Frédéric Robert

Address

Institut Elie Cartan
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.

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.

Editorial activities

Associate editor of "International Journal of Mathematics and Mathematical Sciences" and "International Journal of Analysis".

Some mathematical texts

A. Fourth order equations with critical growth in Riemannian geometry.
Notes from lectures given at Madison and Berlin (not submitted). Download here.
B. Existence et asymptotiques optimales des fonctions de Green des opérateurs elliptiques
d'ordre deux.
(Existence and optimal asymptotics for the Green's function of second order elliptic operators).
Personal notes in French (not submitted). Download here.
C. Construction and asymptotics for the Green's function with Neumann boundary condition. Personal notes (not submitted). Download here..
D. Struwe's compactness for free functionals involving the bi-harmonic operator. Personal notes (not submitted). Download here..
E. Extremals for Hardy-Sobolev type inequalities: the influence of the curvature. . Analytic aspects of problems in Riemannian geometry: elliptic PDEs, solitons and computer imaging, 1-15, Sémin. Congr., 22, Soc. Math. France, Paris, 2011. Download here..
F. On the equivalence of the Kazdan-Warner and the Pohozaev identities, with Olivier Druet. Personal notes (not submitted). Download here..

Talks and conferences:

12/2000: Series of talks at the University of Rome III (Italy).
02/2001: PDE seminar, University of Cergy-Pontoise (France).
03/2001: Analysis seminar, University of Amiens (France).
01/2002: Geometry seminar, University of Nancy (France).
01/2002: Analysis seminar, University of Tours (France).
02/2002: Mathematics Colloquium, Tata Institute, Bangalore (Inde).
03/2002: Series of talks at the University of Rome III (Italy).
10/2002: Analysis seminar, ETH Zurich (Switzerland).
01/2003: Colloquium, University of Fribourg (Switzerland).
02/2003: PDEs and Geometry seminar, Notre Dame University (USA).
02/2003: Geometric Analysis seminar, Princeton University (USA).
03/2003: Geometry and Analysis seminar, University of Nice (France).
04/2003: Complex Geometry seminar, University of Marseille I (France).
06/2003: Department seminar, University of La Rochelle (France).
08/2003: Conference on Partial Differential equations, Oberwolfach (Germany).
09/2003: Conference on Affine Geometry, Bedlewo (Poland).
01/2004: Analysis seminar, University of Amiens (France).
01/2004: Analysis seminar, ETH Zurich (Switzerland).
03/2004: PDEs and applications seminar, ENS Lyon (France).
11/2004: Differential Geometry and PDE seminar, University of British Columbia, Vancouver (Canada).
03/2005: Conference "Recent Advances in Calculus of Variations and PDE's", Pisa (Italy).
05/2005: Conference "Analytic Aspects of Problems in Riemannian Geometry", Brest (France).
09/2005: Conference "Interactions between Complex Geometry and Real Analysis", Hanover (Germany).
11/2005: Complex Geometry seminar, University of Marseille I (France).
02/2006: Analysis seminar, University of Reims (France).
02/2006: Differential Geometry and PDE seminar, University of British Columbia, Vancouver (Canada).
03/2006: Series of graduate courses at the University of Wisconsin, Madison (USA).
03/2006: Geometric Analysis Seminar, University of Wisconsin, Madison (USA).
04/2006: Analysis Seminar, ETH Zurich (Switzerland).
05/2006: Differential Equations Seminar, University of Rome II (Italy).
05/2006: Seminar, University of Rome III (Italy).
06/2006: Analysis Seminar, University of Warwick (England).
06/2006: AIMS Conference, Poitiers (France).
12/2006: Algebra and Geometry Seminar, University of Brest (France).
01/2007: Differential Geometry and Analysis Semianr, University of Magdeburg (Germany).
01/2007: Analysis seminar, University of Amiens (France).
02/2007: Lecture series in PDE, Chinese University of Hong-Kong (Hong-Kong)
02/2007: Colloquium, Chinese University of Hong-Kong (Hong-Kong)
08/2007: Conference "Loss of compactness in nonlinear PDE: Recent trends", Banff (Canada).
11/2007: Colloquium, Australian National University, Canberra (Australia).
01/2008: MIP seminar, University of Toulouse III (France).
02/2008: Analysis seminar, SISSA, Trieste (Italie).
06/2008: Second Canada-France Mathematical Congress 2008, Montréal (Canada).
06/2008: Conference "Conformal Geometry: invariant theory and the variational method", Roscoff (France).
10/2008: Complex geometry seminar, University of Marseille I (France).
11-12/2008: Series of lectures at the Technic University of Berlin (Germany).
01/2009: "Journées Nancéiennes de Géométrie", University of Nancy I (France).
02/2009: Geometric Analysis seminar, Albert-Einstein-Institute, Potsdam, (Germany).
04/2009: Analysis seminar, ETH Zurich (Switzerland).
07/2009: Conference "Asymptotic analysis in the calculus of variations and PDEs", University of British Columbia, Vancouver (Canada).
09/2009: Conference "Workshop in Nonlinear Elliptic PDEs" for Jean-Pierre Gossez's 65th birthday, Free University of Bruxelles (Belgium).
10/2009: Conference " Problèmes non linéaires avec perte de compacité: perspectives et applications", Luminy (France).
10/2009: Geometry and Analysis seminar, University of Nice (France).
10/2009: Interregional Colloquium, University of Saabrucken (Germany).
11/2009: Analysis seminar, Chinese University of Hong-Kong (Hong-Kong).
12/2009 : Analysis, Geometry and Algebra seminar, University of Metz (France).
04/2010: Series of talks, Tata Institute, Bangalore (Inde).
06/2010: Geometry and Analysis seminar, University of Nice (France).
07/2010: France-Asia Summer school "Singularities in pdes", IHES (France).
11/2010: Series of talks, University of Sydney (Australia).
11/2010: Analysis and PDE seminar, Australian National University, Canberra (Australia).
05/2011: Analysis Seminar, Universitaet zu Koeln (Germany).
05/2011: Conference "Higher Order equations in Geometry and Physics", SISSA, Trieste (Italy).
06/2011: Conference "Recent Advances on Elliptic Issues", Université de Besancon (France).
01/2012: Conference "Cocompact imbeddings and profile decomposition", TIFR Bangalore (India).
05/2012: Conference "Workshop on Nonlinear Partial Differential Equations to celebrate the sixtieth birthday of Patrizia Pucci", Universita degli Studi di Perugia (Italy).
06/2012: Conference "Higher order problems in geometric analysis", University of Bath (England).
06/2012: Algebra and Analysis seminar, Université de Brest (France).
11/2012: Analysis seminar, Chinese University of Hong-Kong.
11/2012: Conference "Geometric PDEs", Paris (France).
11/2012: Conference "Singular limit problems in nonlinear PDEs", CIRM, Marseille (France).
04/2013: PDE seminar, Pontificia Universidad Catolica de Chile, Santiago.
07/2013: Conference "Nonlinear PDEs, Functional Analysis and Applications: in celebration of Nassif Ghoussoub's 60th birthday", Vancouver (Canada).
10/2013: PDE seminar, University of British Columbia, Vancouver (Canada).
12/2013: Conference "Geometric Variational Problems", Banff (Canada).
03/2014: Differential Geometry/PDE seminar, University of Washington, Seattle (USA).
05/2014: Conference "Geometric Aspects of Semilinear Ellitpci and Parabolic Equations: recent Advances and Future Perspectives", Banff (Canada).
06/2014: Conference "Rencontre Nicoise d'Analyse Géométrique en l'honneur de Philippe Delanoe", Nice (France).
06/2014: Conference "PDEs in Geometry and Physics", University of Notre-Dame (USA).

Invitations in foreign universities:

12/2000: Universita di Roma III (Italy).
02/2002: Tata Institute, Bangalore (India).
03/2002: Universita di Roma III (Italy).
02/2003: Notre Dame University (USA).
02/2003: Princeton University (USA).
01/2004: ETH Zurich (Switzerland).
11/2004: University of British Columbia, Vancouver (Canada).
07/2005: University of British Columbia, Vancouver (Canada).
02/2006: University of British Columbia, Vancouver (Canada).
03/2006: University of Wisconsin at Madison (USA).
04/2006: ETH Zurich (Switzerland).
05/2006: Universita de Roma II (Italy).
01/2007: Universitaet Magdeburg (Germany).
02/2007: Chinese University of Hong-Kong (Hong-Kong).
05/2007: Universita di Perugia (Italy).
08/2007: University of British Columbia, Vancouver (Canada).
11/2007: Australian National University, Canberra (Australia).
02/2008: Chinese University of Hong-Kong (Hong-Kong).
06/2008: McGill University, Montréal (Canada).
11/2008: Universita de Roma II (Italy).
02/2009: Technische Universitaet, Berlin (Germany).
02/2009: Universitaet Magdeburg (Germany).
04/2009: ETH Zurich (Switzerland).
07/2009: University of British Columbia, Vancouver (Canada).
11/2009: Chinese University of Hong-Kong (Hong-Kong).
04/2010: Tata Institute, Bangalore (India).
04/2009: Chinese University of Hong-Kong (Hong-Kong).
11/2009: University of Sydney (Australia).
08/2011: Universitaet Magdeburg (Germany).
10/2011: Chinese University of Hong-Kong (Hong-Kong).
08/2012: McGill University, Montréal (Canada).
11/2012: Chinese University of Hong-Kong (Hong-Kong).
04/2013: Pontificia Universidad Catolica de Chile, Santiago.

Main publications:

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. 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, to appear. Download here.
34. 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.
35. Sign-changing solutions to elliptic second order equations: glueing a peak to a degenerate critical manifold.
with Jerome Vetois.
Preprint. Download here.