Mathematics

The theory of Optimal Transport finds its roots in the work of Gaspard Monge in 1781, whose interest was in finding the cheapest possible way to transfer some resources from producers to consumers.

After some major contributions due to Leonid Kantorovich (who was later awarded the Nobel Prize in Economics, partly for his work on the subject) in the 1940s, Optimal Transport has been blooming in the last thirty years, with applications covering partial differential equations, geometric analysis, mathematical finance, and machine learning, among the others.

The course is divided into two parts, each related to the control of expanding sets either with a barrier or by removing a fixed amount of area per unit time.

In this series of talks, we are aimed at constructing the solution formula of the Green's functions for various hyperbolic and hyperbolic-parabolic partial differential equations in a half multi-D space domain. We will use the transform variables to derive a master relationships of the Dirichlet-Neumann data of the PDE, and use it to obtain the full Dirichlet-Neumann data in the transform variables; and obtain the Rayleigh surface.