Évènement

Although there are several ways to  »choose a compact hyperbolic surface at random », putting the Weil-Petersson probability measure on the moduli space of hyperbolic surfaces of a given topology is certainly the most natural.

The work of M. Mirzakhani has made possible the study of this probabilistic model: it is one of the only model of  »random riemannian manifolds » where some explicit calculations are actually possible. One may thus ask questions about of the geometry and the spectral statistics of the laplacian of a randomly chosen surface – in analogy with what is usually asked for models of random graphs.

I will be interested in the spectral gap of the laplacian for a random compact hyperbolic surface, in the limit of large genus (j.w. Laura Monk).