Speaker: Jona Röhrig

Title: Gromov compactness in Lorentzian Length Spaces

Abstract:
Since it was started in 2018 by Kunzinger and Sämann, the topic of Lorentzian length spaces has grown in popularity. Its goal is to study geometry on certain types of Lorentzian metric spaces, lowering the regularity conditions necessary for General Relativity as much as possible. This is done by adapting the ideas of metric geometry to the Lorentzian setting. This allows, for example, the definition of sectional curvature or some rungs of the causal ladder in a synthetic version, as well as the Hausdorff dimension.
Additionally, the notion of Gromov-Hausdorff distance can be transferred to the Lorentzian setting, raising the question of whether, and to what extent, the curvature-driven Gromov compactness theorem holds valid.
In my talk, I want to give a brief introduction to the general topic and then shed some light on the last question.