Séminaires : Séminaire d'Algèbre

Equipe(s) : gr,
Responsables :J. Alev, D. Hernandez, B. Keller, Th. Levasseur, et S. Morier-Genoud.
Email des responsables : Jacques Alev <jacques.alev@univ-reims.fr>, David Hernandez <david.hernandez@imj-prg.fr>, Bernhard Keller <bernhard.keller@imj-prg.fr>, Thierry Levasseur <Thierry.Levasseur@univ-brest.fr>, Sophie Morier-Genoud <sophie.morier-genoud@imj-prg.fr>
Salle : Zoom ou hybride selon les orateurs. Info sur https://researchseminars.org/seminar/paris-algebra-seminar
Adresse :Zoom ou IHP Salle 01
Description

Le séminaire est prévu en présence à l'IHP et à distance. Pour les liens et mots de passe, merci de contacter l'un des organisateurs ou de souscrire à la liste de diffusion https://listes.math.cnrs.fr/wws/info/paris-algebra-seminar. L'information nécessaire sera envoyée par courrier électronique peu avant chaque exposé. Les notes et transparents sont disponibles ici.

 

Since March 23, 2020, the seminar has been taking place remotely. For the links and passwords, please contact one of the organizers or

subscribe to the mailing list at https://listes.math.cnrs.fr/wws/info/paris-algebra-seminar. The connexion information will be emailed shortly before each talk. Slides and notes are available here.

 


Orateur(s) Mikhail Kapranov - IPMU Tokyo,
Titre Perverse sheaves and schobers on symmetric products
Date12/09/2022
Horaire14:00 à 15:00
Diffusion
Résume

The talk, based on joint work in progress with V. Schechtman, will first
recall our description of perverse sheaves on $Sym^n(\mathbb{C})$, the symmetric
product of the complex line with its natural stratification by multiplicities.
This description proceeds in terms of contingency matrices, which are certain
integer matrices appearing (besides their origin in statistics) in three
different contexts:
-- A natural cell decomposition of $Sym^n(\mathbb{C})$.
-- Compatibility of multiplication and comultiplication in $\mathbb{Z}_+$-graded Hopf algebras.
-- Parabolic Bruhat decomposition for $GL_n$.
Perverse sheaves on $Sym^n(\mathbb{C})$ are described in terms of certain data
of mixed functoriality on contingency matrices which we call Janus sheaves.
I will then explain our approach to categorifying the concept of Janus sheaves,
in which sums are replaced by filtrations with respect to the Bruhat order.
Such data can be called Janus schobers. Examples can be obtained from
$\mathbb{Z}_+$-graded Hopf categories, a concept going back to Crane-Frenkel,
of which we consider two examples related to representations of groups $GL_n$
over finite fields (Joyal-Street) and $p$-adic fields (Bernstein-Zelevinsky).
(Zoom talk shared with https://nc-shapes.info )

SalleZoom ou hybride selon les orateurs. Info sur https://researchseminars.org/seminar/paris-algebra-seminar
AdresseZoom ou IHP Salle 01
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