Harmonic and Geometric Analysis

We focus mostly on the geometric and analytic study of Riemannian and Lorentzian symmetric spaces. Among our main research directions are:

• harmonic analysis on geometrically finite groups, including scattering theory and trace formulas,
• the structure of pseudo-Riemannian symmetric spaces,
• the geometry of 3-dimensional hyperbolic and anti-de Sitter manifolds,
• the relations between 3-dimensional geometry and Teichmüller theory,
• discrete and polyhedral geometry in relation with constant curvature spaces.