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) Lauren WILLIAMS - Berkeley,
Titre Cluster duality and mirror symmetry for Grassmannians
Horaire14:00 à 15:00
RésumeWe consider the Grassmannian $X=Gr_{n-k,n}$ and its mirror dual Landau-Ginzburg model ($X$-check, $W$), which takes place on a dual Grassmannian. Postnikov's theory of plabic graphs can be used both to parameterize a dense open subset of $X$, and to describe the cluster structure on $X$-check. For each reduced plabic graph $G$ associated to $X$, we describe an associated Newton-Okounkov polytope as a convex hull of certain lattice points. We show that the same polytope, but described in terms of inequalities, can be obtained by ``tropicalizing'' the superpotential $W$, after writing it in terms of the cluster associated to $G$.