, I will delve more deeply into the construction of these algebras, as well as their representation theory. I will also discuss a particularly interesting case of Coulomb branches, corresponding to "quiver gauge theories", where the Coulomb branch is a (generalized) slice in the affine Grassmannian of an algebraic group of ADE type.