Geometry, Lyapunov exponents and rigidity

Amie Wilkinson (Universtiy of Chicago)

Abstract

To each complete Riemannian manifold $M$ is associated a dynamical system — the geodesic flow on the unit tangent bundle $SM$. To what extent are the dynamical properties of this flow wedded to the geometry of $M$? I will discuss some historical highlights, open questions and recent breakthroughs.