# 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 : à distance / remote Adresse : IHP Description Depuis le 23 mars 2020, le séminaire se tient 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) Toshiki NAKASHIMA - Tokyo, Titre Geometric crystals on cluster varietie Date 05/02/2018 Horaire 14:00 à 15:00 Diffusion Résume The notion of geometric crystal was initiated by A.Berenstein and D.Kazhdan to consider certain geometric analogue to the Kashiwara's crystal base theory. Their structures are described by rational maps and rational functions. If all these rational maps are positive'', such geometric crystals are called positive'' and they can be tranfered to the Langlands dual crystal bases'' by tropicalization/ultra-discretization procedure. V.Fock and A.Goncharov defined certain pair of varieties (A,X), called cluster ensemble'' which is obtained by glueing algebraic tori using the A-mutations and X-mutations'' respectively. They gave the conjectures on tropical duality'' between cluster ensemble A-variety and X-variety (called Fock-Goncharov conjectures). We shall define the positive geometric crystal structure on cluster varieties and then obtain the resulting tropicalized crystals, which will be a guide to understand the Fock-Goncharov conjectures in terms of crystal base theory. Finally, we shall show some compatibility of geometric crystal structures on A-variety and X-variety in the classical type A case. Salle à distance / remote Adresse IHP