Colloque - Géométrie et spectre des grands objets - Bram Petri : Bass Notes of Closed Arithmetic Hyperbolic Surfaces

Nalini AnantharamanGéométrie spectraleCollège de FranceAnnée 2025-2026Colloque - Géométrie et spectre des grands objets - Bram Petri : Bass Notes of Closed Arithmetic Hyperbolic SurfacesBram PetriSorbonne UniversitéThe spectral gap (or bass note) of a closed hyperbolic surface is the smallest non-zero eigenvalue of its Laplacian. This invariant plays an important role in many parts of hyperbolic geometry. The talk will start with a brief introduction to the (spectral) hyperbolic surfaces and some of the general motivation for the subject. After that, I will speak about joint work with Will Hide on the question of which numbers can appear as spectral gaps of closed arithmetic hyperbolic surfaces.