G\'eom\'etrie et topologie des vari\'et\'es hyperboliques de grand volume

TL;DR

This paper surveys recent developments in the geometry and topology of hyperbolic manifolds with large volume, including applications to random surfaces, highlighting the asymptotic behavior of sequences of locally symmetric spaces.

Contribution

It compiles recent research on hyperbolic manifolds of increasing volume and explores new applications to the study of random surfaces.

Findings

Sequences of hyperbolic manifolds exhibit specific geometric and topological properties as volume increases.

Applications to random surfaces reveal new insights into their geometric structure.

The survey consolidates recent advances in the field of hyperbolic geometry.

Abstract

This paper is mostly a survey of recent work on sequences of locally symmetric spaces whose Riemannian volume goes to infinity. We also work out some applications to random surfaces.