Expository papers

Here you find references to some expository papers and lecture notes I wrote (typically by invitation, or for submission to proceedings and special volumes).

You could also be interested in my book Optimal Transport for Applied Mathematicians. Contact me in case you want to access some specific parts of the book, or for errata (I mean: to send me a list of mistakes you found).

Gradient flows

Here you will find a survey (approx 65 pages) on the theory of gradient flows (in particular in Wasserstein spaces) and of its latest developments.

Mean Field Games

Here you will find a survey (28 pages) on part of the theory of Mean Field Games, namely on the congested variational case, including some numerics. Written in collaboration with J.-D. Benamou and G. Carlier, to appear in "Active Particles, Volume 1: Theory, Models, Applications", edited by N. Bellomo, P. Degond, and E. Tadmor.

Crowd motion

Here you will find a survey (20 pages) on the theory of density-constrained continuous models for crowd motion, developed with B. Maury, A. Roudneff-Chupin and other collaborators. A long section is devoted to numerical methods. The survey is meant to summarize the theory and its advancements in the last ten years, and clarify the assumptions and the results that have been proven. Written for the proceedings of the SMAI 2017 French Conference.

Traffic Congestion

Here you will find a survey (20 pages) on the continuous theory of traffic congestion that we studied with Carlier, Jimenez, Brasco, Benamnsour and Peyré. Written in collaboration with G. Carlier, published in Zapiski Nauchnykh Seminarov POMI / J. Math. Sci., in the proceedings of a conference organized in St Petersburg in May 2010.

Bourbaki Seminars

I gave two Bourbaki seminars, for which the speaker usually writes some notes. Since "Nicolas Bourbaki a une préférence pour le français", they are both written in French.

In 2011 I gave a seminar about Quantitative Isoperimetric Inequalities (essentially, the work by Figalli, Maggi and Pratelli).

In 2013 I gave a seminar about the general theory of gradient flows (the text has been expanded to become the survey on top of this list, which is itself written in english).

Lecture notes from the Grenoble Summer school, 2009

The notes for the two mini-courses on optimal transport and applications that I gave in Grenoble in 2009 have become (5 years later) chapters in a book: "Optimal Transportation, theory and applications", London Math. Soc.

See here for a general introduction to optimal transport (16 pages).
See here for some applications in economics, traffic and urban planning (16 pages).