TRINO SEMINAR - Tuesday 7 February, at 15:00 (SISSA, Room 133 - via Bonomea, 265)

[ICTP Math Section]

_TRINO SEMINAR AT SISSA_

*Speaker:* Guglielmo Nocera (Université Paris 13)

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

_*Venue*__*:*__Tuesday February 7, at 3pm, SISSA, Room 133 - Via 
Bonomea, 265, 34136 Trieste_

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 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.

https://sites.google.com/view/trinotriestino/home

On behalf of the organisers

-- 
Koutou Mabilo
ICTP Mathematics Group
Leonardo Da Vinci Building
Strada Costiera no. 11
34151 Trieste, Italy
Tel. no.: +39-040-2240455

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