Ricci curvature lower bounds for metric measure spaces.

In the '80s, Gromov proved that sequences of Riemannian manifold with a lower bound on the Ricci curvature and an upper bound on the dimension are precompact in the measured Gromov--Hausdorff topology (mGH for short). Since then, much attention has been given to the limits of such sequences, called Ricci limit spaces. A way to study these limits is to introduce a synthetic definition of Ricci curvature lower bounds and dimension upper bounds. A synthetic definition should not rely on an underlying smooth structure and should be stable when passing to the limit in the mGH topology. In this talk, I will briefly introduce CD spaces, which are a generalization of Ricci limit spaces.