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which are of large scale, or have some particular pedagogical goal), Conference proceedings (and short surveys), Unpublished or locally published works (e.g. texts published in french journals).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

  1. In collaboration with P.L. Lions: Régularité optimale de racines carrées. C.R. Acad. Sci. 321 (1995), 1537-1541. Download
  2. On the Landau equation: weak stability, global existence. Adv. Diff. Eq. 1, 5 (1996), 793-816. Download
  3. On the spatially homogeneous Landau equation for Maxwellian molecules. Math. Meth. Mod. Appl. Sci. 8, 6 (1998), 957-983 Download | Link To Journal
  4. Fisher information estimates for Boltzmann’s collision operator. J. Maths Pures Appl. 77 (1998), 821-837. Download | Link To Journal
  5. On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations. Arch. Rat. Mech. Anal. 143, 3 (1998), 273-307. Download | Link To Journal
  6. Conservative forms of Boltzmann’s collision operator: Landau revisited. Math. Mod. An. Num. 33, 1 (1999), 209-227. Download
  7. In collaboration with G. Toscani: Probability metrics and uniqueness of the solution to the Boltzmann equation for a Maxwell gas. J. Statist. Phys. 94, 3/4 (1999), 619-637. Download | Link To Journal
  8. In collaboration with G. Toscani: Sharp entropy dissipation bounds and explicit rate of trend to equilibrium for the spatially homogeneous Boltzmann equation. Comm. Math. Phys. 203, 3 (1999), 667-706. Download | Link To Journal
  9. Regularity estimates via the entropy dissipation for the spatially homogeneous Boltzmann equation without cut-off. Rev. Matem. Iberoam. 15, 2 (1999), 335-352. Download | Link To Journal
  10. In collaboration with L. Desvillettes: On the spatially homogeneous Landau equation for hard potentials. Part I: Existence, uniqueness and smoothness. Comm. P.D.E 25, 1-2 (2000), 179-259. Download | Link To Journal
  11. In collaboration with L. Desvillettes: On the spatially homogeneous Landau equation for hard potentials. Part II: H-Theorem and applications. Comm. P.D.E 25, 1-2 (2000), 261-298. Download | Link To Journal
  12. Decrease of the Fisher information for solutions of the spatially homogeneous Landau equation with Maxwellian molecules. Math. Mod. Meth. Appl. Sci. 10, 2 (2000), 153-161. Download | Link To Journal
  13. In collaboration with G. Toscani: On the trend to equilibrium for some dissipative systems with slowly increasing a priori bounds. J. Statist. Phys. 98, 5-6 (2000), 1279-1309. Download | Link To Journal
  14. In collaboration with F. Otto: Generalization of an inequality by Talagrand, viewed as a consequence of the logarithmic Sobolev inequality. J. Funct. Anal. 173, 2 (2000), 361-400. Download | More details | Link To Journal
  15. In collaboration with R. Alexandre, L. Desvillettes and B. Wennberg: Entropy dissipation and long-range interactions. Arch. Rat. Mech. Anal. 152 (2000), 327-355. Download | More details | Link To Journal
  16. A short proof of the “concavity of entropy power”. IEEE Trans. Info. Theory 46, 4 (2000), 1695-1696. Download
  17. In collaboration with L. Desvillettes: On the trend to global equilibrium in spatially inhomogeneous systems. Part I: the linear Fokker-Planck equation. Comm. Pure Appl. Math. 54, 1 (2001), 1-42. Download | More details | Link To Journal
  18. In collaboration with F. Otto: Comment on : “Hypercontractivity of Hamilton-Jacobi equations”, by S. Bobkov, I. Gentil and M. Ledoux. J. Math. Pures Appl. (9) 80, 7 (2001), 697-700. Download | Link To Journal
  19. In collaboration with R. Alexandre: On the Boltzmann equation for long-range interactions. Comm. Pure Appl. Math. 55, 1 (2002), 30-70. Download | More details | Link To Journal
  20. In collaboration with E. Caglioti: Homogeneous cooling states are not always good approximations to granular flows. Arch. Rational Mech. Anal. 163, 4 (2002), 329-343. Download | More details | Link To Journal
  21. In collaboration with L. Desvillettes: On a variant of Korn’s inequality arising in statistical mechanics. A tribute to J.-L. Lions. ESAIM Control Optim. Calc. Var. 8 (2002), 603-619 (electronic). Download | More details | Link To Journal
  22. In collaboration with L. Pareschi and G. Toscani: Spectral methods for the non cut-off Boltzmann equation and numerical grazing collision limit. Numer. Mat. 93, 3 (2003), 527-248. Download | Link To Journal
  23. Cercignani’s conjecture is sometimes true and always almost true. Commun. Math. Phys. 234 (2003), 455-490 Download | More details | The original publication is available via Link To Journal
  24. In collaboration with J.A. Carrillo and R. McCann: Kinetic equilibration rates for granular media and related equations: Entropy dissipation and mass transportation estimates. Rev. Matematica Iberoamericana 19 (2003), 1-48. Download | Link To Journal
  25. In collaboration with D. Cordero-Erausquin and B. Nazaret: A new approach to sharp Sobolev and Gagliardo-Nirenberg inequalities. Adv. Math. 182, 2 (2004), 307-332. Download | More details | Link To Journal
  26. In collaboration with R. Alexandre: On the Landau approximation in plasma physics. Ann. Inst. H. Poincaré Anal. Non Linéaire 21, 1 (2004), 61-95. Download | More details | Link To Journal
  27. In collaboration with I. Gamba et V. Panferov: On the Boltzmann equation for diffusively excited granular media. Comm. Math. Phys. 246, 3 (2004), 503-541. Download | More details | Link To Journal
  28. In collaboration with C. Mouhot: Regularity theory for the spatially homogeneous Boltzmann equation with cut-off. Arch. Rational Mech. Anal. 173, 2 (2004), 35-43. Download | More details Link To Journal
  29. In collaboration with L. Desvillettes: On the trend to global equilibrium for spatially inhomogeneous kinetic systems: the Boltzmann equation. Invent. Math. 159, 2 (2005), 245-316. Download | More details
  30. In collaboration with F. Maggi: Balls have the worst best Sobolev inequalities. J. Geom. Anal. 15, 1 (2005), 83-121. DownloadMore details
  31. In collaboration with F. Bolley: Weighted Csiszár-Kullback-Pinsker inequalities and applications to transportation inequalities. Ann. Fac. Sci. Toulouse Math. 14, 3 (2005), 331-352. Download
  32. In collaboration with J. Carrillo and R. McCann: Contractions in the 2-Wasserstein length space and thermalization of granular media. Arch. Rational Mech. Anal. 179 (2006), 217-263. Download
  33. In collaboration with A. Guillin and F. Bolley: Quantitative concentration inequalities for empirical measures on non-compact spaces. Probab. Theory and Related Fields 137, 3-4 (2007), 287-314. Download
  34. In collaboration with J. Lott: Weak curvature conditions and Poincaré inequalities. J. Funct. Anal. 245, 1 (2007), 311-333. Download
  35. In collaboration with J. Lott: Hamilton-Jacobi semigroup on length spaces and applications. J. Math. Pures Appl. 88, 3 (2007), 219-229. Download
  36. In collaboration with A. Figalli: Strong displacement convexity on Riemannian manifolds. Math. Z. 257, 2 (2007), 251-259. Download
  37. In collaboration with F. Maggi: Balls have the worst best Sobolev inequalities. Part II: Variants and extensions. Calc. Var. Partial Differential Equations 31, 1 (2008), 47-74. Download
  38. Stability of a 4th-order curvature condition arising in optimal transport theory J. Funct. Anal. 255, 9 (2008), 2683-2708. DownloadMore details
  39. In collaboration with A. Figalli: An approximation lemma about the cut locus, with applications in optimal transport theory Meth. Appl. Anal. 15, 2 (2008), 149-154. Download
  40. In collaboration with L. Ni, J.-L. Vázquez and P. Lu: Local Aronson-Bénilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds. J. Math. Pures Appl. 91, 1 (2009), 1-19. Download
  41. In collaboration with J. Lott: Ricci curvature for metric-measure spaces via optimal transport. Ann. of Math. 169, 3 (2009), 903-991. Download | More details
  42. In collaboration with N. Grunewald, F. Otto and M. Reznikoff: A two-scale approach to logarithmic Sobolev inequalities and the hydrodynamic limit. Ann. Inst. H. Poincaré Probab. Statist. 45 (2009), 2, 302–351. Download
  43. Hypocoercivity. Mem. Amer. Math. Soc. 202 (2009), no. 950, iv+141 pp. DownloadMore details
  44. In collaboration with V. Panferov and I. Gamba: Upper Maxwellian bounds for the spatially homogeneous Boltzmann equation. Arch. Ration. Mech. Anal. 194 (2009), 1, 253–282. DownloadMore details
  45. In collaboration with G. Loeper: Regularity of optimal transport in curved geometry: the nonfocal case. Duke Math. J. 151 (2010), 431–485. DownloadMore details
  46. In collaboration with E. Carlen, M.C. Carvalho, J. Le Roux and M. Loss: Entropy and chaos in the Kac model. Kinet. Relat. Models 3, 1 (2010), 85–122. Download
  47. In collaboration with A. Figalli and L. Rifford: On the Ma-Trudinger-Wang curvature on surfaces. To appear in Calc. Var. Partial Differential Equations. Download | More details
  48. In collaboration with A. Figalli and L. Rifford: Tangent cut loci on surfaces Download | More Details
  49. In collaboration with A.~Figalli and L.~Rifford: Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifolds. Differential Geom. Appl. 29, 2 (2011), 154-159. Download | More Details
  50. In collaboration with C. Mouhot: On Landau damping. Acta Mathematica 207, 1 (2011), 29-201. Download | More Details
  51. In collaboration with A. Figalli and L. Rifford: Nearly round spheres look convex. Amer. J. Math. 134, 1 (2012), 109-139.Download | More Details

Recent or nearly completed works

In collaboration with Y. Ollivier: A curved Brunn–Minkowski inequality on the discrete cube — or: What is the Ricci curvature of the discrete hypercube? To appear in SIAM J. on Discrete Math. Download


Books and synthesis works

  1. A review of mathematical topics in collisional kinetic theory. In Handbook of Mathematical Fluid Dynamics, S. Friedlander and D. Serre, Eds, Elsevier Science, 2002. Download | More details
  2. Limites hydrodynamiques de l’équation de Boltzmann (d’après C. Bardos, F. Golse, C. D. Levermore, P.-L. Lions, N. Masmoudi, L. Saint-Raymond). Bourbaki Seminar, Exp. 893 (June 2001). Astérisque 282 (2002), 365-405. Download | More details | To Journal
  3. Topics in Optimal Transportation. Graduate Studies in Mathematics 58, American Mathematical Society, Providence (2003) (Sorry, only the preface is available online!) Download | More details
  4. Optimal transportation, dissipative PDE’s and functional inequalities. Notes for the CIME summer school “Optimal transportation and applications” (Martina Franca, September 2002). Lecture notes in mathematics, vol. 1813, L. Caffarelli and S. Salsa, Ed. © Springer-Verlag Download | More details
  5. Convergence to equilibrium: entropy production and hypocoercivity. Text of my Harold Grad lecture at the Rarefied Gas Dynamics 24 (Bari, June 2004). Download | More details
  6. Entropy production and convergence to equilibrium. Notes from a series of lectures in Institut Henri Poincaré, Paris (Fall 2001). In Entropy methods for the Boltzmann equation, Lecture Notes in Math., vol. 1916, F. Golse and S. Olla, Eds. Springer, 2008, pp. 1-70. Download More details
  7. Mathematics of granular materials. J. Stat. Phys. 124 (2006), no. 2-4, 781-822. Download | More details
  8. Hypocoercive diffusion operators. Proceedings of the International Congress of Mathematicians (Madrid, 2006). Download | More details
  9. Optimal transport, old and new. Grundlehren der mathematischen Wissenschaften, Vol.338, Springer-Verlag, 2009. Download
  10. Hypocoercivity. Mem. Amer. Math. Soc. 202 (2009), no. 950. More details This memoir includes a debugged version of my obsolete text, “Hypocoercive diffusion operators in Hörmander form”. In the present version (updated August 2008) it also contains a new section (Appendix 22) on local positivity estimates for Fokker-Planck type equations, together with a few additions in Appendix 21. Download
  11. Paradoxe de Scheffer-Shnirelman revu sous l’angle de l’intégration convexe (d’après C. De Lellis, L. Székelyhidi). Bourbaki Seminar, Exp. 1001 (November 2008). Download | More details
  12. Transport optimal. Leçons de Mathématiques d’Aujourd’hui, Vol.4 (2011).Download Lecture given in Bordeaux, 2005, for graduate students; edited in 2008.
  13. Regularity of optimal transport and cut locus: from nonsmooth analysis to geometry to smooth analysis. Review article on the relation between the regularity of optimal transport and the geometry of cut locus (2010). Download | More details
  14. Landau damping. Notes for a course given in Cotonou, Benin, and in CIRM, Luminy, Summer 2010. Download | More details
  15. (Ir)rréversibilité et entropie / (Ir)reversibility and entropy. Séminaire Poincaré (Bourbaphy) XV (Le Temps, 2010). In french: Download In English: Download

Conference proceedings and short surveys

  1. In collaboration with P. Markowich: On the trend to equilibrium for the Fokker-Planck equation: an interplay between physics and functional analysis. Mat. Contemp. 19 (2000), 1-29. Download | To Journal
  2. In collaboration with L. Desvillettes: Entropic methods for the study of the long time behavior of kinetic equations. The Sixteenth International Conference on Transport Theory, Part I (Atlanta, GA, 1999). Transport Theory Statist. Phys. 30, 2-3 (2001), 155-168. Download | To Journal
  3. On the trend to equilibrium for kinetic equations. Inhomogeneous random systems (Cergy-Pontoise, 2001). Markov Process. Related Fields 8, 2 (2002), 237-250. Download | To Journal
  4. In collaboration with I. Gamba and V. Panferov: On the inelastic Boltzmann equation with diffusive forcing. In Nonlinear Problems in Mathematical Physics and Related Topics II, in honor of Professor O.A. Ladyzhenskaya, Int. Math. Ser. 2, New York (2002), 179-192. Download
  5. In collaboration with A. Arnold, J.A. Carrillo, L. Desvillettes, J. Dolbeault, A. Jüngel, C. Lederman, P.A. Markowich and G. Toscani: Entropies and equilibria of many-particle systems: An essay on recent research. Monatsh. Math. 142, 1-2 (2004), 35-43. Download | To Journal
  6. Trend to equilibrium for dissipative equations, functional inequalities and mass transportation. Notes for the summer school “Mass transportation methods in kinetic theory and hydrodynamics” (Ponta Delgada, Azores, 2000). Recent Advances in the Theory and Applications of Mass Transport, M. C. Carvalho and J. F. Rodrigues, editors, Contemporary Mathematics, vol. 353, Amer. Math. Soc., Providence, RI (2004), 95-109. © AMS Download
  7. Entropy production and convergence to equilibrium for the Boltzmann equation. Notes for the 14th International Congress of Mathematical Physics (Lisbon, 2003) Download
  8. Convergence to equilibrium: Entropy production and hypocoercivity. Notes for my Harold Grad lecture delivered at the 24th Rarefied Gas Dynamics conference (Bari, 2004) (Also listed as a “Synthesis work” above) Download
  9. Hypocoercive diffusion operators. Proceedings of the International Congress of Mathematicians (Madrid, 2006). (Also listed as a “Synthesis work” above)Download
  10. Current trends in optimal transport — A tribute to Ed Nelson. Text of my lecture for the Conference in the honor of Edward Nelsons’ seventieth birthday (Vancouver, juin 2004). Appeared in Diffusion, quantum theory, and radically elementary mathematics, Math. Notes, 47, Princeton Univ. Press, Princeton, NJ, 2006, pp. 141-156. Download
  11. Transport optimal et courbure de Ricci. Text of my lecture at the seminar of geometry and spectral theory in Grenoble (identical, up to minor corrections, to the text of my lecture at the X-EDP Seminar in École Polytechnique). Sémin. Théor. Spectr. Géom. 24, Année 2005-2006 (2007), 79-100. Download
  12. H-Theorem and beyond: Boltzmann’s entropy in today’s mathematics. Expanded version of my lecture at the Boltzmann memorial in Munich. In Boltzmann’s legacy, ESI Lect. Math. Phys., Eur. Math. Soc., Zürich, 2008, pp.129-143. Download
  13. In collaboration with A. Figalli: Optimal transport and curvature. Notes for my CIME course in Cetraro, June 2008. Download
  14. Local-to-global principles in Riemannian geometry and optimal transport. Download Oberwolfach Report, 2008.
  15. Landau damping. Download Oberwolfach Report, 2009.
  16. Optimal transport: Monge meets Riemann, and Fourier. Download Conference proceedings from a French-Egyptian mathematics conference in Cairo, May 2010.
  17. L’écriture des mathématiciens. Proceedings of the conference Écritures: sur les traces de Jack Goody, organized in ENSSIB Lyon by Éric Guichard, for a broad audience of sociologists and other scientists, January 2008. Download
  18. In collaboration with C. Mouhot: Landau damping. J. Math. Phys. 51 (50th anniversary issue), 015204 (2010) Download
  19. Landau damping. Proceedings of the International Conference of Mathematicians (Hyderabad, 2010) Download
  20. Particle systems and nonlinear Landau Damping. Lecture Notes, written for my address at the meeting of the Division of Plasma Physics of the American Physics Society, Salt Lake City, November 2011. Download
  21. Nash et les équations aux dérivées partielles. Matapli Vol.108, 35-53, November 2015 Download

Unpublished or locally published works

I published a short broad-audience paper about optimal transportation, entitled
Transport optimal: coup de neuf pour un très vieux problème
in Images des Mathématiques 2004, a publication by CNRS.

The following short text, which was part of my PhD Thesis, was edited and put online on the suggestion of Henri Cabannes and Li-Shi Luo:
Is there any backwards solution of the Boltzmann equation?
Although the results there are extremely partial, the problem which is explained might be of interest to some readers.

Here is another short unpublished text, containing some strange identities about the Fokker-Planck-Landau equation, derived in particular from discussions with Benoît Desjardins:
Some identities satisfied by the Coulomb potential
Included is a remark about the existence of stationary self-similar solutions when there is a source term at zero velocity.


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