# Frédéric Robert

Institut Elie Cartan de Lorraine
Université de Lorraine
BP 70239
F-54506 Vandoeuvre-lès-Nancy Cedex
France

## Fields of interest

 Nonlinear analysis on manifolds. Elliptic equations of high order.

## Education:

 1992: Distinction at the "Concours Général" in Physics. 1994: "École Normale Supérieure de Cachan", Cachan, France. 1997: "Agrégation" of Mathematics. Rank: 15. 1998: Phd studies. Thesis advisor: Emmanuel Hebey. Thesis defended on November 26th, 2001. 2007: Habilitation to conduct researches. Defended on June 28th, 2007. Download .pdf file (in French).

## Status:

 1994-1999: École Normale Supérieure de Cachan 1999-2002: Allocataire Moniteur Normalien, Université de Cergy-Pontoise. 2002-2003: Assistant, ETH Zurich. 2003-2009: Maître de Conférences (Associate Professor), Université de Nice. 2009-present: Professeur des Universités (full professor), Université de Lorraine. 2013-2014: On leave, appointed in the CNRS unit PIMS (UBC, Vancouver) during the first semester. 2014: Promotion to First Class Professor.

## Organization of conferences

11/2005: Week-end nicois d'Analyse Géométrique Conforme in Nice, France.
08/2006: Geometric and nonlinear analysis in Banff, Canada.
06/2007: Geometric Analysis in Nice in Nice, France.
03/2008: Analyse non linéaire et phénomènes critiques à Cergy-Pontoise, France.
06/2011: Geometric and Nonlinear Analysis: Meeting in Lorraine" in Nancy, France.
08/2012: Recent trends in Geometric and Nonlinear Analysis in Banff, Canada.
12/2012: "Géométrie et EDP", Nancy, France.

## Video

 The Hardy-Schrodinger operator with interior singularity: mass and blow-up analysis. Talk given on May 24th 2017 at la Casa Matematica Oaxaca (CMO), BIRS center, Mexico.

## Talks and conferences:

 1. Asymptotic behaviour of a nonlinear elliptic equation with critical Sobolev exponent. The radial case, Advances in Differential Equations, 6, (2001), 821-846. 2. Asymptotic profile for the sub-extremals of the sharp Sobolev inequality on the sphere, with Olivier Druet, Communications in Partial Differential Equations, 26, (2001), 743-778. 3. Coercivity and Struwe's compactness for Paneitz type operators with constant coefficients, with Emmanuel Hebey, Calculus of Variations and Partial Differential equations, 13, (2001), 491-517. 4. Asymptotic behaviour of a nonlinear elliptic equation with critical Sobolev exponent: The radial case II. Nonlinear Differential Equations and Applications, 9, (2002), 361-384. 5. Positive solutions for a fourth order equation invariant under isometries, Proceedings of the AMS, 131, (2003), 1423-1431. 6. Mountain-Pass critical points for Paneitz-Branson operators, with Pierpaolo Esposito, Calculus of Variations and Partial Differential Equations, 15, (2002), 493-517. 7. Fourth order equations of critical Sobolev growth. Energy function and solutions of bounded energy in the conformally flat case, with Veronica Felli and Emmanuel Hebey, Nonlinear Differential Equations and Applications, 12, (2005), 171-213. 8. Blow-up theory for elliptic PDEs in Riemannian geometry, with Olivier Druet and Emmanuel Hebey Mathematical Notes, Princeton University Press, Volume 45. Result announced in Electronic Research Announcements of the AMS, 9, (2003), 19-25. 9. Sharp solvability conditions for a fourth order equation with perturbation, with Kunnath Sandeep, Differential and Integral Equations, 16, (2003), 1181-1214. 10. Asymptotic profile for a fourth order pde with critical exponential growth in dimension four, with Michael Struwe. Advanced Nonlinear Studies, 4, (2004), 397-415. 11. Compactness and global estimates for the geometric Paneitz equation in high dimensions, with Emmanuel Hebey. Electronic Research Announcements of the AMS, 10, (2004), 135-141. 12. Critical functions and optimal Sobolev inequalities, Mathematische Zeischrift, 249, (2005), 485-492. 13. Compactness and global estimates for a fourth order equation of critical Sobolev growth arising from conformal geometry, with Emmanuel Hebey and Yuliang Wen. Communications in Contemporary Mathematics, 8, (2006), 9-65. Download .ps or .pdf file. 14. The effect of curvature on the best constant in Hardy-Sobolev inequalities, with Nassif Ghoussoub. Geometric And Functional Analysis (GAFA), 16, (2006), 1201-1245. Download .ps or .pdf file. 15. Bubbling phenomena for fourth-order four-dimensional PDEs with exponential growth, with Olivier Druet. Proceedings of the AMS, 134, (2006), 897-908. Download .ps or .pdf file. 16. Concentration estimates for Emden-Fowler equations with boundary singularities and critical growth, with Nassif Ghoussoub. International Mathematics Research Papers (IMRP), Volume 2006, Article ID 21867, 1-85. Download .ps or .pdf file. 17. Concentration phenomena for Liouville's equation in dimension four, with Adimurthi and Michael Struwe. Journal of the European Mathematical Society, 8, (2006), 171-180. Download .ps or .pdf file. 18. Concentration phenomena for a fourth order equation with exponential growth: the radial case. Journal of Differential Equations, 231, (2006), 135-164. Download .ps or .pdf file. 19. Quantization effects for a fourth order equation of exponential growth in dimension four. The Royal Society of Edinburgh Proceedings A, 137A, (2007), 531-553. Download .ps or .pdf file. 20. On the local Nirenberg problem for the Q-curvatures with Philippe Delanoe. Pacific Journal of Mathematics, 231, (2007), 293-304. Download .ps or .pdf file. 21. On the influence of the Kernel of the bi-harmonic operator on fourth order equations with exponential growth. Sixth international conference on "Dynamical Systems and Differential Equations", Poitiers, June 2006. Discrete and continuous dynamical systems, Supplement 2007, 875-882. Download .ps or .pdf file. 22. Asymptotic behavior of a fourth order mean field equation with Dirichlet boundary condition, with Juncheng Wei. Indiana University Mathematics Journal, 57, (2008), 2039-2060. Download .ps or .pdf file. 23. Elliptic equations with critical growth and a large set of boundary singularities, with Nassif Ghoussoub. Transactions of the AMS, 361 (2009), no. 9, 4843-4870. Download .ps or .pdf file. 24. On a p-Laplace equation with multiple critical nonlinearities, with Roberta Filippucci et Patrizia Pucci. Journal des Mathématiques Pures et Appliquées, 91, (2009), 156-177. Download .ps or .pdf file. 25. Positivity and almost positivity of biharmonic Green's functions under Dirichlet boundary conditions, with Hans-Christoph Grunau. Archive for Rational Mechanics and Analysis, 195, (2010) 865-898. Download .ps or .pdf file. 26. The heat flow with a critical exponential nonlinearity, with Tobias Lamm et Michael Struwe. Journal of Functional Analysis, 257, (2009), 2951-2998. Download .ps or .pdf file. 27. Admissible $Q-$curvatures under isometries for the conformal GJMS operators. Nonlinear elliptic partial differential equations, 241-259, Contemporary Mathematics, 540, Amer. Math. Soc., Providence, RI, 2011. Volume in the honor of Jean-Pierre Gossez. Download .pdf file. 28. The Lin-Ni's conjecture for mean convex domains . with Olivier Druet and Juncheng Wei. Memoirs of the AMS, 218, (2012), 105pp. Download here. 29. Asymptotic analysis for fourth order Paneitz equations with critical growth . with Emmanuel Hebey. Advances in the Calculus of Variations, 4, (2011), 229-275. Download here. 30. Optimal estimates from below for biharmonic Green functions . with Hans.-Christoph Grunau and Guido Sweers. Proceedings of the AMS, 139, (2011), 2151-2161. Download here. 31. Sign-changing blow-up for scalar curvature type equations . with Jerome Vetois. Communications in Partial Differential Equations, Volume 38, Issue 8, August 2013, pages 1437-1465. Download here. 32. Uniform estimates for polyharmonic Green functions in domains with small holes. with Hans-Christoph Grunau. Contemporary Mathematics, 595, (2013), 263-272. Download here. 33. A general theorem for the construction of blowing-up solutions to some elliptic nonlinear equations via Lyapunov-Schmidt's finite-dimensional reduction. with Jerome Vetois. Concentration Compactness and Profile Decomposition, (TIFR CAM, Bangalore, 2011), Trends in Mathematics, 95-116, Springer. Download here. 34. Examples of non-isolated blow-up for perturbations of the scalar curvature equation on non locally conformally flat manifolds. with Jerome Vetois. Journal of Differential Geometry,, 98, (2014), 349-356. Download here. 35. Sign-changing solutions to elliptic second order equations: glueing a peak to a degenerate critical manifold. with Jerome Vetois. Calculus of Variations and PDEs, 54, (2015), 693-716. DOI10.1007/s00526-014-0802-1 . Download here. 36. On the Hardy-Schrodinger operator with a boundary singularity . with Nassif Ghoussoub. Analysis and PDEs, 10-5, (2017), 1017-1079. DOI 10.2140/apde.2017.10.1017. Download here. 37. Sobolev inequalities for the Hardy-Schr\"odinger operator: Extremals and critical dimensions, with Nassif Ghoussoub. Bulletin of Mathematical Sciences, {\bf 6}, (2016), no. 1, 89-144. DOI: 10.1007/s13373-015-0075-9. Download here.. 38. Sharp asymptotic profiles for singular solutions to an elliptic equation with a sign-changing nonlinearity . with Florica Cirstea. Proceedings of the London Mathematical Society, (3), 114, (2017), 1-34. DOI: 10.1112/plms.12003. Download here. 39. Nondegeneracy of positive solutions to nonlinear Hardy-Sobolev equations . Advances in Nonlinear Analysis, 6, (2017), no. 2, 237-242. DOI: 10.1515/anona-2016-0267. Download here. 40. The Hardy-Schrodinger operator with interior singularity: The remaining cases, with Nassif Ghoussoub. Calculus of Variations and PDEs, to appear. Download here.. 41. Mass and asymptotics associated to fractional Hardy-Schr\"odinger operators in critical regimes, avec N.Ghoussoub, S.Shakerian et M.Zhao. Preprint (2017). Download here..