The two talks will cover recent advances in low-regularity spacetime geometry, motivated by the need for a unified mathematical framework for quantum and gravitational physics.

The first talk will introduce an approach to synthetic Lorentzian geometry based exclusively on a 2-point function—referred to as the Lorentzian distance—which satisfies a reverse triangle inequality. This framework will be shown to recover the spacetime topology and define chronological/causal orders. Additionally, results on the validity of the limit curve theorem and the existence of time functions will be presented.