In the first half of this talk we will review several notions of coarse or weak
Ricci Curvature on metric measure spaces which include the work of Yann
Ollivier. The discussion of the notion of coarse Ricci curvature will serve as
motivation for developing a method to estimate the Ricci curvature of a an
embedded submaifold of Euclidean space from a point cloud which has applications
to the Manifold Learning Problem. Our method is based on combining the notion of
``Carre du Champ" introduced by Bakry-Emery with a result of Belkin and Niyogi
which shows that it is possible to recover the rough laplacian of embedded
submanifolds of the Euclidean space from point clouds. This is joint work with
Micah Warren.