For Mathematicians

Research articles, courses, reviews, lectures… for specialists and students in mathematics.

    Complete List of Publications

  • I have separated my works into several categories: Research papers (published or accepted for publications), Books and synthesis works (books but also surveys which are of large scale, or have some particular pedagogical goal), Conference proceedings (and short surveys), Unpublished or locally published works (e.g. texts published in french journals). Research papers, published or accepted for publication In collaboration with P.L. Lions: Régularité optimale de racines carrées. C.R. Acad. Sci. 321 (1995), 1537-1541. Download On the Landau equation: weak stability, global existence. Adv. Diff. Eq. 1, 5 (1996), 793-816. Download On the spatially homogeneous Landau equation for Maxwellian molecules. Math. Meth. Mod. Appl. Sci. 8, 6 (1998), 957-983 Download | Link To Journal Fisher information estimates for Boltzmann’s collision operator. J. Maths Pures Appl. 77 (1998), 821-837. Download | Link • Read more →

  • Presentation of my Research

  • Below is a selection of some of my most significant research papers (the choice is of course subjective). All the rest of my papers can be found in my publication list. There you can also find electronic links to the journals in which these papers have been published. I divided this selection (sometimes a bit artificially) into various themes and sub-themes: Collisional kinetic theory (Boltzmann type) Regularizing effects of grazing collisions Grazing collisions limit Cercignani entropy production conjecture Space-inhomogeneous convergence to equilibrium Qualitative properties of kinetic models for granular media Collisionless kinetic theory (Vlasov type) Collisionless relaxation (Landau damping) Optimal transport Optimal transport, Ricci curvature and geometric inequalities Optimal transport and isoperimetric/Sobolev inequalities Regularity of optimal transport in curved geometry In the explanations, I shall recall only basic facts and • Read more →

  • Surveys / Books

  • Below is a selection of research-level texts which I have written for pedagogical purposes. They are mainly focused on recent research, and describe other researchers’ contributions as well as mine. Here I only put those texts which I consider most significant; the other ones can be found in my publication list. A Review of Mathematical Topics in Collisional Kinetic Theory This is a book-size review paper about kinetic models describing collisions between particles, such as Boltzmann’s equation and its variants. The emphasis is on the mathematical point of view, and many recent contributions are reviewed as well as old problems. Chapter 1 describes models and problems, Chapter 2 is about the theory of the Cauchy problem (including regularity and estimates on solutions), Chapter 3 enters into the links and analogies • Read more →

  • Lecture Notes for Students / Cours pour Étudiants

  • Below is a compilation of some lecture notes (mostly in French) which I have written for my regular teaching activities, at undergraduate or graduate level. These notes are unfinished, and hopefully will be completed some day. In some cases there are also repositories of the modifications, used during the courses to inform the students of the various updates. Cours d’Intégration et Analyse de Fourier Ces notes ont été rédigées pour un cours que j’ai enseigné à l’ENS Lyon (niveau licence) entre 2003 et 2008. Elles contiennent une présentation de la théorie moderne de la mesure, ainsi que de l’analyse de Fourier. On y trouve des motivations historiques, des liens entre intégrale de Riemann et de Lebesgue, des résultats subtils de construction de mesures de probabilités (Kolmogorov, Hewitt-Savage), des chapitres sur • Read more →

  • Errata sheets

  • Here you will find errata sheets for my books and surveys, and occasionally some papers. All these errors have been fixed in the versions that you can currently download from this site; so these errata sheets are rather intended to people who work with the published version, or who already downloaded a previous version of the text. Do not hesitate to report all bugs, misprints, mistakes, etc. to me via regular mail or e-mail. A Review of Mathematical Topics in Collisional Kinetic Theory PDF File Topics in Optimal Transportation PDF File Hypocoercivity PDF File Optimal Transport, Old and New PDF File

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