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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 Téléphone: +33 02 51 12 59 13 Télécopie : +33 02 51 12 59 12
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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,
Annales Henri Poincaré, Annales Henri Poincaré, Volume 25, pages 3805-3830, (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), submitted
pdf file.
[34] (with Thierry Daudé, Bernard Helffer and Niky Kamran),
Global counterexamples to uniqueness for a Calderon problem with C^k conductivities,
ArXiv:2406.14063 (2024), submitted,
pdf file.
[35] (with Bernard Helffer), Trace formulas for the magnetic Dirichlet to Neunmann map - Explicit expansions,
ArXiv:2407.08671, to appear in Asymptotic Analysis (2025),
pdf file.
[36] (with Bernard Helffer), On the magnetic Dirichlet to Neumann operator on the disk - strong diamagnetism and strong magnetic field limit -,
ArXiv:2411.15522 (2024), submitted
pdf file.
[37] (with Bernard Helffer and Ayman Kachmar), Lower and Upper bounds for the magnetic lowest Dirichlet-to-Neumann eigenvalue for general domains,
in preparation, (2024),
pdf file.
[38] (with Thierry Daudé, Fabricio Macià, Cristobal Merono),
Factorization for the Calderon problem : the conductivity case,
in preparation, (2024),
pdf file.
[39] (with Vincent Bruneau and Nicolas Frantz), The spectral shift function for non-self adjoint operators,
in preparation, (2024),
pdf file.
[40] (with Damien Gobin and Benoît Grébert), Uniqueness results for a radially symmetric potential from two spectral sequences,
in preparation, (2024),
pdf file.
[41] (with Thierry Daudé and Niky Kamran), The Calderon problem for Painlevé manifolds,
in preparation, (2024),
pdf file.
PhD's studients :
Habilitation
à diriger les recherches :
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 à Nantes Université.
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.
[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.