# 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 : 001 Adresse : IHP Description

 Orateur(s) Lauren WILLIAMS - Berkeley, Titre Cluster duality and mirror symmetry for Grassmannians Date 26/01/2015 Horaire 14:00 à 15:00 Résume We 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 $G$. Salle 001 Adresse IHP