Abstract: The marked length spectrum of a closed Riemannian
manifold of negative curvature is a function on the free homotopy
classes of closed curves which assigns to each class the length of its
unique geodesic representative. It is known in certain cases that the
marked length spectrum determines the metric up to isometry, and this
is conjectured to be true in general. In this talk, we explore to what
extent the marked length spectrum on a sufficiently large finite set
approximately determines the metric.