Fouad EL ZEIN

Institut de Mathématiques de Jussieu-Paris Rive Gauche
Equipe Géométrie et Dynamique
Université Paris 7
France

New Publications:

1) Hodge theory, pdf file
Co-editors: Eduardo Cattani, Fouad El Zein, Philip A. Griffiths, Le Dung Trang, Princeton Series. 2013, 533 pp. Proceedings of ICTP summer school on Hodge theory and related topics 2010.

2) Filtration perverse et théorie de Hodge, pdf file
Comptes rendus - Mathématique 352 (2014) pp. 1045-1049.

3) Du Théorème de Décomposition à la pureté locale, pdf file
Comptes rendus - Mathématique 352 (2014) pp. 1051-1055.

4) De la Pureté locale à la décomposition, pdf file
Comptes rendus - Mathématique 353 (2015) pp. 75-80.

Research domains

Geometry, Topology and Analysis.

Thesis: Complexe dualisant, Director: Jean Louis Verdier.

Fields of Specialization Topology of Algebraic Varieties, Hodge Theory.

I am a geometer whose main interests include the study of the topology of complex algebraic varieties

(mainly projective varieties i.e defined by the set of common zeros of a finite number of homogeneous complex polynomials).

The interaction between topology and geometry is my main subject of study.

Cohomology and Hodge theories are the domains that I use.

Topics of current interest to me are duality theory and Deligne'92s mixed Hodge structures on the cohomology of varieties.

Perverse sheaves are the objects I want to understand and manipulate in my recent work, in order to reach

a better understanding of the decomposition theorem and its applications.

Publications

Books co-edited

1- Proceedings of an ICTP school at Samarkand university 2009

2 - Arrangements and Local Systems. Progress in Math. Vol. 283 (2009). Birkhauser Verlag Basel/Switzerland.

3 -Théorie de Hodge 1987 , Astérisque France, Proceedings of a CIRM conference.

4 -Structure de Hodge mixte. 1991 Hermann, Paris.

Recent Articles

1- A topological construction of the weight filtration.pdf file
Authors: El Zein Fouad; Le D.T.; Migliorini Luca , Manuscripta mathematica. 133 (2010) n 1-2, 173 - 182.

2- Local Systems and constructible sheaves. pdf file
Authors: Fouad El Zein and Jawad Snoussi. Progress in Math. Vol. 283 (2009), pp 111-153, Birkhauser Verlag Basel Switzerland.

3-Topology of Algebraic morphisms.pdf file.
Singularities I. Algebraic and Analytic Aspects.International Conference in Honor of Le Dung Trang. Contemporary Mathematics Vol. 474 (2008), pp 25-84. Amer.Math.Soc. USA.

4-Invariants d'une désingularisation et singularités des morphismes.pdf file
Authors:B.Audoubert, F.Elzein and Le D.T. Compositio Math. 140 (2004) pp. 993-1010.

5-Topology of algebraic varieties. Authors: Fouad Elzein and Andras Némethi.pdf file
Ann.Scuola Norm.Pisa Cl.Sci.(5) vol.I (2002), pp. 869-903, Italy.

See more publications below.

International conferences and schools

06/2010 Hodge theory (ICTP school, Trieste, Italy).

10/2009 Foliation theory, algebraic geometry and Constructible sheaves (ICTP school, Samarkand, Uzbekistan).

08/2007 Algebraic geometry. Tripoli, Libya.

06/2007 Constructible sheaves.Cimpa school, Turkey.

06/2004 Les Travaux de Thom et la théorie des Singularités (Nantes).

07/2004 Théorie algébrique et Arithmétique des courbes (Cimpa school, CAMS, Beyrouth).

10/1997 Singularités des applications polynomiales et stratifications de Thom Whitney

01/1992 Théor'emes de Lefschetz (CIRM).

06/1987 Théorie de Hodge (CIRM).

06/1983 Syst'emes différentiels et Singularités (CIRM).

Short term visits

08/1970 Nordic Summer School in Mathematics, Oslo;
06/1976 Aarhus university, Denmark
01/1978 Math. Institut- Oberwolfach;
05/1979 Institut Mittag-Leffler Stockholm;
09/1980 M.I.T Cambridge, USA;
03/1981 Purdue university, USA;
06/1981 A.M.S - Summer School on Singularities - Arcata;
08/1982 Math.Institut Oberwolfach;
10/1982 International Conference on Maths in the Gulf Area;
04/1983 Warwick Symposium on Algebraic Geometry;
08/1985 Math. Institut - Oberwolfach;
12/1987 Max-Planck Institut - Bonn;
04/1989 Massachussets university;
08/1991 Trieste I.C.T.P. Italy;
06/1992 Munster university, Germany
12/1992 Humbold university in Berlin (colloquium);
04/1998 Bologna university, Italy
09/1998 MSRI at Berkeley USA;
08/1999 ICTP, Trieste, Italy;
2004- 2009 CAMS, AUB, Beirut, Lebanon
08/2006 ICTP, Trieste, Italy;
01/2007 Le's fest. Cuernavaca, Mexico;
04/2008 Hodge theory BIRS, Banff, Canada;
03/2010 AUS, Sharja, UAE;
07/2010 ICTP, Trieste, Italy.
06/2011 Teheran univ., Iran.

More Publications

C.R.A.S: Comptes rendus de l'Académie des Sciences.
1969: Résidus en Géométrie Algébrique,C.R.A.S. Paris t.272, 1971, S'erie A, p.878-881.
1970: Résidus en Géométrie Algébrique. Compositio Mathematicae, Groningen, Holland, t.23, 1971, pdf file.
p.379-405 and in Algebraic Geometry - Oslo 1970. F.Oort. Wolters Noordhoff.
1972: Classe fondamentale d'un cycle, C.R.A.S. Paris, t.276, 1973, S'erie A, p.1615-1618.
1973: La classe fondamentale d'un cycle,Compositio Mathematicae, Groningen, Holland, t.29, 1974, p.9-33. pdf file.
1974: Comparaison des résidus de Grothendieck et de Herrera,C.R.A.S. Paris, t.278, 1974, Série A, p.863-866.
1975: Complexe Dualisant et Applications,Thesis at Paris VII, 1976.
1976: Complexe Dualisant et Applications 'a la classe fondamentale d'un cycle. Bull. Soc. Math. France. Mémoire n.58, 1978.pdf file.
1977: La Classe fondamentale relative d'un cycle. Appendix with the collaboration of B. Angéniol.pdf file.
1979: Mixed Hodge structures. C.R.A.S. Paris, t.292, 1981, série I, p.409-412.
1980: Mixed Hodge Structures, Transactions of the Amer. Math. Soc. vol.275. January 1983.
1981:Mixed Hodge Structures. Proceedings of Symp. in Pure Maths, vol.40. Part I, A.M.S.,1983.
1981: Extendability of normal functions associated to Algebraic Cycles with the collaboration of S. Zucker. Annals of Math. studies n.106. Princeton. Editor : P. Griffiths.
1982: Complexe de Hodge mixte filtré,C.R.A.S. Paris, t.295, 1982, série I, p.669-672.
1982: Dégénérescence diagonale I, C.R.A.S. Paris, t.296, 1983, série I, p.51-55.
1982: Dégénérescence diagonale II, C.R.A.S. Paris, t.296, 1983, série I, p.199-202.
1982: Suites spectrales de structures de Hodge mixtes. Astérisques n.130 : Syst'emes différentiels et singularités (Ed. Galligo et al.), 1985.
1982:Mixed Hodge Structures. Proceedings of the first International Conference on Mathematics in the Gulf Area, 1982.
1986 Théorie de Hodge des cycles évanescents. Ann. Scient. Ecole Normale Supérieure t.19, 1986 p.107-184.pdf file
1988. Riemann-Roch par désingularisation.With the collaboration of B. Angéniol. Bull. Soc. Math. France.pdf file
1988. Théorie de Hodge `a coefficients - Etude locale.C.R.A.S. t.307, Série I, p.593, 1988.
1995. Geometric invariants on cohomology: mixed Hodge structures. In Singularity theory, I.C.T.P. World Scientific, Eds. Le D.T.... 1995.