## Geometry Seminar - Abstracts

### Talk

Monday 13 January 2020, 15:30-16:30 in HG03.085

**Annegret Burtscher** (RU)

*On the metric structure and convergence of spacetimes*

### Abstract

One of the most powerful objects in geometry are curves. Minimizing
the arc lengths of curves between two points on Riemannian manifolds defines a
distance function which induces a natural length metric space structure on the
manifold. In turn, notions of metric convergence interact with the Riemannian
structure and (weak) curvature bounds. No such profound metric theory is yet
available for Lorentzian manifolds because the Lorentzian distance function
does not give rise to a metric. For spacetimes with suitable time functions,
however, the recently introduced null distance of Sormani and Vega provides an
alternative metric that naturally interacts with the causal structure and also
yields a length metric space and an integral current space. In this talk we
compare the metric space structure of Riemannian and Lorentzian manifolds and
show how different notions of metric convergence interact with the null
distance of warped product spacetimes. This is joint work with Brian Allen.

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