Section: New Results

Optimal transport

Participants : Ludovic Rifford, Alice Erlinger, Ahed Hindawi, Alessio Figalli, Bernard Bonnard, Jean-Baptiste Caillau, Lionel Jassionesse, Robert Mc Cann [U. of Toronto] .

This year has seen new results or starting directions in many areas of optimal cotrol.

• The very general condition for continuity of the transport map given in [47] motivated exploration of conditions for convexity of the tangent injectivity domain [10] , [3] on. Lionel Jassionnesse's PhD is in part devoted to Ma-Tudinger-Wang tensor that also plays an important role in this matter.

• In Ahed Hindawi's PhD [1] , defended this year, results in optimal transport for sub-Riemannian costs (see the survey [16] ) are generalized to costs coming from optimal control problems with quadratic cost and a drift.

• Alice Erlinger's PhD, joint with University of Toronto is exploring Optimal Transport's application to modeling in economics