Speaker: Jona Röhrig (HU Berlin)

Title: Gromov compactness in Lorentzian length spaces

Abstract:
In this talk, we discuss necessary conditions for a timelike sectional curvature driven Gromov compactness theorem in the context of Lorentzian length spaces (LLS). We begin with an overview of length spaces as a generalization of Riemannian manifolds and Lorentzian length spaces as generalizations of spacetimes, alongside the notion of synthetic sectional curvature bounds in these spaces. Next, we examine how to adapt the Gromov-Hausdorff distance for the Lorentzian context and explore the generalization of Gromov compactness theorems from the metric to the Lorentzian setting. For a potential curvature-driven compactness theorem in the Lorentzian case, we propose an initial proof approach and provide examples of GH-diverging LLS to outline key requirements.