I review Lorentzian causality theory paying particular attention to the optimality and
generality of the presented results. I include complete proofs of some foundational results …

We develop causality theory for upper semi-continuous distributions of cones over manifolds
generalizing results from mathematical relativity in two directions: non-round cones and non …

We introduce an analogue of the theory of length spaces into the setting of Lorentzian
geometry and causality theory. The rôle of the metric is taken over by the time separation …

The goal of the present work is three-fold. The first goal is to set foundational results on
optimal transport in Lorentzian (pre-) length spaces, including cyclical monotonicity, stability …

A bstract Inflationary spacetimes have been argued to be past geodesically incomplete in
many situations. However, whether the geodesic incompleteness implies the existence of an …

For a Lorentzian space measured by m in the sense of Kunzinger, Sämann, Cavalletti, and
Mondino, we introduce and study synthetic notions of timelike lower Ricci curvature bounds …

The goal of this survey is to give a self-contained introduction to synthetic timelike Ricci
curvature bounds for (possibly non-smooth) Lorentzian spaces via optimal transport and …

On the occasion of Sir Roger Penrose's 2020 Nobel Prize in Physics, we review the
singularity theorems of General Relativity, as well as their recent extension to Lorentzian …

We define a one-parameter family of canonical volume measures on Lorentzian (pre-)
length spaces. In the Lorentzian setting, this allows us to define a geometric dimension …

Continuing recent efforts in extending the classical singularity theorems of General Relativity
to low regularity metrics, we give a complete proof of both the Hawking and the Penrose …