2025 - T2 - WS1 - Higher rank geometric structures, Higgs bundles and physics

Collection 2025 - T2 - WS1 - Higher rank geometric structures, Higgs bundles and physics

Organizer(s) Canary, Richard ; Garcia-Faide, Elba ; Labourie, François ; Li, Qiongling ; Neitzke, Andrew ; Pozzetti, Beatrice ; Wienhard, Anna
Date(s) 19/05/2025 - 27/05/2025
linked URL https://indico.math.cnrs.fr/event/11569/
11 20

On the length spectrum of random hyperbolic 3-manifolds

By Anna Roig Sanchis

We are interested in studying the behavior of geometric invariants of hyperbolic 3-manifolds as their complexity increases. A way to do so is by using probabilistic methods, that is, through the study of random manifolds. There are several models of random manifolds. In this talk, I will explain one of the principal probabilistic models for 3 dimensions and I will present a result concerning the length spectrum -the set of lengths of all closed geodesics- of a 3-manifold constructed under this model. If time allows, I will discuss in more detail an element in the spectrum with particular importance, the systole.

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