Date/heure
27 mai 2024
14:00 - 15:00
Lieu
Salle de conférences Nancy
Oratrice ou orateur
Guglielmo Nocera
Catégorie d'évènement Séminaire de géométrie complexe
Résumé
Title: The E3-structure on the spherical Hecke category
of a reductive group
Abstract: let G be a reductive group over the complex numbers, e.g. GLn,C . The
notion of affine Grassmannian associated to G leads to the introduction of
a monoidal dg/∞-category Sph(G), called the spherical category of G, which
plays an important role in the Geometric Langlands program. For example,
its behaviour provides important constraints in the formulation of the Geometric Langlands Conjecture.
This monoidal ∞-category is not symmetric
monoidal (although its homotopy category is), but it admits a t-structure whose
heart is symmetric monoidal: more precisely, by the Geometric Satake Theorem
(Ginzburg, Mirkovic–Vilonen) the heart is monoidal-equivalent to the category
of representations of the Langlands dual of G with its (symmetric monoidal)
tensor product.
In this talk, I will present how to upgrade the existing E1 -monoidal struc-
ture on Sph(G) to an E3 -monoidal one, which formally recovers the symmetric
monoidal structure of the heart. The construction implements ideas of Jacob
Lurie and uses a topologically-flavoured presentation of Sph(G), namely as an
∞-category of equivariant constructible sheaves over a stratified space.