Section: New Results

Optimal transport

Participants : Ludovic Rifford, Alice Erlinger, Alessio Figalli [U. of Texas at Austin, USA] , Thomas Gallouet [Inria, SIMPAF team] , Bernard Bonnard, Jean-Baptiste Caillau, Lionel Jassionesse, Robert Mc Cann [U. of Toronto] .

• The very general condition for continuity of the transport map given in [41] motivated exploration of conditions for convexity of the tangent injectivity domain [42] , [3] . Lionel Jassionnesse's PhD is in part devoted to Ma-Trudinger-Wang tensor that also plays an important role in this matter. Ludovic Rifford has an ongoing collaboration with Alession Figalli and Thomas Gallouet on the link between this MTW tansor and the convexity of injectivity domains; They already improved a result by Loeper and Villani (the preprint “Ma-Trudinger-Wang condition vs. convexity of injectivity domains” is available from the authors) and aim at proving a conjecture due to Villani, that would hold in the case of anlaytic surfaces.

• The goal of Alice Erlinger's PhD, joint with University of Toronto, is to explore Optimal Transport's application to modeling in economics. She unfortunately stopped her PhD, but some results have already been obtained.