## Geometry Seminar - Abstracts

### Talk

Tuesday 13 June 2023, 16:00 - 17:00 in HG01.028

**Leonardo GarcĂa Heveling** (RU)

*Metric geometry in Lorentzian signature*

### Abstract

In Riemannian geometry, it is often useful to view Riemannian
manifolds as part of the larger class of metric spaces. For example, it allows
us to obtain limit spaces using Gromov-Hausdorff convergence. Similar notions
are desired for Lorentzian manifolds (which model spacetime in general
relativity!), but have turned out to be more complicated to define. In this
talk, I will review two recent approaches to Lorentzian metric spaces and
Gromov-Hausdorff convergence, and discuss some results of my PhD thesis in
this context. Along the way, I will introduce some important concepts in
Lorentzian geometry, such as global hyperbolicity and time functions.

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