Appears in collection : 2025 - T2 - WS1 - Higher rank geometric structures, Higgs bundles and physics

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.