The pentagram map

Abstract: The pentagram map was introduced by Schwartz as a dynamical system on polygons in the real projective plane. The map sends a polygon to the shape formed by intersecting certain diagonals. This simple operation turns out to define a discrete integrable system, meaning roughly that, after a birational change of coordinates, it is a translation on a family of real tori. We will explain how the real, complex, and finite field dynamics of the pentagram map are all related by the following generalization: the pentagram map is birational to a translation on a family of Jacobian varieties.

algebraic geometry

Audience: researchers in the topic

Algebraic Geometry NorthEastern Series (AGNES)