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 : Info sur https://researchseminars.org/seminar/paris-algebra-seminar
Adresse :

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) Lucien Hennecart - Edinburgh,
Titre (Canonical) bases of the elliptic Hall algebra
Horaire14:00 à 15:00
RésumeThe global nilpotent cone is a closed substack of the stack of Higgs sheaves on a smooth projective curve whose geometry has been studied in depth and is also an essential object in the geometric Langlands program. It is a highly singular stack and in particular it has several irreducible components which were rather recently explicitly described by Bozec. In this talk, we will concentrate on elliptic curves. We will recall Bozec's parametrization of the set of irreducible components of the global nilpotent cone and present another parametrization of the same set using (a refinement of) the Harder-Narasimhan stratification of the stack of coherent sheaves on the elliptic curve. Then, we raise the question of the comparison of these two bases, showing the emergence piecewise linear structures. We will also see how the second description can be useful to understand a part of the cohomological Hall algebra of an elliptic curve.
SalleInfo sur https://researchseminars.org/seminar/paris-algebra-seminar