Mathematical Physics Seminar

Since the end of the nineties, the relations of optimal transport with many functional inequalities with geometric content has been revealed and explored by several authors (Barthe, Caffarelli, Cordero, McCann, Otto and others). Sobolev inequalities, for instance, have acquired a new interpretation involving qualitative transport of probability measures. I will review this theme, including recent work in collaboration with J. Lott about functional inequalities in metric-measure spaces.