Orateur
Description
The constant curvature Lorentzian metrics having a finite number of conical singularities offer new examples of geometric structures on the torus, naturally generalizing the analogous Riemannian case. In the latter, works of Troyanov show that the data of the conformal structure and of the angles at the singularities entirely classify the metrics with conical singularities. In this talk, we will introduce the Lorentzian metrics with conical singularities, construct some examples, and present a rigidity phenomenon: de-Sitter tori with a singularity of fixed angle are determined by the topological equivalence class of their lightlike bifoliation. Contrarily to the Riemannian case, we will see that in the Lorentzian case this rigidity is intimately linked to one-dimensional dynamics phenomena.
