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Event Series Event Series: Colloquium

Liouville Theory and Weil-Petersson Geometry

May 6, 2024 @ 4:30 pm - 5:30 pm


Speaker: Sarah Harrison (Northeastern University)

Title: Liouville Theory and Weil-Petersson Geometry

Abstract: Two-dimensional conformal field theory is a powerful tool to understand the geometry of surfaces. Liouville conformal field theory in the classical (large central charge) limit encodes the geometry of the moduli space of Riemann surfaces. I describe an efficient algorithm to compute the Weil–Petersson metric to arbitrary accuracy using Zamolodchikov’s recursion relation for conformal blocks, focusing on examples of a sphere with four punctures and generalizations to other one-complex-dimensional moduli spaces. Comparison with analytic results for volumes and geodesic lengths finds excellent agreement. In the case of M_{0,4}, I discuss numerical results for eigenvalues of the Weil-Petersson Laplacian and connections with random matrix theory.

Based on work with K. Coleville, A. Maloney, K. Namjou, and T. Numasawa.


May 6, 2024
4:30 pm - 5:30 pm
Event Category:


CMSA Room G10
CMSA, 20 Garden Street
Cambridge, MA 02138 United States
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