The pentagram map and the arithmetic of abelian varieties

ALGEBRAIC DYNAMICS

Speaker:

Max Weinreich - Brown University

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 that it is birational to a translation on a family of abelian varieties. Soloviev proved this over the complex numbers in 2013. We extend the result to any algebraically closed field of characteristic not equal to 2, and discuss the implications for the dynamics of rational maps over finite fields.

On Zoom. Go to http://people.math.harvard.edu/~demarco/AlgebraicDynamics/ for more information