abstract: The goal of the talk is to discuss and present few consequences of the recent non-smoothsynthetic definition of timelike Ricci curvature bounded below and dimension bounded above (based on optimal transport) in Lorentzian synthetic spaces. After recalling the general setting I will discuss some stability properties, an extension of the celebrated Hawking's Singularity Theorem and a sharp isoperimetric inequality. The talk is based on joint projects with A. Mondino.