Sobolev Calculus in Synthetic Lorentzian Geometry

Explore Sobolev calculus in synthetic Lorentzian geometry through this 27-minute conference talk delivered at the Workshop on "Non-regular Spacetime Geometry" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the study of time functions on measured Lorentzian length spaces, inspired by the theory of Sobolev functions on metric measure spaces. Learn about the concept of weak lower differential and its application in defining a Sobolev class of functions. Discover how this machinery enables the proof of d'Alembert comparison results in the synthetic setting. Gain insights into this ongoing joint project involving researchers Tobias Beran, Mathias Braun, Matteo Calisti, Nicola Gigli, Robert McCann, Clemens Sämann, and Felix Rott.