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 : 001
Adresse :IHP


Orateur(s) Lara BOSSINGER - Cologne,
Titre Toric degenerations from representation theory, tropical geometry and cluster algebras (Projet ERC QAffine)
Horaire14:00 à 15:00
RésumeIn this talk I will explain how toric degenerations arise from the tropicalization of a (projective) variety. In the context of varieties that are interesting from a representation theoretic point of view (e.g. Grassmannians or flag varieties) I will explain a construction of toric degenerations due to Fang, Fourier, and Littelmann called birational sequences and compare to degenerations obtained from the cluster structure on these varieties. I will present many examples and some results on how these constructions are related. For example, I will present computational results on the tropicalization of the full flag variety for n=4 and 5 and compare the obtained toric degenerations to some classical degenerations from representation theory (string polytopes and the FFLV polytope) that arise in the context of birational sequences.