An introduction to anti-de Sitter geometry

The aim of this minicourse is to give an introduction to anti-de Sitter geometry and anti-de Sitter manifolds, focusing especially on the case of dimension 3 and on its deep relations with hyperbolic geometry in dimension 2 and Teichmüller theory. The main emphasis will be on a particular class of Lorentzian (2+1)-manifolds called "globally hyperbolic maximal Cauchy compact anti-de Sitter 3-manifolds". We will describe properties of both their internal geometry (e.g. their convex core and the structure of its boundary) and of the structure of their associated deformation spaces (see e.g. Mess' classification result).

Date and time info
Late January/Early February

Keywords
Anti-de Sitter space and its isometries, globally hyperbolic spacetimes, geometric structures, hyperbolic surfaces, Teichmüller space

Prerequisites
Experience with classical tools of Differential Geometry (Riemannian metrics, Gaussian and sectional curvature, geodesic and metric completeness) will be necessary. Some familiarity with the geometry of hyperbolic surfaces (the hyperbolic plane and its isometries, ) will be extremely helpful.

Language
English