Appears in collections : Evolution equations on singular spaces / Équations d'évolution sur les espaces singuliers, Exposés de recherche

In this somewhat speculative talk I will briefly describe recent results with Xuwen Zhu on the boundary behaviour of the Weil-Petersson metric (on the moduli space of Riemann surfaces) and ongoing work with Jesse Gell-Redman on the associated Laplacian. I will then describe what I think happens for the wave equation in this context and what needs to be done to prove it.