# 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).