|Location:||MSRI: Simons Auditorium|
The Wasserstein space of a compact metric space X is the space of Borel probability measures P(X), equipped with a certain metric W_2. This metric comes from the problem of how to optimally transport mass on X. If X is equipped with additional structure then the Wasserstein space inherits additional structure as well. I will give a historical introduction to these ideas and indicate why they are relevant to Riemannian geometry.