univ. de Nantes
           François NICOLEAU
          
Maître de conférences, hdr.

          
Responsable parcours Master 2-PSE (Préparation à l'agrégation de mathématiques) avec Sylvain Gervais.

           e-mail prenom.nom[at]univ-nantes[dot]fr
             T
éléphone:  +33 02 51 12 59 13
            
Télécopie :  +33 02 51 12 59 12

          Laboratoire de Mathématiques Jean Leray UMR 6629
          2 Rue de la Houssinière BP 92208
          F-44322 Nantes Cedex 03




 

Research interests :

 

 


Publications :

 

[1] (with Didier Robert), Théorie de la diffusion pour des perturbations à longue et courte portée du champ magnétique,
Annales de la Faculté de Toulouse, Vol. XII, (2), (1991), ps file.


[2] Approximation semi-classique du propagateur d'un système électromagnétique et phénomène de Aharonov-Bohm,
Helv. Phys. Acta, Vol. 65, (1992), ps file.


[3] Matrice de diffusion pour l'opérateur de Schrödinger avec champ magnétique,
Journées Equations aux Dérivées Partielles, Ecole Polytechnique, (1993), ps file, pdf file.


[4] Matrice de diffusion pour l'opérateur de Schrödinger en présence d'un champ magnétique. Phénomène de Aharonov-Bohm,
Annales Institut Henri Poincaré, Vol. 61, (3), (1994), ps file, pdf file.
Erratum, Annales Institut Henri Poincaré Vol. 4, (2003) ps file, pdf file.


[5]  A stationary approach to inverse scattering for Schrödinger operators with first order perturbation,
Communications in PDE, Vol. 22, (3&4), (1997), ps file, pdf file.


[6] An inverse scattering problem with the Aharonov-Bohm effect,
Journal of Mathematical Physics, Issue 8, pp. 5223-5237, (2000), ps file, pdf file.


[7] Inverse scattering for Stark Hamiltonians with short-range potentials,
Asymptotic Analysis, 35 (3-4), pp. 349-359, (2003), ps file, pdf file,


[8]  A constructive procedure to recover asymptotics of short-range or long-range potentials,
Journal of Differential Equations 205, p. 354-364, (2004), ps file, pdf file.


[9] An inverse scattering problem for short-range systems in a time-periodic electric field,
Mathematical Research Letters, Vol. 12, Issue 16, pp. 885-896, (2005),  ps file, pdf file.
 

[10] Inverse scattering for a Schrödinger operator with a repulsive potential,
Acta Mathematica Sinica, Springer, Vol. 22, Number 5, (2006),  ps file, pdf file.


[11]  An inverse scattering problem for the Schrödinger equation in a semiclassical process,
Journal de Mathématiques Pures et Appliquées, vol. 86, pp. 463-470, (2006),  pdf file.


[12] (with Thierry Daudé),  Recovering the mass and the charge of a Reissner-Nordström black hole by an inverse scattering experiment,
Inverse Problems, Vol. 24, n°2, (2008),  pdf file , Erratum.


[13] (with Thierry Daudé), Inverse scattering in de Sitter-Reissner-Nordström black hole spacetimes,
Reviews in Mathematical Physics,  Vol 22, Issue 4, pp 431-484, (2010), pdf file .


[14] (with Thierry Daudé), Inverse scattering at fixed energy in de Sitter-Reissner-Nordström black hole,  
Annales Henri Poincaré, Vol. 12, pp. 1-47, (2011), pdf file.

 

[15] (with Xiaoyao Jia and Xue Ping Wang), A new Levinson's theorem for potentials with critical decay, 
Annales Henri Poincaré, Vol. 13, Issue 1, pp. 41-84, (2012),
pdf file.

 

[16] (with Thierry Daudé ), Direct and inverse scattering at fixed energy for massless charged Dirac fields by Kerr-Newman-de Sitter black holes, 
Memoirs of the AMS, Volume 247, Number 1170, 119 pages, (2017)
pdf file.

 

[17] (with Thierry Daudé and Damien Gobin), Local inverse scattering results at fixed energy in spherically symmetric asymptotically hyperbolic manifolds, 
Inverse Problems and Imaging, Volume 10, Number 3, pages 659-688, (2016).
pdf file.

 

[18] (with Thierry Daudé and Niky Kamran), Inverse scattering at fixed energy on asymptotically hyperbolic Liouville surfaces, 
Inverse Problems, Volume 31, Number 12, 39 pages, (2015).
pdf file.

 

[19] (with Thierry Daudé), Local inverse scattering at a fixed energy for radial Schrödinger operators and localization of the Regge poles, 
Annales Henri Poincaré 17, 55 pages 2849-2904, (2016).
pdf file.

 

[20] (with Thierry Daudé and Niky Kamran), Non-uniqueness results in the anisotropic Calderon problem with data measured on disjoints sets, 
Annales de l'Institut Fourier, Vol. 69, n°1, pp. 119-170, (2019).
pdf file.

 

[21] (with Daniel Parra and Serge Richard ), Does Levinson's theorem count complex eigenvalues ?, 
Journal of Mathematical Physics, 58, 102101, (2017).
pdf file.

 

[22] (with Thierry Daudé and Niky Kamran), On the hidden mechanism behind non-uniqueness for the anisotropic Calderon problem with data on disjoint sets, 
Annales Henri Poincaré, Volume 20 , Issue 3, pp. 859-887, (2019),
pdf file.

 

[23] (with Thierry Daudé and Niky Kamran), A survey of non-uniqueness results for the anisotropic Calderon problem with disjoint data, 
Harvard CMSA Series in Mathematics, Volume 2: Nonlinear Analysis in Geometry and Applied Mathematics, ed. T. Collins and S.-T. Yau, 21 pages, (2018),
pdf file.

 

[24] (with Thierry Daudé and Niky Kamran), The anisotropic Calderon problem for singular metric of warped product type : the borderline between uniqueness and invisibility, 
Journal of Spectral Theory, Volume 10, Issue 2, pp. 703-746, (2020),
pdf file.

 

[25] (with Jérémy Faupin), Scattering matrices for dissipative quantum systems, 
Journal of Functional Analysis, Volume 277, Issue 9, pp. 3062-3097, (2019),
pdf file.

 

[26] (with Thierry Daudé and Niky Kamran), Stability in the inverse Steklov problem on warped product Riemannian manifolds, 
The Journal of Geometrical Analysis, 31 (2), 1821-1854, (2021)
pdf file.

 

[27] (with Thierry Daudé and Niky Kamran), On non-uniqueness for the anisotropic Calderon problem with partial data, 
Forum of Mathematics, Sigma, Volume 8, e7, (2020),
pdf file.

 

[28] (with Thierry Daudé and Niky Kamran), Separability and symmetry operators for Painlevé metrics and their conformal deformations, 
SIGMA 15 , 069, (Symmetry, Integrability and Geometry : Methods and Applications), 42 pages, (2019),
pdf file.

 

[29] (with Thierry Daudé and Niky Kamran), The anisotropic Calderon problem on 3-dimensional conformally Stäckel manifolds, 
Journal of Spectral Theory, Volume 11, Issue 4, pp. 1669-1726, (2021),
pdf file.

 

[30] (with Rémi Deterre, Qiao Lin, Nadane Allanic, Pierre Mousseau), The Flow of Power-Law Fluids in Concentric annuli: a full analytical approximated solution, 
Journal of Non-Newtonian Fluid Mechanics, 285, 104392, (2020),
file (non-disclosure agreement).

 

[31] (with Thierry Daudé and Bernard Helffer), Exponential localization of Steklov eigenfunctions on warped product manifolds : the flea on the elephant phenomenon, 
Annales Mathématiques du Québec, https://doi.org/10.1007/s40316-021-00185-3, (2021),
pdf file.

 

[32] (with Thierry Daudé and Niky Kamran), Hölder Stability in the Inverse Steklov Problem for Radial Schrödinger operators and Quantified Resonances, 
to appear in Annales Henri Poincaré, (24 pages), (2024),
pdf file.

 

[33] (with Thierry Daudé, Fabricio Macià, Cristobal Merono), Stable factorization on the Calderon problem via the Born approximation, 
ArXiv:2402.06321, (2024),
pdf file.

 

[34] (with Bernard Helffer), Trace formulas for the magnetic Dirichlet to Neunmann map, 
in preparation, (2024).
pdf file.

 

[35] (with Thierry Daudé and Niky Kamran), The Calderon problem for Painlevé manifolds, 
in preparation, (2024).
pdf file.

 

 

PhD's studients :


1 - Damien GOBIN (2013-2016) : Etude de diffusion inverse à énergie fixée pour des variétés asymptotiquement hyperboliques.

Thesis co-directed with Thierry DAUDE (Université de Cergy-Pontoise). Thesis defended june, 26th, 2016.

Current position (2016-2018) : Post-doc McGill University. From September 2019, PRAG Polytech Tours.


2 - Germain GENDRON (2017- 2020) : Unicité et stabilité pour le problème inverse de Steklov.

Thesis co-directed with Thierry DAUDE (Université de Cergy-Pontoise).
Current position (from September 2020) : Professeur en classes préparatoires aux grandes écoles, Angers.

 

 

Habilitation à diriger les recherches :


[H1] Une étude de diffusion inverse pour un opérateur de Schrödinger avec champ électromagnétique,
Université de Nantes, 17 décembre 2004, (rapport de recherche) ps file, pdf file.


[H2] Une étude de diffusion inverse pour un opérateur de Schrödinger avec champ électromagnétique,
Université de Nantes, 17 décembre 2004, (transparents) ps file, pdf file.