报告题目：The Mystery of Pentagram Maps
主 讲 人：Prof. Dr. BorisKhesin
单 位：University of Toronto
ZOOM ID：567 306 5241
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 will also describe the continuous limits of such maps as an evolution of curves in space and explain the relation of this dynamics with equations of the Korteweg-de Vries hierarchy, generalizing the Boussinesq equation in 2D.
Boris Khesin studied mathematics at the Moscow State University,Russia. After obtaining his PhD in 1990 under the guidance of Vladimir Arnold, he spent several years at UC Berkeley and Yale University, USA, before moving to Toronto, Canada. Currently he is a Professor of Mathematics at the University of Toronto. His research interests include infinite-dimensional groups, geometry, and Hamiltonian dynamics. Arnold and Khesin authored the book Topological Methods in Hydrodynamics, which appears to be accepted as one of the main references in the field. Since then his main pursuit in mathematics is to find geometry hidden in any fluid motion. Outside of academia Boris likes traveling, tennis, tango, and batonchiki Rot Front -- all t-words.