# 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 , David Hernandez , Bernhard Keller , Thierry Levasseur , Sophie Morier-Genoud 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 Date 12/09/2022 Horaire 14:00 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 ) Salle Zoom ou hybride selon les orateurs. Info sur https://researchseminars.org/seminar/paris-algebra-seminar Adresse Zoom ou IHP Salle 01