I. Monograph:

1. Vortices in the Magnetic Ginzburg-Landau Model,(with Etienne Sandier), Progress in Nonlinear Differential Equations and their Applications, vol 70, Birkhauser, (2007).

Erratum to the book (replacement for pages 148-151)

II. Lecture Notes:

1.Coulomb Gases and Ginzburg-Landau Vortices, Zurich Lectures in Advanced Mathematics, EMS. pdf file   link

2. Microscopic description of Log and Coulomb gases, proceedings of the Park City Summer school 2017, 38 pages. .pdf file

III. Articles in journals :

1.  Solutions stables de l'équation de Ginzburg-Landau en présence de champ magnétiqueCompte Rendus de l'Académie des Sciences, tome 326 No 8, série I, (1998), 949-954.

2. Local Minimizers for the Ginzburg-Landau Energy near Critical Magnetic Field, part I,   Communications in  Contemporary Mathematics , Vol 1 , No. 2, (1999), 213-254.

3. Local Minimizers for the Ginzburg-Landau Energy near Critical Magnetic Field, part II, Communications in Contemporary Mathematics , Vol 1, No. 3, (1999), 295-333.

4. Stable Configurations in Superconductivity : Uniqueness, Multiplicity and Vortex-Nucleation,  Archive for Rational Mechanics and Analysis, 149,  (1999), 329-365.

5. Global Minimizers for the Ginzburg-Landau Functional below the First Critical Magnetic Field,   Annales IHP, Analyse non linéaire, 17, No. 1,  (2000), 119-145. (with Etienne Sandier)

6. On the Energy of Type-II Superconductors in the Mixed Phase, Reviews in  Mathematical  Physics,  12, No 9, (2000), 1219-1257. (with Etienne Sandier)  .ps file

7. A Rigorous Derivation of a Free-Boundary Problem Arising in Superconductivity, Annales Scientifiques de l'ENS, 4e Ser, 33, (2000), 561-592. (with Etienne Sandier) .ps file

8. Pinning Phenomena in the Ginzburg-Landau model of Superconductivity, J. Math. Pures Appl.,  80, No 3, (2001), 339-372. (with Amandine Aftalion and Etienne Sandier)  .ps file

9. Limiting Domain-Wall Energy for a Problem Related to Micromagnetics, Comm. Pure Appl Math., 54, No3, (2001), 294-338.(with Tristan Riviere .ps file

10.  On a Model of Rotating Superfluids, ESAIM: Controle, Opt. et Calcul des Variations, 6, (2001), 201-238. .ps file

11. A variational formulation for the two-sided obstacle problem with measure data, Comm Contemp. Math, 4, No 2, (2002), 357-374. (with H. Brezis)  .ps file

12. Compactness, kinetic formulation and entropies for a problem related to micromagnetics, Comm PDE, 28, No 1 and 2, (2003), 249-269. (with Tristan Riviere)    .ps file

13.  Limiting Vorticities for the Ginzburg-Landau Equations,  Duke Math J., 117, No 3, (2003), 403-446. (with Etienne Sandier) .ps file   .dvi file

14.   Ginzburg-Landau Minimizers Near the First Critical Field Have Bounded Vorticity, Calc of Var PDE , 17, 1 (2003), 17-28. (with Etienne Sandier)  .ps file

15. Neel and Cross-Tie Wall Energies for Planar Micromagnetic Configurations,  ESAIM : COCV, 8, volume dedicated to Jacques-Louis Lions, (2002), 31-68. (with F. Alouges and T. Riviere)   .ps file

16. The decrease of bulk-superconductivity near the second critical field in the Ginzburg-Landau model, SIAM Journal Math Anal, 34, No 4,  (2003), 939-956. (with Etienne Sandier)   .ps file   .dvi file

17. A product estimate for Ginzburg-Landau and application to the gradient-flow,  Compte Rendus de l'Académie des Sciences, 336, (2003), 997-1002. (with Etienne Sandier)

18. A product-estimate for Ginzburg-Landau and corollaries,  J. Func. Anal., 211, No 1 , (2004),  219-244. (with Etienne Sandier) .ps file. dvi file

19. Gamma-convergence of gradient flows with applications to Ginzburg-Landau, Comm. Pure Appl. Math, 57, No 12, (2004), 1627-1672. (with Etienne Sandier).ps file   .dvi file

20 . Stability in 2D Ginzburg-Landau passes to the limit, Indiana Univ. Math. J., 54, No. 1, (2005), 199-222 .ps file  .dvi file 

21. A deterministic-control based approach to motion by curvature,  Comm. Pure Appl Math, 59, No. 3, (2006), 344-407.  (with Robert V. Kohn) .ps file

22. Vortex collisions and energy-dissipation rates in the Ginzburg-Landau heat flow, part I: Study of the perturbed Ginzburg-Landau equation, Journal Eur. Math Society , 9, No 2, (2007), 177-217. .dvi file .pdf file

23. Vortex collisions and energy-dissipation rates in the Ginzburg-Landau heat flow, part II: The dynamics, Journal Eur. Math Society, 9, No 3, (2007), 383-426. .dvi file  .pdf file

24. A gradient-flow approach for an evolution problem arising in superconductivity, Comm. Pure Appl. Math. 61, (2008), No 11, 1495--1539. (with L. Ambrosio) .pdf file .dvi file

25. Lowest Landau level approach in superconductivity for the Abrikosov lattice close to H_c2, Selecta Math. 2,13, (2007) (with A. Aftalion) .dvi file .pdf file

26. Lorentz Space Estimates for the Ginzburg-Landau Energy, J. Func. Anal. 254 (2008), No 3, 773--825 (with Ian Tice) .dvi file .pdf file

27. Critical Points of Ambrosio-Tortorelli converge to critical points of Mumford-Shah in the one-dimensional Dirichlet case, ESAIM: COCV 15 (2009), 576-598 (with Gilles Francfort and Nam Le), .pdf file

28. A deterministic-control based approach to fully nonlinear parabolic and elliptic equations, Comm. Pure Appl. Math., 63, (2010), 1298--1350. (with R. V. Kohn) .pdf file

29. Repeated games for eikonal equations, integral curvature flows and non-linear parabolic integro-differential equations, Disc. Cont. Dyn. Systems- A, 29, No 4, (2011), 1517-1552 (with C. Imbert).pdf file

30. Gamma-convergence of gradient flows on Hilbert and metric spaces and applications, Disc. Cont. Dyn. Systems, A, 31, No 4, (2011), 1427-1451, special issue in honor of De Giorgi and Stampacchia .pdf file

31. Gradient flow of the Chapman-Rubinstein-Schatzman model for signed vortices, Annales IHP Anal. non lin. 28, No 2, (2011), 217-246 (with L. Ambrosio and E. Mainini) .pdf file

32. Improved lower bounds for Ginzburg-Landau energies via mass displacement, Analysis & PDE 4-5 (2011), 757--795. (with E. Sandier) .pdf file

33. Ginzburg-Landau vortex dynamics with pinning and strong applied currents, Arch. Rat. Mech. Anal., 201, No 2 (2011), 413-464 (with I. Tice) .pdf file

34. Lorentz Space Estimates for the Coulombian Renormalized Energy, Comm. Contemp Math, 14, (2012), No 4, 1250027, (with I. Tice) .pdf file

35. Energy estimates and cavity interaction for a critical-exponent cavitation model, Comm. Pure Appl. Math. (2012), 1-74 (with D. Henao) link

36. Large Vorticity Stable Solutions to the Ginzburg-Landau Equations, Indiana Univ. Math. J. 61 (2012), 1737-1763. (with A. Contreras) .pdf file.

37. From the Ginzburg-Landau Model to Vortex Lattice Problems, Comm. Math. Phys. 313 (2012), 635--743.(with E. Sandier) .pdf file

38. Renormalized Energy Concentration in Random Matrices, Comm. Math. Phys., 320, No 1, (2013), 199-244 (with A. Borodin), .pdf file

39. A Mean Field Equation as Limit of Nonlinear Diffusions with Fractional Laplacian Operators, Calc Var. PDE (2013) (with J.L. Vazquez) .pdf file

40. Quantum Hall states of bosons in rotating anharmonic traps, Phys. Rev. A, 87, (2013), 023618 (with N. Rougerie and J. Yngvason) .pdf file

41. Quantum Hall phases and plasma analogy in rotating trapped Bose gases, J. Stat. Phys. 154 (2014), no. 1-2, 2–50. (with N. Rougerie and J. Yngvason) .pdf file

42. The Gamma-limit of the two-dimensional Ohta-Kawasaki functional. Part I: Droplet density, Arch. Ration. Mech. Anal. 210 (2013), no. 2, 581–613. (with D. Goldman and C. Muratov) .pdf file

43. Bogoliubov spectrum of interacting Bose gases, Comm. Pure Appl. Math. 68 (2015), no 3, 413-471 (with M. Lewin, P.T. Nam, and J.P. Solovej) .pdf file

44. Ginzburg-Landau vortices, Coulomb gases, and Renormalized Energies, J. Stat. Phys. 154 (2013), no. 3 , 660-680.
45. The Gamma-limit of the two-dimensional Ohta-Kawasaki functional. Part II: Droplet arrangement via the Renormalized Energy, Arch. Ration. Mech. Anal. 212 (2014), no. 2, 445--501 (with D. Goldman and C. Muratov) .pdf file

46. Remarks on a constrained optimization problem for the Ginibre ensemble, Potential Analysis, 41, no 3, (2014), 945-958 (with S. Armstrong and O. Zeitouni) arXiv

47. Renormalized Energy Equidistribution and Local Charge Balance in 2D Coulomb Systems, to appear in International Math. Research Notices (with S. Rota Nodari) .pdf file

48. 2D Coulomb Gases and the Renormalized Energy, Annals of Proba, 43, no 4, (2015), 2026-2083  (with E. Sandier) .pdf file

49. Higher Dimensional Coulomb Gases and Renormalized Energy Functionals, Comm. Pure Appl. Math. 69 (2016), 519-605. (with N. Rougerie) .pdf file

50. 1D Log Gases and the Renormalized Energy: Crystallization at Vanishing Temperature, Proba. Theor. Rel. Fields, 162, no 3, (2015), 795-846. (with E. Sandier) .pdf file

51. Ginzburg-Landau vortices, Coulomb Gases and Abrikosov lattices, Comptes-Rendus Physique, Vol 15 - N° 6 - juin 2014.

52. Next Order Asymptotics and Renormalized Energy for Riesz Interactions, J. Institut Math. Jussieu, 16 (2017) No. 3, 501–569. (with M. Petrache) .pdf file

53. Branched Microstructures in the Ginzburg-Landau Model of Type-I Superconductors, SIAM J. Math Anal, 48 (2016), No. 4, 2994-3034. (with S. Conti and F. Otto) .pdf file

54. Large Deviations for the Two-Dimensional Two-Component Plasma, Comm. Math. Phys. 350 (2017), no. 1, 301-360 (with T. Leblé and O. Zeitouni) .pdffile


55. Mean Field Limits of the Gross-Pitaevskii and Parabolic Ginzburg-Landau Equations,  JAMS, 30 (2017), No. 3, 713-768. .pdf file

56. Large Deviation Principle for Empirical Fields of Log and Riesz Gases (with T. Leblé), to appear in Inventiones Math. .pdf file


57. Large Systems with Coulomb interactions: Variational Study and Statistical mechanics, Portugaliae Math. 73, No. 4 (2016), 247-278. .pdf file

58.  A Two-Scale Gamma-Convergence Approach for Random Non-Convex Homogenization, to appear in Calc. Var. PDE (with L. Berlyand and E. Sandier) .pdf file

III. Preprints:

1. Fluctuations of Two-Dimensional Coulomb Gases (with T. Leblé) .pdf file

2. Mean-Field dynamics for Ginzburg-Landau vortices with pinning and applied force (with M. Duerinckx) .pdf file

3. Large Deviations Principle for Hypersingular Riesz Gases (with D. Hardin, T. Leblé and E. Saff) .pdf file

4. A branched transport limit of the Ginzburg-Landau functional (with S. Conti, M. Goldman and F. Otto) .pdf file

5. CLT for Fluctuations of Beta-Ensembles with General Potential (with F. Bekerman and T. Leblé) .pdf file

IV. Some proceedings:

1. On the Ginzburg-Landau Equation with  Magnetic Field, in Calculus  of  Variations and Differential  Equations, A. Ioffe S. Reich and I. Shafrir, editors, Chapman &
Hall/CRC Research Notes in Mathematics Series, Vol. 410, CRC Press, Boca Raton, FL, (1999).

2. Sur l'équation de Ginzburg-Landau avec champ magnétique,  Proceedings of the ``Journées Équations aux Dérivées Partielles, Saint-Jean-de-Monts'', (1998).

3.  Etude mathématique de l'équation de Ginzburg-Landau des supraconducteurs soumis à un champ magnétique,  in  Compte-Rendus de la 2ème Rencontre du Non-Linéaire, IHP Paris, (Y. Pomeau, R. Ribotta), Paris Onze Edition, (1999).

4. Vorticité dans les équations de Ginzburg-Landau de la supraconductivitéSéminaire: Equations aux Dérivées Partielles, 1999-2000, Exp. No. VI, 16 pp.,  Sémin. X EDP, École Polytech., Palaiseau, (2000).

5. Vorticity for the Ginzburg-Landau Model of Superconductors in a Magnetic Field, in CRM Proceedings and Lecture Notes, Volume 27, (2001).

6. Vortices for Ginzburg-Landau Equations: With Magnetic Field Versus Without, (with E. Sandier), in Noncompact Problems at the Intersection of Geometry, Analysis and Topology, Proceedings of the Brezis-Browder Conference on Noncompact Variational Problems and General Relativity, A. Bahri, S. Klainerman, and M. Vogelius, Eds, Contemporary Mathematics, 350, (2004).

7. Vortices in the Ginzburg-Landau model of superconductivity.  European Congress of Mathematics,  837--850, Eur. Math. Soc., Zürich, 2005.

8. Vortices in the Ginzburg-Landau model of superconductivity, Proceedings of the International Congress of Mathematicians, Madrid, Spain, 2006, vol III, 267--290, Eur. Math. Soc., 2006.

9. Gamma-convergence of gradient flows and applications to Ginzburg-Landau vortex dynamics. Topics on concentration phenomena and problems with multiple scales, 267--292, Lect. Notes Unione Mat.

 Ital., 2,

 Springer, Berlin, 2006

10. Some methods and issues in the dynamics of vortices in the parabolic Ginzburg-Landau equations. Perspectives in nonlinear partial differential equations, 459--483, Contemp. Math., 446, Amer. Math. Soc., Providence, RI, 2007.

11. Second-order PDE's and deterministic games. ICIAM 07—6th International Congress on Industrial and Applied Mathematics, 239–249, Eur. Math. Soc., Zürich, 2009, (with R.V. Kohn).

12. Vortex patterns in Ginzburg-Landau minimizers (with E. Sandier). XVIth International Congress on Mathematical Physics, 246–264, World Sci. Publ., 2010.

13. Lois de conservation et régularité par compensation pour les systèmes antisymétriques et les surfaces de Willmore (d'après Tristan Rivière). Séminaire Bourbaki. Vol. 2009/2010. Exposés 1012–1026. Astérisque No. 339 (2011), Exp. No. 1024, ix, 357–370.