# Coulomb branches in 3D gauge theory

# Coulomb branches in 3D gauge theory

**Zoom link: https://princeton.zoom.us/j/96282936122**

**Passcode: 998749**

I will discuss an amusing appearance of twistings and curvings in equivariant cohomology and K-theory from a quaternionic representation of a compact group. As a background, topological gauge theory in 3 dimensions is controlled by the holomorphic symplectic geometry of the Toda integrable system. Algebraic modifications of this system have been proposed in physics under the name of “Coulomb branches”. Rigorous constructions of these spaces, for gauge theory with fields in linear representations, were proposed by Nakajima, Braverman, Finkelberg and collaborators, first for doubles of complex representations and more recently in general. I will quickly review the construction in the doubled case, where it relates quantum and symplectic cohomology, and explain the interesting topology behind the general case.