Speaker: Dmitry Jakobson (McGill)

Title: Probability measures on manifolds of Riemannian metrics

Abstract: This is joint work with Y. Canzani, B. Clarke, N. Kamran, L. Silberman and J. Taylor. We construct Gaussian measures on the manifold of Riemannian metrics with the fixed volume form. We show that diameter, Laplace eigenvalue and volume entropy 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.