TRINO Geometry Seminar announcement Feb 7

[LEWANSKI DANILO]

The TRINO Trieste Seminar<https://sites.google.com/view/trinotriestino/home> in Geometry is humbled to announce the following seminar next week on February 7, 2023 (SISSA, 15h00, room 133).

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Speaker: Guglielmo Nocera (Université Paris 13)

Title: The E3-structure on the spherical category of a reductive group.

Abstract: Let G be a reductive group over the complex numbers, e.g. GL_{n,C}. The notion of affine Grassmannian associated to G leads to the introduction of a monoidal triangulated/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, 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 a category of representations of a group (the
Langlands dual of G) with its (symmetric monoidal) tensor product.
In this talk, I will present how to upgrade the existing E1-monoidal structure 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 strongly topologically-flavoured presentation of Sph(G), namely as an ∞-category of constructible sheaves over a stratified space.
Part of this work is joint with Morena Porzio.

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