Friday Morning Seminar: Langlands duality and the quantum differential equation

Speaker: Samuel DeHority (Perimeter Institute; Yale University)

Time: 2026-03-20 10:00-12:00
Location: 1610, SIMIS

Abstract:

We will present conjectures concerning the quantum differential equation of moduli spaces of parabolic Higgs bundles, and its relationship with the double affine Hecke algebra and with conformal blocks for vertex algebras. Specifically, when both can be defined, the equivariant quantum differential equation for Langlands dual moduli spaces are conjectured to be related by analytic continuation, and the resulting D module is conjectured to be equivalent to the D module of conformal blocks for a vertex algebra. Parts of these conjectures will be proven in simple examples.