## 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.