Given a Lie group $G$ and a representation $V$ of $G$, physicists are interested in studying a space called the Coulomb branch of the associated 3-dimensional $\mathcal{N}=4$ gauge theory, which has a proposed mathematical definition given by Braverman, Finkelberg and Nakajima.

"Unfortunately, this involves some pretty complicated things" (-Alexander Braverman) and "I don't know any physics" (-HK). As a result, we'll very informally discuss why their construction is (conjecturally) useful for mathematicians and in the case where $G=GL_n$, we'll give a concrete description of the construction as well as some of the few examples I think I understand with the help of our fine friend in the picture.