Geometric Representation Theory

Representation theory (i.e., the study of linear actions of Lie groups, algebraic groups, Lie algebras, and finite groups) investigates the classification representations, their internal structure, as well as the structure of the category of representations as a whole. Somewhat surprisingly, algebraic geometry often provides the best structure in which to express and understand the answers to many questions in representation theory. The study of this rich interplay is the area known as geometric representation theory.Interactions between representation theory and physics are also enjoying much activity at the moment. Work of Bezrukavnikov and collaborators has established deep connections between the structure encountered in the modular representations of reductive Lie algebras and ideas from physics such as stringy moduli spaces,through a variant of Bridgeland’s stability spaces. And the work of Braverman, Finkelberg and Nakajima has provided the first mathematical definition of the Coulomb branch of supersymmetric gauge theories. Their work has already had important applications in the study of symplectic duality, and is now a topic of intense investigation.

Registration for this event will close on Monday, June 15, 2020.