Seminar

We de fine higher pentagram maps on polygons in any dimension, which extend R. Schwartz's de nition of the 2D pentagram map. These maps turn out to be integrable for both closed and twisted polygons. The corresponding continuous limit of the pentagram map in dimension d is shown to be the (2,d+1)-equation of the KdV hierarchy, generalizing the Boussinesq equation in 2D. In the 3D case we describe the corresponding spectral curve, first integrals, Liouville tori, and the motion along them. This is a joint work with Boris Khesin (University of Toronto).