Some open questions on anti-de Sitter geometry

TL;DR

This paper discusses open questions in anti-de Sitter (AdS) geometry, exploring its connections with homogeneous spaces, discrete subgroups, Teichmüller theory, and hyperbolic geometry, aiming to guide future research in the field.

Contribution

It compiles and analyzes key open problems in AdS geometry, highlighting their relations to other mathematical areas and suggesting directions for future work.

Findings

Identification of key open questions in AdS geometry

Connections established between AdS geometry and Teichmüller theory

Potential analogs between AdS and hyperbolic geometries

Abstract

We present a list of open questions on various aspects of AdS geometry, that is, the geometry of Lorentz spaces of constant curvature -1. When possible we point out relations with homogeneous spaces and discrete subgroups of Lie groups, to Teichm\"uller theory, as well as analogs in hyperbolic geometry.