This course will cover some state-of-the-art applications of modern computational optimal transport using entropic regularisation. We will start with a brief introduction to optimal transport and entropic regularisation before discussing three topics in more detail: second order mean field games, Arnold’s Euler geodesics, and semi-martingale optimal transport.

Lecture 2  (Second Order Mean Field Games as Entropic Multi Marginal OT) 

  1. The Schroedinger problem, static versus dynamic formulations.
  2. Extension to second order Mean Field Games.
  3. Application of Multi Marginal Sinkhorn algorithms to solve them.

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