Dima Jakobson

This is joint work with Y. Canzani, B. Clarke, N. Kamran, L. Silberman and J. Taylor. We construct Gaussian measure on the manifold of Riemannian metrics with the fixed volume form. We show that diameter and Laplace eigenvalue functionals are all integrable with respect to our measures. We also compute the characteristic function for the L^2 (Ebin) distance from a random metric to the reference metric. If time permits, we shall outline some geometric ideas behind a different project with L. Chen, where we construct a "canonical" measure on a conformal class of metrics in higher dimensions using conformally covariant operators.