Damien Simon: Vertex algebras of chiral differential operators on a reductive group and Langlands duality

mardi 20 janv. 2026, 10:30 → 11:30 Europe/Paris

Vertex algebras of chiral differential operators on a complex reductive group G are "Kac-Moody" versions of the usual algebra of differential operators on G. Their categories of modules are especially interesting because they are related to the theory of algebraic D-modules on the loop group of G. That allows one to reformulate some conjectures of the quantum geometric Langlands program in the language of vertex algebras. For instance, in view of the geometric Satake equivalence, one may expect the appearance of the category of representations of the Langlands dual group of G. I will explain concretely how, for generic values of the deformation parameter, Langlands duality appears.