EVENT DETAILS AND ABSTRACT

Title: The 2--Wasserstein metric and its applications to PDEs
Speaker: Professor Wilfrid Gangbo
Speaker Info: Georgia Institute of Technology
Brief Description:
Special Note:
Abstract:

We introduce the 2--Wasserstein metric on the set of probabilities and study several constrained variational problems in that metric. We analyze the induced geometry of the set of densities satisfying the constraint on the variance and means and we determine all the geodesics on it. These analysis were motivated by questions in kinetic theory.

The evolution of many mechanical systems can be represented by paths in the set of probability measures. These paths may consist of measures which are not absolutely continuous. It is necessary have a notion of infinite dimensional Hamiltonian systems on the whole set of measures. We give examples of evolutive systems that have a amiltonian structure according to that new concept.