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) Gleb KOSHEVOY - IHES,
Titre Polyhedral parametrization of canonical bases
Horaire14:00 à 15:00

 Parametrizations of the  canonical bases, string basis and theta basis, can be obtained by the tropicalization of  the Berenstein-Kazhdan decoration function and the Gross-Hacking-Keel-Kontsevich potential respectively. For  a classical Lie algebra and a reduced decomposition $\mathbf i$,  the decorated graphs are constructed algorithmically, vertices of such graphs are labeled by monomials which constitute the set of monomials of the Berenstein-Kazhdan potential.  Due to this algorithm;  we obtain a characterization of $\mathbf i$-trails introduced by Berenstein and Zelevinsky. Our algorithm uses multiplication and summations only, its complexity is linear in time of writing the monomials of the potential. For SL_n, there is an algorithm due to Gleizer and Postnikov which gets all monomials of the Berenstein-Kazhdan potential using combinatorics of wiring diagrams. For this case, our algorithm uses simpler combinatorics and is faster than the Gleizer-Postnikov algorithm. The cluster algorithm due to Genz, Schumann and me is polynomial in time but it uses divisions of polynomials of several variables.
If time permits, I will report on applications of decorated graphs to analysis of the Newton polytopes of F-polynomials related to the Gross-Hacking-Keel-Kontsevich potentials. The talk is based on joint works with Volker Genz and Bea Schumann and with Yuki Kanakubo and Toshiki Nakashima.

The talk will take place in hybrid mode at the Institut Henri Poincaré