Published on *Max Planck Institute for Mathematics* (https://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Laura Monk
Affiliation:

IRMA Strasbourg
Date:

Thu, 17/12/2020 - 16:30 - 18:00 The main aim of this talk is to present geometric and spectral properties of typical hyperbolic surfaces. More precisely, I will:

- introduce a probabilistic model, first studied by Mirzakhani, which is a natural and convenient way to sample random hyperbolic surfaces

- describe the geometric properties of these random surfaces: diameter, injectivity radius, Cheeger constant, Benjamini-Schramm convergence...

- explain how one can deduce from this geometric information estimates on the number of eigenvalues of the Laplacian in an interval [a,b], using the Selberg trace formula.

**Links:**

[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] https://www.mpim-bonn.mpg.de/node/3050