EVENT DETAILS AND ABSTRACT

Title: Cluster Algebras, Poisson Geometry and Integrable Systems
Speaker: Professor Michael Gekhtman
Speaker Info: University of Notre Dame
Brief Description:
Special Note:
Abstract:

A notion of a cluster algebra introduced by Fomin and Zelevinsky was motivated by a study of dual canonical bases and the total positivity in reductive groups. For example, coordinate rings of Double Bruhat cells in flag varieties and Grassmannians possess a cluster algebra structure. I will talk about a joint work with M. Shapiro and A. Vainshtein, in which we introduced a Poisson variety compatible with a given cluster algebra structure and computed a number of connected components in the union of generic symplectic leaves. Examples will include refined open Bruhat cells in real Grassmannians, and Teichmueller spaces.