Mathematics

Synthetic spacetime geometry is a relatively new and exciting research direction in Lorentzian/spacetime geometry and mathematical General Relativity. For the physical understanding of singularities and other similar phenomena, such synthetic/nonsmooth formulations and extensions of geometric results to these settings are paramount. In this talk, we will begin by briefly introducing the setting of synthetic spacetimes, while motivating the definitions with well-known properties from smooth spacetime geometry. We will then go on to talk about the appropriate curves and functions on these spaces. The main part of the talk will concern the differential calculus of these objects. Notions such as causal speed and maximal weak subslopes will be discussed, as well as the important consequences of these techniques, such as the lifting theorem, horizontal and vertical derivatives, and p-d'Alembertian comparison.The contents of this talk are based on joint work together with T. Beran (U. Vienna), M. Braun (U. Toronto), M. Calisti (U. Vienna), N. Gigli (SISSA), R. McCann (U. Toronto), F. Rott (U. Vienna) and C. Sämann (U. Oxford).