Séminaire des doctorants
The spectral gap of a hyperbolic surface
20
May 2026
May 2026
| Intervenant : | Julien Moy |
| Heure : | 14h00 - 15h00 |
| Lieu : | 2L8 |
Le séminaire des doctorants se propose de fournir aux doctorants une occasion de s'ouvrir aux autres domaines des mathématiques que le leur. A chaque séance, un intervenant réalise un exposé sur un fait standard de leur domaine d'étude, de niveau adapté à l'ensemble des doctorants.
---
The first nontrivial eigenvalue of the Laplacian on a closed Riemannian manifold (called the spectral gap) is a geometrical invariant that encodes many interesting properties of the manifold. Notably, it gives some quantitative information on the connectedness of the manifold, on the rate of convergence to equilibrium of the heat flow, or the speed of mixing of the geodesic flow in some cases.
I will focus on hyperbolic surfaces, which are closed manifolds of dimension 2 with constant curvature -1. After defining these objects, I will review some old and new results about the spectral gap in this setting. Recent developments provide probabilistic constructions of random surfaces that display optimal spectral gaps.
The PhD students seminar aims to provide PhD students with an opportunity to explore other areas of mathematics beyond their own. At each session, a speaker gives a presentation on a standard topic in their field of study, at a level suitable for all doctoral students.