Poisson brackets for Grassmannian pentagram maps
The pentagram map is a discrete dynamical system on the space of plane polygons. It was proved to be integrable by Ovsienko, Schwartz, and Tabachnikov. Later on, Gekhtman, Shapiro, Vainshtein, and Tabachnikov gave another proof of integrability using a combinatorial model of networks drawn on a cylinder. Recently, a generalization of the pentagram map was defined where the polygons are in some Grassmannian manifold. I will discuss a noncommutative version of the techniques of Gekhtman et. al., and how it can be used to define a Poisson structure for the Grassmannian pentagram map and to show integrability.
The talk will be via Zoom at: https://utoronto.zoom.us/j/99576627828