HABIB Georges - Institut Élie Cartan de Lorraine

Fonction : Membre associé

Équipe : Géométrie

Domaines de recherche :

• Differential Geometry: geometry of submanifolds, of Kählerian and Sasaki manifolds, of Riemannian foliations
• Analysis on manifolds: spectral geometry of Dirac-type operators
• Functional Analysis: Müntz spaces

Coordonnées :

IECL – Site de Nancy
Faculté des sciences et Technologies
Campus, Boulevard des Aiguillettes
54506 Vandœuvre-lès-Nancy

Email : ghabib@ul.edu.lb

Partenaires

Coauthors/Co-auteurs:

Curriculum vitæ

Personnal data

Lebanese citizenship
Born October 12, 1980 in Beirut (Lebanon)
Family status: Married

Positions

2022- 2023: Senior Fellow at the Alfried Krupp Wissenschaftskolleg, Greifswald, Germany
2021- Present: Associate member of the geometry group at IECL, University of Lorraine, France
2013- Present: Professor at the Department of Mathematics of the Faculty of Sciences of the Lebanese University
2008-2013: Associate Professor at the Department of Mathematics of the Faculty of Sciences of the Lebanese University
2007-2008: Postdoctoral research position at the Max-Planck Institut für Mathematik, Leipzig, Germany
2005-2007: ATER (teaching and research assistant position) at University Henri Poincaré, Nancy I, France

Education

2020-2021: Habilitation thesis (HDR) in Mathematics at University of Lorraine, France
Title: Cohomologie sur les feuilletages riemanniens et étude spectrale des opérateurs du type laplacien
Academic Host: Benoît Daniel
Jury: Ilka Agricola (Ref.), Vicente Cortés (Pres.), Nadine Grosse, Yuri Kordyukov, Andrei Moroianu, Liviu Ornea (Ref.), Alessandro Savo, Robert Wolak (Ref.)
2003-2006: Ph.D. thesis in Mathematics at University of Henri Poincaré, Nancy I, France
Title: Tenseur d’impulsion-énergie et feuilletages
Advisor: Oussama Hijazi
Jury: Jean-Pierre Bourguignon (Pres.), Aziz ElKacimi Alaoui (Ref.), Andrei Moroianu (Ref.), Kris Galicki, Sebastien Montiel, Harold Rosenberg
2002-2003: D.E.A. (master degree) in Mathematics at the Lebanese University
Title: Basic Dirac operator on spin foliations
Advisor: Oussama Hijazi

Research grants and fellowships

2023-2024: Atiyah UK-Lebanon Fellowship from London Mathematical Society (LMS) and the Center for Advanced Mathematical Sciences (CAMS) for a stay of 3 months at University of Durham, UK.
2023-2024: Grant from the Centre National de la recherche Scientifique (CNRS) of the research program International Emerging Actions (IEA) in partnership with Nicolas Ginoux (Univ. of Lorraine) and Simon Raulot (Univ. of Rouen).
2022-2023: Fellowship from the the Alfried Krupp Wissenschaftskolleg, for a stay of one year in Greifswald, Germany.
2022: Grant from the French Embassy in Beirut of the program SAFAR for a research stay of two weeks at University of Lorraine, France.
2020-2022: Research group Linkage funded by Alexander von Humboldt Foundation in partnership with Sylvie Paycha (Univ. of Potsdam) and Florian Bertrand (Amer. Univ. of Beirut ). Title of the project: At the confluence of Geometry, Analysis and Mathematical Physics.
2020-2021: CEDRE Lebanese-French research program in partnership with Isabelle Chalendar (Univ. Gustave Eiffel) . Title of the project: Théorie spectrale des semi-groupes d’opérateurs de composition pondérés.
2019: Grant from the DAAD (German Academic exchange service) for a research stay for 2 months at University of Greifswald. Host: Ines Kath.
2018: Grant from the Agence Universitaire de la Francophonie (AUF) of the research program Perfectionnement Formation-Recherche for a stay of two weeks at Université de Lorraine, France.
2017-2019: Grant from the Research program Innovation and Development at the Lebanese University in partnership with Fida El Chami (Leb. Univ.) and Ola Makhoul (Leb. Univ.), Spectral Geometry of operators of type Laplacian on hypersurfaces of space forms.
2016-2018: Grant from the Research program Innovation and Development at the Lebanese University in partnership with Ihab Al Alam (Leb. Univ.), Functional spaces and their geometric properties.
2015-2017: Humboldt Research Fellowship for experienced researchers for a stay of 9 months within 3 years at University of Potsdam and University of Greifswald, Germany. Hosts: Sylvie Paycha and Ines Kath
2015-2017: CEDRE Lebanese-French research program in partnership with Ihab Al Alam (Leb. Univ.), Fares Maalouf (Saint Joseph Univ.) and Pascal Lefèvre (Univ. of Artois), Espaces fonctionels.
2014-2016: Grant from the Research program Innovation and Development at the Lebanese University in partnership with Fida El Chami (Leb. Univ.), Analytical aspects of geometric problems: Q-curvature and geometric flows.
2011-2013: Grant for the Research group of Differential Geometry, Doctoral School of Sciences and Technology, Lebanese University

Research stays and talks

July 2024: Research stay (1 week) at Jagiellonian University, Krakow, Poland.
June-August 2024: Research stay (3 months) and conference talk at University of Durham as part of Atiyah UK-Lebanon fellowship.
April 2024: Research stay (3 days) and seminar talk in the framework of IEA HOPF at University of Lorraine, France.
December 2023: Research stay (1 week) and seminar talk at University of Potsdam, Germany.
September 2023: Research stay (1 week) at University of Lorraine, France.
June 2023: Research stay (2 weeks) at Jagiellonian University, Poland.
June 2023: Research stay (1 week) and conference talk in the framework of IEA HOPF, Rouen, France.
June 2023: Seminar talk at University of Greifswald, Germany.
March 2023: Research stay (2 days) at University of Heidelberg, Germany.
March 2023: Seminar talk at University of Mulhouse, France.
February 2023: Research stay (3 days) at University of Gustave Eiffel, France.
February 2023: Research in Pairs (1 week) with Nicolas Ginoux (Univ. of Lorraine) and Simon Raulot (Univ. of Rouen) at CIRM, Luminy, France.
February 2023: Research stay (1 week) and seminar talk at University of Potsdam, Germany.
February 2023: Research stay (1 week) and seminar talk at University of Ioannina, Greece.
January 2023: Seminar talk at University of Marburg, Germany.
January 2023: Seminar talk at University of Hamburg, Germany.
January 2023: Fellow lecture at Alfried Krupp Wissenschaftskolleg, Greifswald, Germany.
December 2022: Seminar Talk at University of Greifswald, Germany.
September 2022: Research stay (1 week) at University of Gustave Eiffel, France.
August 2022: Research stay (2 weeks) at Jagiellonian University, Poland.
August 2022: Research stay (5 weeks) and seminar talk at University of Potsdam, Germany.
July 2022: Research in Pairs (2 weeks) with Nicolas Ginoux (Univ. Lorraine) and Simon Raulot (Univ. Rouen) at MFO, Germany.
June 2022: Research stay (2 weeks) at University of Lorraine, France.
May 2022: Research stay (3 days) and seminar talk at University of Brunel, UK.
May 2022: Research stay (2 weeks) and seminar talk at University of Durham, UK.
September 2021: Research stay (1 week) at University of Gustave Eiffel, France.
September 2021: Research in Pairs (2 weeks) with Ken Richardson (Texas Christian Univ.) at CIRM, Luminy, France.
September 2021: Research stay (1 week) at University of Potsdam, Germany.
August 2021: Research stay (1 month) at Max-Planck Institut für Mathematik, Bonn, Germany.
June 2021: Online talk at the « Ege Geometry day 3″, Ege University, Turkey.
June 2021: Online talk at the conference « Emerging Trends in Pure and Applied Mathematics », University of Bahrein.
April 2021: Research stay (1 month) and seminar talk at University of Potsdam, Germany.
March 2021: Research stay (1 month) at Max-Planck Institut für Mathematik, Bonn, Germany.
February 2021: Seminar talk within the GAMP project (online).
November 2019: Seminar talk at University of Cyprus, Cyprus.
August 2019: Research stay (1 week) at University of Regensburg, Germany.
July 2019: Research stay (3 days) and seminar talk at University of Potsdam, Germany.
July-August 2019: Research stay (2 months) at University of Greifswald, Germany.
June 2019: Talk at the 9th Annual meeting of the “Lebanese Society for Mathematical Sciences”, Lebanese University, Beirut, Lebanon.
April 2019: Research stay (1 week) and talk at the conference ”Riemannian and Kähler geometry”, IMAR, Bucharest, Romania.
March 2019: Talk at the conference “Microlocal and Global Analysis, Interactions with Geometry”, University of Potsdam, Germany.
May 2018: Talk at the 8th Annual meeting of the “Lebanese Society for Mathematical Sciences”, LAU, Byblos, Lebanon.
February 2018: Research stay (2 weeks) at the University of Lorraine, France.
June-September 2017: Research stay (3 months) at the University of Potsdam and Greifswald, Humboldt Research Fellowship, Germany.
March 2017: Research in pairs (1 week) with Ken Richardson (Texas Christian Univ.) at the Centro Internazionale per la Ricerca Matematica, (CIRM), Trento, Italy.
January 2017: Research stay (1 week) at University of Artois, France.
October 2016: Talk at the conference “Géométrie et théorie spectrale”, Lebanese University, Tripoli, Lebanon.
June-September 2016: Research stay (3 months) at University of Potsdam and Greifswald, Humboldt Research Fellowship, Germany.
July 2016: Research stay (1 week) at University of Stuttgart, Germany.
May 2016: Talk at the 6th Annual meeting of the “Lebanese Society for Mathematical Sciences”, Lebanese University, Beirut, Lebanon.
January 2016: Research stay (1 week) and talk at the conference “Journées Nancéiennes de Géométrie”, Nancy, France.
October 2015: Seminar talk at the American University of Beirut, Lebanon.
June-September 2015: Research stay (3 months) at the University of Potsdam and Greifswald, Humboldt Research Fellowship, Germany.
April 2015: Talk at the conference “Conference on Differential Geometry”, Notre Dame University, Beirut, Lebanon.
November 2014: Seminar talk at Saint-Joseph University, Lebanon.
July 2014: Invitation (3 days) to the University of La Rochelle, France.
August 2013: Research stay (3 weeks) at Texas Christian University, U.S.A.
February 2013: Research in Pairs (2 weeks) with Nicolas Ginoux (Univ. of Lorraine) at CIRM, Luminy, France.
October 2012: Research stay and seminar talk at University of Brest, France.
October 2012: Invited Professor (1 month) at University of Lorraine, France.
April 2012: Research stay (3 days) at Max-Planck Institut für Mathematik, Bonn, Germany.
February 2012: Talk at the CIMPA research school “Sub-Riemannian Geometry”, Lebanese University, Beirut, Lebanon.
July-August 2011: Research stay (2 months) at Max Planck Institut für Mathematik, Leipzig, Germany.
August 2011: Research stay (1 week) at University of Regensburg, Germany.
August 2010: Talk at the conference “Differential geometry and its applications”, Brno, Czech Republic.
July-August 2010: Research stay (2 months) at Max-Planck für Mathematik, Leipzig, Germany.
July 2010: Research stay (1 week) at University of Regensburg, Germany.
July-August 2009: Research stay (2 months) at Max-Planck Institut für Mathematik, Leipzig, Germany.
July 2008: Talk at the “VIII International Colloquium on Differential Geometry”, Santiago De Compostela, Spain.
May 2008: Research stay (1 week) at University of Greifswald, Germany.
December 2007: Seminar talk at University of Jussieu, France.
November 2007: Seminar talk at University of Luxembourg, Luxembourg.
May 2007: Seminar talk at University of Tours, France.
March 2006: Research stay (1 week) and seminar talk at Humboldt University of Berlin, Germany.
February 2006: Research stay (1 week) and seminar talk at University of Potsdam, Germany.
March 2005: Research stay (1 week) and seminar talk at University of Neuchâtel, Switzerland.
February 2005: Seminar talk at University of Nantes, France.
January 2005: Seminar talk at University of Valenciennes, France.

Organization of conferences

2023-2024: Organizer with Sylvie Paycha of the online colloquium « Mathematics in Lebanon and beyound ».
October 2023: Organizer with Giuseppe Della Sala and Sylvie Paycha of the conference « At the confluence of Geometry, Analysis and Mathematical Physics », AUB, Beirut, Lebanon.
June 2023: Organizer of « Sasakian manifolds, Riemannian foliations, and related topics », Krakow, Poland.
June 2023: Organizer of « Journée rouennaise d’analyse géométrique », Rouen, France.
2010-2022: Seminar organizer at the Mathematics department of the Lebanese University
July 2022: « Journées Nancéiennes de Géométrie », IECL, France.
June 2022: Member of the scientific committee of the « Ege Geometry day 4″, University of Ege, Turkey.
March 2022: Online workshop « At the confluence of Geometry, Analysis and Mathematical Physics », funded by Alexander von Humboldt foundation.
February 2020: Workshop “At the confluence of Geometry, Analysis and Mathematical Physics”, funded by Alexander von Humboldt foundation, Lebanese University
March 2019: “North-South days on Geometric Analysis”, Faculty of Sciences III and IV, Lebanese University
February 2018:“Humboldt Kolleg conference: At the confluence of Analysis, Geometry and Modern Mathematical Physics”, Doctoral School of Sciences and Technology, Lebanese University
May 2016: “Meeting on Differential Geometry”, American University of Beirut (AUB).
April 2015: “Meeting on Differential Geometry”, Notre Dame University (Lebanon) and CAMS.
October 2014: “Spin Geometry and Analysis on Manifolds”, CIRM, Marseille, France.
May 2014: “Journées de Géométrie différentielle”, Faculty of Sciences II, Lebanese University
March 2013: “Journées de Géométrie différentielle”, Faculty of Sciences II, Lebanese University
December 2011: “Journées de Géométrie différentielle”, Faculty of Sciences II, Lebanese University
December 2010: “Journées de Géométrie différentielle”, Faculty of Sciences II, Lebanese University
January 2010: “LSMS First annual meeting”, Faculty of Sciences II, Lebanese University

Supervision

2023-2026: Supervision of PhD student, Rodolphe Abou Assali, together with Nicolas Ginoux and Samuel Tapie (University of Lorraine, France). Thesis funded by SAFAR’s program from the French embassy in Beirut, IECL and Lebanese University. Title: « Problème de Steklov biharmonique sur les formes différentielles ».
2020-2023: Ph. D. student, Joelle Jreis in partnership with Pascal Lefèvre (Univ. of Artois) and Ihab Al Alam (Leb. Univ.). Title: Opérateurs de type Volterra sur les espaces de fonctions analytiques: idéaux et semi-groupes d’opérateurs.
2009-2013 Ph.D. student, Safaa El Sayed, in partnership with Emmanuel Humbert (Univ. of Tours). Title: Chirurgie et second invariant de Yamabe.
2008-Present: Supervision of several Master degree students and member of the jury for thesis defences.

Service

2022: Reviewer of a research project for the Swiss National Science foundation
July 2014: Reviewer of the Ph.D. thesis of Ghina El Mir at University of La Rochelle, France
2008-Present: Reviewer for Mathematics reviews of the AMS and Zentralblatt MATH
2008-Present: Reviewer for several journals: Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg, Annals of Global Analysis and Geometry, Documenta Mathematica, Journal of Geometry and Physics, Central European Journal of Mathematics, Advances in Applied Clifford Algebras, Journal of Geometric Analysis, Differential Geometry and its Applications, SIGMA

Administrative activities

2019-2023: Cochair of the departmental Master program committee, Lebanese University
2019-2023: Member of the council of the Department of Mathematics, Lebanese University
2013-2017: Member of the council of the Department of Mathematics, Lebanese University

Others

Languages: Arabic (native), French and English (fluent)

Publications

- - Geometric singularities and Hodge theory (with Lashi Bandara)
    Submitted, (2024).
  - Transverse geometric formality (with Ken Richardson and Robert Wolak)
    Submitted, (2024).
  - A Poincaré formula for differential forms and applications (with N. Ginoux and S. Raulot)
    SIGMA 19 (2023), 088.
  - A generalised Ricci-Hessian equation on Riemannian manifolds (with N. Ginoux)
    Submitted.
  - A pseudodifferential analytic perspective on Getzler’s rescaling (with S. Paycha)
    SIGMA 20 (2024), 010.
  - Eigenvalue estimates for the magnetic Hodge Laplacian on differential forms (with M. Egidi, K. Gittins and N. Peyerimhoff)
    J. Spectral Theory, 13 (2023), no. 4, 1297–1343.
  - Biharmonic Steklov operator on differential forms (with N. Ginoux, F. El Chami and O. Makhoul)
    Submitted.
  - Eigenvalue estimates on weighted manifolds (with V. Branding)
    Results in Math. 79 (2024), 187.
  - Skew Killing spinors in four dimensions (with N. Ginoux and I. Kath)
    Ann. Glob. Anal. Geom. 59, 501-535 (2021).
  - An Obata-type characterisation of Calabi metrics on line bundles (with N. Ginoux, M. Pilca and U. Semmelmann)
    North-West. Eur. J. Math. 6, 119-136 (2020).
  - An Obata-type characterisation of doubly-warped product Kähler manifolds (with N. Ginoux, M. Pilca and U. Semmelmann)
    Münster J. Math. 14, 295-321 (2021).
  - New eigenvalue estimates involving Bessel functions (with F. El Chami and N. Ginoux)
    Publ. Mat. 65, 681-726 (2021).
  - New cohomological invariants of foliations (with K. Richardson)
    Asian J. Math.
  - A splitting theorem for Riemannian manifolds of generalized Ricci Hessian type (with N. Ginoux and I. Kath)
    Preprint.
  - The Bochner formula for Riemannian flows (with F. El Chami)
    Results in Math. 77:25, (2022).
  - Eigenvalue bounds of the Robin Laplacian with magnetic field (with A. Kachmar)
    Archiv. der Math. 110, 501-513 (2018).
  - Essential norms of Cesàro operators on Lp and Cesàro spaces (with I. Al Alam, L. Gaillard, P. Lefèvre and F. Maalouf)
    J. Math. Anal. and Appli. 467, 1038-1065 (2018).
  - Homotopy invariance of cohomology and signature of a Riemannian foliation (with K. Richardson)
    Math. Zei. 293, 579-595 (2019).
  - Riemannian flows and adiabatic limits (with K. Richardson)
    Inter. J. Math. 29, 1850011 (2018).
  - Rigidity results for spin^c manifolds with foliated boundary (with F. El Chami, N. Ginoux and R. Nakad)
    Results in Math. 72, 1773-1806 (2017).
  - Essential norms of Volterra and Cesàro operators on Müntz spaces (with I. Al Alam, P. Lefèvre and F. Maalouf)
    Collo. Math. 151, 157-169 (2018).
  - Eigenvalue estimate for the basic Laplacian on manifolds with foliated boundary, part II (with F. El Chami, O. Makhoul and R. Nakad)
    Medit. J. Math. 15:67, (2018).
  - Eigenvalue estimate for the basic Laplacian on manifolds with foliated boundary (with F. El Chami, O. Makhoul and R. Nakad)
    Ricer. di Math. 67, 765-784 (2018).
  - Rigidity results for spin manifolds with foliated boundary (with F. El Chami, N. Ginoux and R. Nakad)
    J. Geom. 107, 533-555 (2016).
  - A new upper bound for the Dirac operator on hypersurfaces (with N. Ginoux and S. Raulot)
    Pacific J. Math. 278, 79-101 (2015).
  - Riemannian foliations with a parallel or harmonic basic form (with F. El Chami and R. Nakad)
    Archivum Math. 51, 71-85 (2015).
  - Some remarks on Calabi-Yau and Hyper-Kähler foliations (with L. Vezzoni)
    Diff. Geom. and Appli. 41, 12-32 (2015).
  - The twisted spin^c Dirac operator on Kähler submanifolds of the complex projective space (with R. Nakad)
    J. Geom. Phys. 77, 43-47 (2014).
  - The energy-momentum tensor on low dimensional spin^c manifolds (with R. Nakad)
    Int. J. Math. 23, 1250090 (2012).
  - Skew Killing spinors (with J. Roth)
    Cent. Eur. J. Math. 10, 844-856 (2012).
  - The spectrum of the twisted Dirac operator on Kähler submanifolds of the complex projective space (with N. Ginoux)
    Manus. Math. 137, 215-231 (2012).
  - A spectral estimate for the Dirac operator on Riemannian flows (with N. Ginoux)
    Cent. Eur. J. Math. 8, 950-965 (2010).
  - Modified differentials and basic cohomology for Riemannian foliations (with K. Richardson)
    J. Geom. Anal. 23, 1314-1342 (2013).
  - Remarques sur les spineurs de Killing transversaux (with N. Ginoux)
    C. R. Acad. Sci. Paris Sér. I Math. 346 no 11-12, 657-659 (2008).
  - Geometric aspects of transversal Killing spinors on Riemannian flows (with N. Ginoux)
    Abh. Math. Sem. Univ. Hamburg 78, 69-90 (2008).
  - A brief note on the spectrum of the basic Dirac operator (with K. Richardson)
    Bull. London Math. Soc. 41, 683-690 (2009).
  - Eigenvalues of the basic Dirac operator on Quaternion-Kähler foliations
    Ann. Glob. Anal. Geom. 30, 289-298 (2006).
  - Eigenvalues of the transversal Dirac operator on Kähler foliations
    J. Geom. Phys. 56, 260-270 (2005).
  - Energy-Momentum tensor on foliations
    J. Geom. Phys. 57, 2234-2248 (2007).

Theses

Cohomologie sur les feuilletages riemanniens et étude spectrale des opérateurs du type laplacien, Habilitation thesis, University of Lorraine, 2021
Tenseur d’impulsion-énergie et feuilletages, PhD thesis, University Henri Poincaré, Nancy I, 2006