Mar 27, 13h:00 - Boris Khesin (University of Toronto)

The pentagram map on polygons in the projective plane was introduced by R.Schwartz in 1992 and is by now one of the most popular and classical discrete integrable systems. We survey definitions and integrability properties of the pentagram maps on generic plane polygons and their generalizations to higher dimensions. In particular, we define long-diagonal pentagram maps on polygons in , encompassing all known integrable cases. We also describe the corresponding continuous limit of such pentagram maps: in dimension d it turns out to be the -equation of the KdV hierarchy, generalizing the Boussinesq equation in 2D. This is a joint work with F.Soloviev and A.Izosimov.