  Two-dimensional conformal field theory is a powerful tool to understand the
geometry of surfaces. Here, we study Liouville conformal field theory in the
classical (large central charge) limit, where it encodes the geometry of the
moduli space of Riemann surfaces. Generalizing previous work, we employ this to
study moduli spaces of higher genus surfaces, surfaces with boundaries, and
surfaces with cone points. In each case, the knowledge of classical conformal
blocks provides an extremely efficient approximation to the Weil-Petersson
metric on moduli space. We find detailed agreement with analytic results for
volumes and geodesic lengths on moduli space.
