The Lyapunov spectrum of an invariant measure for a geodesic flow describes the asymptotic exponential growth rates of Jacobi fields along almost every geodesic with respect to this measure. We prove that the geodesic flow of a closed negatively curved locally symmetric space is characterized among nearby smooth flows by the structure of its Lyapunov spectrum with respect to volume. We deduce that these locally symmetric spaces are locally characterized up to isometry by the Lyapunov spectra of their geodesic flows. We will discuss some geometric aspects of the proof, which draw on quasiconformal mapping theory and the geometry of 2-step Carnot groups. Speaker(s): Clark Butler (U Chicago)