January 11, 2022
TITLE: Moduli Stacks and Global Categorical Symmetry
ABSTRACT: I will discuss aspects of moduli spaces in supersymmetric gauge theories that take the form of conical symplectic singularities or resolutions thereof. They often admit Hamiltonian group actions arising from continuous global symmetries and feature prominently in geometric representation theory. I will argue that it is useful to promote moduli spaces to moduli stacks, which capture the presence of a topological sector such as a discrete gauge theory in the IR physics at a point on the underlying moduli space. I will explain how moduli stacks admit actions of higher-form and higher group global symmetries, generalizing the action of ordinary global symmetries on the underlying moduli space. I will present some examples of how such structures are mapped under three-dimensional mirror symmetry.