Integrability and non-integrability of pentagram maps

par Prof. Boris KHESIN (University of Toronto & IHÉS)

vendredi 10 juil. 2015, 14:30 → 15:30 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

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).