14:00-15:00
Title: Symmetries of Hamiltonian actions and of supersymmetric gauge theories
Abstract: [This is the first of two independent talks describing joint work with Sam Gunningham, this one coming from the perspective of geometry and physics.] Classical and quantum Hamiltonian actions of reductive groups, respectively, give rise to ubiquitous families of commuting flows and of commutative rings of operators. I will explain how a construction independently due to Knop and Ngô (from the proof of the Fundamental Lemma) providesa universal integration of these flows for classical systems. I will then explain, following joint work with Sam Gunningham, how to quantize this action to obtain universal symmetries of the corresponding quantum systems. The action can be understood as an aspect of the Seiberg-Wittengeometry of supersymmetric gauge theories.
15:00-16:00
Title: Langlands parameters for categorical representations of reductive groups
Abstract: [This is the second of two independent talks describing joint work with Sam Gunningham, this one coming from the perspective of algebra and representation theory.] The representation theory of reductive groups on categories is a geometric counterpart to the representation theory of reductive groups over finite fields. I will describe, following joint work with Sam Gunningham, a geometric counterpart for Lusztig’s Jordan decomposition for characters, which is a finite field shadow of the local Langlands correspondence. Our construction combines the familiar commutativity and less familiar centrality of the theory of Whittaker models.