Optimal transport in gradient flows and partial differential equations

Optimal transport has become a central tool for analysing gradient-flow PDEs, from the linear Fokker-Planck and nonlinear porous-medium equations to models of fluid mechanics, collective behaviour, chemotaxis, mean-field games and density functional theory. Through this link such equations become accessible to the calculus of variations and convex optimisation, and to numerical schemes that respect their transport structure. The workshop addresses current questions of well-posedness, regularity and numerical approximation for existing and new transport-related PDEs.