Optimal transport theory & its applications in astrophysics

I shall show that the dynamics of the Universe on large scales can be described by the Monge-Ampere equation. 

I shall discuss how fast new numerical algorithms based on the optimal transport theory provide a unique solution to this equation, and highlight the links to the variational principle.

Finally I will apply our method to both Hubble volume simulations of structure formation and to observational data, in order to constrain models of gravity and the early Universe.