Abstract: Introduced by R. Schwartz almost 20 years ago, the pentagram map acts on plane n-gons, considered up to projective equivalence, by drawing the diagonals that connect second-nearest vertices and taking the new n-gon formed by their intersections. I shall survey recent work on the pentagram map, in particular, I shall demonstrate that the dynamics of the pentagram map is very regular: the map is completely integrable. I shall show that the pentagram map is a discretization of the Boussinesq equation, a well known completely integrable partial differential equation. An unexpected relation between the spaces of polygons and combinatorial objects called the 2-frieze patterns (generalizing the frieze patterns of Coxeter) will be revealed. Eight new configuration theorems of projective geometry will be demonstrated. The talk will be illustrated by computer animation.

Coffee will be served at 12:00 before the lecture
at Schreiber building 006