Michael Shapiro: Cluster algebras, planar networks, and Integrability of generalized pentagram maps

The pentagram map that associates to a projective polygon a new one formed by intersections of short diagonals was introduced by R. Schwartz and was shown to be integrable by V. Ovsienko, R. Schwartz and S. Tabachnikov. M. Glick demonstrated that the pentagram map can be put into the framework of the theory of cluster algebras.
We extend and generalize Glick's work by including the pentagram map into a family of discrete completely integrable systems.

In this talk we will discuss our approach to integrability of pentagram map using cluster algebra.
 

This is a joint with M.Gektman, S.Tabachnikov, and A.Vainshtein