Given a smooth Riemannian manifold with boundary M, we get a distance function on the boundary given by the length of the shortest geodesic in M joining two given boundary points. We can ask to what extent this boundary distance function determines the metric on the whole space. In the case of negatively curved surfaces (with boundary), it is known that the boundary distance function determines the surface up to isometry. In this talk, I will outline Otal's proof of this result. If time permits, I will discuss the relation between the boundary rigidity problem and the marked length spectrum rigidity problem. No prior background in dynamics or Riemannian geometry will be assumed. Speaker(s): Karen Butt (UM)