Mathematical Relativity, Scalar Curvature and Synthetic Lorentzian Geometry

The synthetic approach towards understanding Ricci curvature in the Riemannian setting has lead to groundbreaking results over the past quarter century. Recent advances towards developing a synthetic version of sectional and Ricci curvature in the Lorentzian setting and of Scalar curvature in the Riemannian setting is highly promising and should lead to deeper understanding of Einstein's theory of gravity. Identifying the relevant notions of convergence for spacetimes is another topic of current interest encompassed by this workshop.