Lyapunov exponents, the determinant of the Laplacian and volumes of strata in genus 0.

We prove a formula relating the sum of the first g Lyapunov
exponents of the Teichmuller geodesic flow to a constant in an
asymptotic formula counting periodic trajectories on a flat surface.

The derivation passes via the determinant of the Laplace operator in the flat metric on a surface.

This is joint work with M. Kontsevich and A. Zorich