Explore a conference talk from the Arithmetic Quantum Field Theory Conference where Sarah Harrison from Northeastern University delves into the relationship between two-dimensional conformal field theory and surface geometry. Learn how Liouville conformal field theory in the classical limit maps to the geometry of Riemann surface moduli spaces. Discover an efficient algorithm for computing the Weil-Petersson metric using Zamolodchikov's recursion relation for conformal blocks, with specific focus on four-punctured spheres and similar one-complex-dimensional moduli spaces. Examine numerical findings about Weil-Petersson Laplacian eigenvalues and their connections to random matrix theory in the M_{0,4} case, while reviewing comparisons between computational results and analytical measurements of volumes and geodesic lengths.