Mathematics Colloquium

Richard Schwartz (Brown). In this talk I'll describe several maps defined on the space of polygons. These maps are described in terms of simple straight-line constructions, and are therefore natural with respect to projective geometry. One of them, the pentagram map, is now known to be a discrete completely integrable system. I'll concentrate on a variant of the pentagram map, which behaves somewhat like heat flow on convex polygons but which does crazy things to non-convex polygons.