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 3 (Generalised Euler geodesics as  Multi Marginal OT) 

  1. Intro to Arnold’s Euler geodesics.
  2. Brenier relaxation 1 : Lagrangian discretisation and solutions. 
  3. Brenier relaxation 2 : Eulerian formulation and MMOT and Entropic approximation via Sinkhorn. 

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