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Emmanuel Hebey
Professeur des universitésEH2020

Géométrie Riemannienne et analyse géométrique
Analyse non linéaire sur les variétés
Equations aux dérivées partielles
Physique mathématique


Cours ETH
      2012Adresse:
Université de Cergy-Pontoise
Département de Mathématiques
2 avenue Adolphe Chauvin
95302 Cergy-Pontoise cedex
France
Email:

emmanuel(dot)hebey(at)cyu(dot)fr

WebPage: hebey.u-cergy.fr

Curriculum Vitae
Publications

Curriculum Vitae et Liste de Publications.
Fichier téléchargeable:  pdf


Poster A quoi servent les mathématiques

Emmanuel Hebey. Professor of mathematics.
Research interests in Partial Differential Equations and the
Calculus of Variations, Geometric Analysis, Mathematical
Physics and Differential Geometry.
Born april 1964 at Paris, France.
Studies at the University of Paris 6.  PhD in 1990 and «habilitation à
diriger des recherches» in 1991.
Associate professor at the University of Paris 6 from 1990 to 1993.
Full professor at the University of Cergy-Pontoise since 1993.
«Marie Guido Triossi» price of the French Academy of  Sciences, 1995.
Short Courses lectures, Courant Institute, NYU, 1998.
Nachdiplom lectures, ETH Zürich, 2012.
Director of the math department (1994-1997).
Director of the math research lab (1997-2004 and  2015-2019).
Member of the scientific board of the university (2008-2016).
Member of the board of CYU - University of Cergy-Pontoise (2020-2025).
International Mathematics Research Notices (associate editor).
International Journal of Differential Equations (associate editor).
Potential Analysis (associate editor).
Tunisian Journal of Mathematics
(associate editor).
Differential and Integral Equations (associate editor)
PHD Students: Marie Dellinger, Zindine Djadli, Olivier Druet, Antoinette
Jourdain, Benoit Pausader, Bruno Premoselli, Frédéric Robert, Nicolas Saintier,
Pierre-Damien Thizy, Jérôme Vétois.
Most cited mathematicians (PhD year 1990)
Genealogy Project
Ascendant genealogy



Monographies de recherche:  
(Some research monographs)  
[1] Nonlinear analysis on manifolds: Sobolev spaces and inequalities,
CIMS Lecture
Notes, Courant Institute of Mathematical Sciences,
New York University, Volume 5, 1999. Seconde édition publiée BooksIcon
conjointement avec l'American Mathematical Society, 290 pages,
AMS/CIMS Lecture Notes , Volume 5, 2000.
Version traduite en russe, Editions Tamara Rozhkovskaya, 2008.

[2] The AB program in Geometric Analysis. Sharp Sobolev inequalities
and related
problems,
Memoirs of the American Mathematical Society , avec O.Druet,
98 pages,
MEMO/160/761, 2002.
[3] Blow-up theory for elliptic PDEs in Riemannian geometry,
Mathematical Notes
, Princeton University Press, avec O.Druet et
F.Robert, 218 pages, Volume 45, 2004.

[4] Elliptic equations of Yamabe type, avec O.Druet,
International Mathematics 
Research Surveys, IMRS, Issue 1, 1-113, 2005.
[5] Compactness and stability for nonlinear elliptic equations,
Zurich Lectures in Advanced Mathematics, ZLAM, 291 pages, European
Mathematical Society, Volume 20, 2014. 

Textes en libre service:
(Unpublished texts with free access)
[1] Sharp Sobolev-Poincaré inequalities on compact Riemannian manifolds,
NotesSharpSP.pdf , 121 pages, 2002. Contains unpublished results.
[2] Variational methods and elliptic equations in Riemannian geometry,

Notes from lectures given at ICTP, Math Icon
NotesICTP.pdf , 63 pages, 2003. 
[3] Manifolds which are close to space forms and the Bemelmans, Min-Oo
and Ruh smoothing effect of the Ricci flow,

NotesSF.pdf , 5 pages, 2002. Unpublished results.
[4] An introduction to fourth order nonlinear wave equations, avec B.Pausader,
FourthOrderWaves.pdf , 48 pages, 2008. Contains unpublished results.
[5] Super critical energy scale invariant equations in critical spaces, SuperCrit.pdf,
6 pages, 2010.
Rewriting of a known result.
[6] A short (informal) introduction to Bopp-Podolsky-Schrödinger-Proca
and Schrödinger-Poisson-Proca systems in the electro-magneto-static case,
BPSPHebeySurvey.pdf, 20 pages, 2022.


Transparents / Slides from various talks:
[1] Existence, stability and instability for Einstein-scalar field Lichnerowicz
equations, EinLich.pdf, Slides, Contains unpublished results, 46 pages, 2008/2009.
[2] Elliptic stability for stationary Schrödinger equations, Retro Projecteur
Part I, PartII, and PartIII.
Slides from a three parts course given in 2013.
[3] Companion tables for the above slides on elliptic stability, Tables, 2013.
Updated version, March 2021, UpdatedVersion2021.
[4] Elliptic stability for stationary Schrödinger equations,
Part I, Part II, Part III, Part IV, Part V, Part VI.
Slides (extended version) of a course given in 2015.
[5] Klein-Gordon-Maxwell-Proca systems in closed manifolds, KGMPSlides, Slides
from a talk, 37 pages, 2014.
[6] Nonnegative solutions of stationary Kirchhoff systems, KirchhoffSyst, Slides
from a talk, 30 pages, 2015.
[7] Sationary Kirchhoff equations with powers, KPowersSlides, Slides
from a talk, 32 pages, 2017.
[8]
Klein-Gordon-Maxwell-Proca systems in the Riemannian setting, KGMPSlides2,
Slides from a talk, 39 pages, 2018.
[9] Schrödinger-Proca constructions in the closed setting, SPConstructions,
Slides from a talk, 44 pages, 2022.

Quelques articles récents:
(Some recent research papers)
[1] Stationary Kirchhoff equations with powers,
Advances in the Calculus of Variations
, 11, 139-160, 2018.
[2] Klein-Gordon-Maxwell-Proca type systems in the electro-magneto-static
case, avec P.D.Thizy,
Journal of Partial Differential Equations
, 31, 119-158, 2018.
[3]
Klein-Gordon-Maxwell-Proca type systems in the electro-magneto-static case:
the high  dimensional case, avec P.D.Thizy,

Calculus of Variations and Partial Differential Equations,
58, 116 (31 pages), 2019.
[4]
Electro-Magnetic-Static study of the nonlinear Schrödinger equation coupled
with Bopp-Podolsky electrodynamics in the Proca Setting,

Discrete and Continuous Dynamical Systems - Series A, 39, 6683-6712, 2019.
[5] Strong convergence of the Bopp-Podolsky-Schrödinger-Proca system to the
Schrödinger-Poisson-Proca system in the electro-magneto-static case,
Calculus of Variations and Partial Differential Equations, 59, 198 (25 pages), 2020.
[6] Schrödinger-Poisson-Proca systems in EMS regime,
Communications in Contemporary Mathematics
, 24, 2150038, 2021.
[7] Blowing-up solutions to Bopp-Podolsky-Schrödinger-Proca and
Schrödinger-Poisson-Proca systems in the electro-magneto-static case,
Advances in  Differential Equations, 27, 253-332, 2022.
[8] A twist in sharp Sobolev inequalities with lower order remainder terms,
Advances in the Calculus of Variations,
24 pages, à paraître.
[9] Strong convergence in Bopp-Podolsky-Proca type constructions,
Discrete and Continuous Dynamical Systems, Vol. 43, 2371-2380, 2023.
[10] Stability and critical dimension for Kirchhoff systems in closed manifolds,
Advances Nonlinear Studies, Volume in honor of Joel Spruck, 12 pages, à paraître.

Comités éditoriaux:
International Journal of Differential Equations (associate editor),
International Mathematics Research Notices
(associate editor),
Potential Analysis (associate editor),
Tunisian Journal of Mathematics
(associate editor),
Differential and Integral Equations (associate editor).

Quelques conférences:
Modern Trends in PDE's, Geometric Analysis and Mathematical Physics
(Sept. 2011, org. V.Georgescu, E.Hebey et A.Shirikyan, université de Cergy-Pontoise)
Recent trends in geometric and nonlinear analysis
(Août 2012, org. E.Hebey et F.Robert, Banff International Research Station, Canada)
Cocompact Imbeddings, Profile Decompositions, and their Applications to PDE
(Janvier 2012, membre du comité scientifique, Tata Institute of Fundamental Research, Bangalore, Inde)PosterCYDays
Géométrie conforme et géométrie Kählérienne
(Sept. à Dec. 2012, Trimestre de l'Institut Henri-Poincaré, org. M.Gursky, E.Hebey, F.Pacard, J.Viaclovsky)
Three weeks Thematic Program on Nonlinear PDEs in Geometry and Physics
(Summer 2014, University of Notre-Dame, Indiana, org. M.Gursky, E.Hebey)
Asymptotics for Nonlinear Geometric PDEs
(Nov.2014, SNS Pisa, org. E.Hebey, G.Lebeau, F.Merle, F.Planchon, N.Visciglia)
Nonlinear Analysis in Rome
(June 2017, Rome, org. M. Gursky, E.Hebey, A.Malchiodi).
Conférence en l'honneur des 25 ans des laboratoires AGM et LPTM
(June 2017, Cergy-Pontoise, org. E.Hebey, F.Koukiou).
CY Days in Nonlinear Analysis
(March 2022, Cergy-Pontoise, membre du comité d'organisation)
Advances in nonlinear analysis & nonlinear waves
(May 2023, A conference in honor of Frank Merle for his 60th birthday, membre du comité scientifique)


Image
Enseignement:
Calcul Différentiel Avancé: Chapitre 1 , Chapitre 2 , Chapitre 3 , Chapitre 4 ,
Chapitre 5 , Chapitre 6 , Chapitre 7 , Chapitre 8
Algèbre bilinéaire et intégration: La page du cours 2019-2020
Les fondamentaux de l'algèbre linéaire non matricielle: Rappels
Petit précis de calcul tensoriel: Calcul Tensoriel
Les polycopiés:
    Polycopié Probabilités         Polycopié Algèbre Linéaire        Calcul Diff Avancé

De gauche à droite: Une Introduction aux Probabilités, Algèbre Linéaire 3, Calcul Différentiel Avancé.
Cliquer sur les images pour afficher le polycopié.
    Polycopié Algèbre Bilinéaire        Polycopié Intéhration         Cahier exercicies corrigés

De gauche à droite: Algèbre Bilinéaire, Intégration, Cahier d'Exercices Corrigés.
Cliquer sur les images pour afficher le polycopié.

Dernières dates de mise à jour/enrichissement des polycopiés:
Probabilités (25/11/2023), Algèbre linéaire 3 (15/01/2024), Calcul différentiel
avancé (12/2023), Algèbre bilinéaire (24/01/2024), Intégration (17/01/2024),
Cahier d'Exercices corrigés (12/2023).
Comment travailler en mathématiques
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Mise à jour: Janvier 2024