Speaker:  Tudor Dimofte (UC Davis)

Abstract:  A 3d N=4 gauge theory is labelled by a compact group G and a quaternionic representation R. Such physical theories also admit two distinct "A" and "B" topological twists, each of which gives rise to many layers of algebraic and geometric structures. I will review some of what's known and expected about these twists, and then discuss a proposed mathematical definition of one particular layer of structure: the (braided, monoidal) categories of line operators. The categories of line operators provide a generalization of the recent Braverman-Finkelberg-Nakajima construction of Coulomb branches, play an important role in symplectic duality, and have direct applications to the construction of HOMFLY link homologies.