Date:
Tue, 22/07/2014 - 14:30 - 15:00
To a flat vector bundle over a Riemannian manifold, one can associate its Lyapunov exponents, the logarithmic growth rates of sections when parallel transported along the geodesic flow. Flat bundles occurring in nature are the relative cohomology bundles associated to families of curves, or more generally Kaehler manifolds. In the case of a family of curves over a hyperbolic curve, there is a beautiful formula, first discovered by Kontsevich, that relates the sum of Lyapunov exponents to the degrees of certain line bundles.