Integrability and non-integrability of pentagram maps
(University of Toronto & IHÉS)
Amphithéâtre Léon Motchane (IHES)
Amphithéâtre Léon Motchane
Le Bois Marie
35, route de Chartres
We define pentagram maps on polygons in any dimension, which extend R. Schwartz's definition of the 2D pentagram map, as well as describe recent results on integrable cases for these higher-dimensional generalizations. The corresponding continuous limits of such maps coincide with equations of the KdV hierarchy, generalizing the Boussinesq equation in 2D. We discuss their geometry and a numerical evidence of non-integrability of certain cases. This is a joint work with Fedor Soloviev (Univ. of Toronto).