Optimal Transport

2-Wasserstein Geodesic joining the Pac-Man and the Ghost normalized characteristic functions

Optimal transport is motivated by the following question: given two (or more) distributions of goods (typically modelled by probability measures), what is the cheapest way (with respect to a given cost function) to move one into the other?   

The topic has connections with economics, probability, partial differential equations, geometry, to mention a few. The research in the OxPDE group is focused on the following aspects:

- Partial differential equations via optimal transport,  including: gradient flows, linear and nonlinear diffusion equations, mean field limits

- Functional and geometric inequalities via optimal transport tools

- Synthetic Ricci curvature lower bounds via optimal transport and applications to the geometric analysis of metric measure spaces.

Faculty: José A. Carrillo, Andrea Mondino

Postdoctoral Fellows:  Immanuel Ben Porat, Antonio Esposito and Jakub Skrzeckowski 

Students: Alessandro Cucinotta, Francesco Fiorani, Carles Falco I Gandia, Shuchen Guo, Alejandro Fernández Jiménez,  Dimitri Navarro and Vanessa Ryborz