ICMAT-UCM Colloquium
INTEGRABLE PDES AND PENTAGRAM MAPS
Speaker: Boris Khesin (University of Toronto)Date: Wednesday, 16 December 2020 - 17:30Place: Online - Zoom: zoom.us/j/96217594283?pwd=R29lOTdyNDF5STRrTC9GK25RZHFZdz09 (ID: 962 1759 4283; access code: 932294)
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 and the
geometry of this map in higher dimensions. 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.
