Polyhedral surfaces in Cauchy-compact $3$-dimensional flat spacetimes with BTZ-like singularities with help from Teichmüller

Orateur: BRUNSWIC Léo
Localisation: Université d'Avignon, France
Type: Séminaire de géométrie
Site: Hors LAMA , IMJ P7
Salle: 2015
Date de début: 20/02/2017 - 13:30
Date de fin: 20/02/2017 - 13:30

In the 1990's, T'Hooft suggested to study 3-dimensional singular flat spacetimes with polyhedral Cauchy-surfaces as toy model to understand quantum gravity. This motivates the study of singular spacetimes however the type of a singularity in a Lorentzian manifold depends on both the type of the axis and the causality around it which strongly contrast with the riemannian context. BTZ-like singularities are limit cases of "massive particles" which are close Lorentzian equivalent to conical singularities. We present some classification results on Cauchy-compact spacetimes with BTZ and present ramifications of the convex hull method used by Penner to construct a cellulation of his decorated Teichmüller space.