I will discuss a variant of the classical optimal transport dynamical problem, 

in which the entropy along the curve is minimized additionally to the kinetic energy.

This results into a regularization of optimal transport curves and can be used as a 

smooth approximation of the Wasserstein geodesic on compact manifolds. 

The approach uses techniques from mean field game theory, elliptic equations, 

displacement convexity arguments.

 

This seminar is part of the activities of the PRIN project 2022W58BJ5 ``PDEs and optimal control methods in mean field games, population dynamics and multi-agent models'', funded by the European Union – Next Generation EU.