My research interests are in optimal transportation, calculus of variations, and nonlinear partial differential equations. In particular, I am interested in fluid mechanics and gradient flows results for problems in applied optimal transport. Recently, I've been interested in variational mean field games theory associated only to optimal transportation, and kinetic equations like the Vlasov-Poisson equation.
- An optimal transportation principle for interacting paths and congestion .(2021) arxiv.org/abs/2109.01946, submitted
- A Benamou-Brenier theory for interacting paths and the Vlasov-Poisson equation. In collaboration with Nestor Guillen. (In preparation)