The goal of the talk is to discuss and present few consequences of the recent non-smooth/synthetic 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 geometric comparison results, stability properties
and an extension of the Hawking's Singularity Theorem (in sharp form) to the synthetic setting.
The talk is based on the paper "Optimal transport in Lorentzian synthetic spaces, synthetic timelike Ricci curvature lower bounds and applications” (w/ Mondino)
and it is ideally the continuation of the previous talk by Mondino.