GDMSeminar: Abstracts of the talks (2020/1)

Pentagram maps and integrable hierarchies
Tuesday, May 19, 2020, 15:00 GMT

Abstract: The pentagram map was originally defined by R.Schwartz in 1992 as a map on plane convex polygons, where a new polygon is spanned by the “shortest” diagonals of the initial one. It turned out to be a beautiful discrete completely integrable system with many relations to other mathematical domains. We describe various extensions of this map to higher dimensions, their geometry, Lax forms, and some of its properties. We also describe the corresponding continuous limits of such maps, which happen to coincide with equations of the KdV hierarchy, generalizing the Boussinesq equation in 2D. This is a joint work with Fedor Soloviev and Anton Izosimov.