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 1 (Introduction to OT, Multi Marginal OT and entropic OT)  

  1. OT, its CFD (kinetic energy) interpretation and their Kantorovich (optimisation in measure space) relaxation. 
  2. Time discretisation and Multi Marginal OT.
  3. Entropic regularisation and Sinkhorn.
  4. Shortlist of problem addressed in the lecture series.  

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