Optimal transport, localisation and martingales

In the first part of the talk I shall discuss an approach to the localisation technique, for spaces satisfying the curvature-dimension condition, by means of L1-optimal transport. I shall present work on a generalisation of the technique to multiple constraints setting.

In the second part I shall discuss work in progress concerning general localisation scheme, which includes both the L1-localisation and the irreducible convex paving of the martingale transport theory.