**Title: **Global rigidity of the periodic Lyapunov spectrum for geodesic flows of negatively curved locally symmetric spaces

**Speaker: **Clark Butler, Princeton

**Abstract:** We show that if a smooth Anosov flow f^{t} is orbit equivalent to the geodesic flow g^{t} of a negatively curved locally symmetric space X of dimension at least three and the Lyapunov spectra of the flow f^{t} at all periodic points are multiples of the corresponding Lyapunov spectra of g^{t} then f^{t} is smoothly orbit equivalent to g^{t}. If f^{t} is itself the geodesic flow of a negatively curved space Y then we further conclude that Y is homothetic to X. We deduce the Mostow rigidity theorem as a corollary.