Can you hear the shape of a Hyperbolic Marimba? Concerto di Superfici Iperboliche

Hyperbolic surfaces have historically been played as drums, with little success. By work of Vignéras and Sunada, the frequencies at which a hyperbolic drum vibrates do not determine the surface up to isometry. In this talk, we are going to change perspective and play a hyperbolic surface as a marimba: we assign notes to a finite collection of closed geodesics and, following a random geodesic on the surface, we play a note when the corresponding closed curve is hit. We investigate to what extent the melodies produced determine the hyperbolic surface. We will try to introduce topics in a way that makes the content understandable by a broad audience.