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) Pierre-Guy PLAMONDON - Orsay,
Titre Associahedra and the Grothendieck group of an extriangulated structure on the cluster category
Horaire14:00 à 15:00

The associahedron is a polytope that encodes Catalan families. One of its many avatars is as a polytopal realization of the g-vector fan of a cluster algebra of type A.  Given a cluster algebra with fixed initial seed, the space of all polytopal realizations of its g-vector fan has been of interest to physicists, appearing for instance in the work of Arkani-Hamed, Bai, He and Yan. 

In this talk, we will see how a description of the set of all polytopal realizations of the g-vector fan of any cluster algebra of finite type with any initial seed can be described by looking for a minimal set of relations between its g-vectors.  To find such a set, we will see how a sub-extriangulated structure of the triangulated structure of the cluster category allows for a categorification of g-vectors, and find all relations in its Grothendieck group. 

This is a report on a joint work with Arnau Padrol, Yann Palu and Vincent Pilaud.

SalleInfo sur https://researchseminars.org/seminar/paris-algebra-seminar