Geometry and spectra of random hyperbolic surfaces

The study of lengths of closed geodesics and of the Laplace spectrum on hyperbolic surfaces was initiated by work of Huber in the 1970’s where he used the Selberg trace formula to determine various asymptotics and bounds. Another major development came with Mirzakhani’s thesis and subsequent works, in which she developed new techniques to integrate functions over moduli spaces of hyperbolic surfaces. This opened the way for proving results about random surfaces or for proving existence results based on probabilistic arguments. In the past few years, there has been a renewed interest for the Selberg trace formula, especially in combination with Mirzakhani’s integration technique. Various other models of random surfaces have also been studied with great success, and we now understand the behaviour of several geometric invariants thanks to recent breakthroughs, but many open problems remain.

The goal of this discovery school is to introduce graduate students and advanced undergraduate students to the above circle of ideas and give them the chance to learn about recent advances from leading experts in the field.

We support the statement of inclusiveness. Everyone is welcome to attend.