Docteur ès Sciences Mathématiques (PhD), University of Geneva, Switzerland, 1976.

Diplôme de Mathématicien (MS), University of Geneva, Switzerland, 1972

Licence ès Sciences Mathématiques (B.S), University of Geneva, Switzerland, 1971.
 
 

-1992-present : Professor of Mathematics  and  Director of Graduate Studies( 2000- 2003),

The Pennsylvania State University,

University Park, PA 16802

-1984-1992 : Associate Professor of Mathematics,

The Pennsylvania State University,

University Park, PA 16802

-1982-1984 : Assistant Professor of Mathematics,

Boston University,

Boston MA

-1978-1982 : Benjamin Pierce Assistant Professor of Mathematics,

Harvard University,

Cambridge, MA

-1977-1978: Research Fellow , Member of the The Institute for Advanced Study ,

Princeton, N.J. 08540

-1975-1977 Swiss National Science Foundation Research Fellow,

University of Geneva,

Switzerland
 

Visiting appointments

18. University of Provence, Marseille, Professeur invité (1 month ) May 30, 99

17. University of Benin, IMSP, Porto Novo, Professeur invité (10 months Oct 98 - July 99)

16.University of Benin, IMSP. Porto Novo, Professeur invité (1 month) June 1997

15.University of Benin,IMSP, Porto-Novo,Professeur invite (1 month),July 11- Aug.11,1996

14.University of Provence, Marseille, Professeur invite ( 1 month), June 10- July 10,1996

13.University of Montpellier, Professeur invité ( 1 month) June 1995

12.University of Provence, Marseille, Professeur invite (1/2 month) July 1994

11.University of Strasbourg, Professur invité, (2 months),May-July 1994

10.Howard University, Visiting Professor, (10 months) Aug.92-May 93

9.University of Provence, Marseille, Professeur invite (1 month) June 92

8.University of Montpellier, Professeur invité (1 month) May 92

7.University of Maryland ( 4 weeks) Feb./March 92

6.University of Paris XI (Orsay), Professeur invite ( 6 months) Feb.-Aug.91

5.Swiss Institute of Technology (ETH-Zurich)(5 monthsNov.90-Feb.91

4.Institut Fourier, University of Grenoble (3 months: May-July 84) ,Professeur invite

3.National University of Rwanda,Butare (6 months) Feb.-July 80

2.University of Warwick, UK ( 1 month),1976

1.University of Louvain, Belgium, Chargé de cours invite,(3 months),1976
 

Other Professional Experience

a. Master's and PhD thesis supervised

1.Christophe Poteet, M.Ed, 1987 (Linear algebra and Geometry in High School).

2.Andrew McInerney, M.S. 1988 (The Hopf invariant).

3.Philippe Rukimbira, PhD 1991 (Some properties of almost contact flows).

4.Peter A.Chaiyasema , PhD 1993 (Radar and Sonar ambiguity

functions and group theory).

5.Carlos Torre, PhD 1993 (On a theorem of Kirillov ).

6.Andrew McInerney, PhD 1994 (On the group of contact diffeomorphisms).

7.Gilbert Honnouvo, DEA (Diplome d'Etudes Approfondies), University of Benin, 1999

8. Basil Nanayakkara, MS, 2000 (The geometry of contact connected sum)

9.Hassan Ait Haddou, DEA, University of Benin, 2002

10. Alain Musesa, DEA, University of Benin, 2002

11. Hee Jung Kim, PhD 2002 (Almost complex structures arising in contact geometry)
 

b. Referal of Mathematical papers submitted to:

Topology ( 2 in 1999)

Commentarii Mathematice Helveticae

Annales de l'Institut Fourier, Grenoble

Journal of Differential Geometry

Communications on Mathematical Physics

Indian Journal of Mathematics

Journal of Indian Institute of Science

Journal of the American Mathematical Society

Results in Mathematics

Collectanae Mathematica (University of Barcelona)

Annales Polonici Mathematici

The Houston Journal of Mathematics

Publicationes Mathematicae Debrecen (Hungary)
 

c. Consulting

1981, 1982, 1983 ( one month each year) : UNESCO consultant

Started, and run a graduate program in Mathematics

The National University of Rwanda
 

d. Service to the Mathematics Department and the University Community

Member of the Marker Lectures Series Committee (1988)

Chair of the Marker Lecture Series Committee (1989)

Member of the A. Dixon Johnson Memorial Lecture Series (1988)

Adviser of the African Student Association (1993-1995)

Member of the Personnel Committee ( 1993- 97 )

Member of the CES Screening Committee (1996- present)

Member of the Library Committee (1997-2000)

Member of the Search Committee for the Dean of the College of Sciences (1997- 98)

Member of the Promotion and Tenure Committee (1999-2000)

Member of the Undergraduate Studies Committee (1999-2002)

July 1, 2000 - June 30 , 2003 : Associate Chair of the Mathematics Department for Graduate Studies ( Director of Graduate Studies)

Member of the Personnel Committee (2000-2003)
 

f. Organisation of Conferences

Conference on ; SPMquot; Infinite dimensional Lie Groups and Geometry;SPMquot; Howard Ubiversity, August 17- 21, 2000, co-organizer

International Workshop on Contemporary Problems in Mathematical Physics, Scientific Advisory Committee member. Porto-Novo, Benin, November 1999

Geometry Week at Howard University, Washington DC, May 1993, Co-organizer

Symplectic Geometry Workshop at Penn State U., February 1996, co-organizer

Penn State Conference on low dimensional Topology, May 1996, chief organizer

Penn State workshop on Quantization, April 1997, co-organizer

Penn State workshop on symplectic geometry and microlocal analysis, April 1998, co-organizer
 

g. Professional Awards and Honors

Prize Vacheron - Constantin , Univ.Geneva, 1976

Suiss National Science Foundation Post doctoral Fellowship, 1976-77

NSF Grant # DMS 9403196 , 1994-1996

Fulbright Scholar's award, 1998-99

Mathematical Association of America (MAA) Visiting Lecturer ,1992-96

Member Amer .Math.Soc. CD-ROM Task force

Editor of Afrika Matematika, the Journal of the African Mathematical Union.

Marquis Who's Who in the World.
 

h. Recent invited addresses and Lecture Series

39. Infinite dimensional Lie groups conference, Howard University August, 19, 2000; On a geometric integration of the Lee homomorphism;

38. Bronks Community College, N.Y. May 10, 2000;  Symmetry vs skew-symmetry;

37. Bronks Community College, N.Y. May 11, 2000 ; Projective geometry as an umbrella for all plane geometries;

36. Howard University; Locally conformal symplectic structures;  Nov. 19, 1999

35. International Workshop on Contemporary problems of Mathematical Physics, Cotonou (Benin) . Some geometrical structures underlying Mechanics, Nov. 3,1999

34. Virginia Tech. The geometry of transformation groups or the Erlanger Program Revisited., Oct. 8, 1999

33. Université Nationale du Benin, IMSP. Series of lectures on Gauge Theory, Topological Quantum field theory, Floer Homology, Chaotic Dynamics, Symplectic and Poisson Geometry . From Dec 1998 to July 1999.

32. Brown University, Providence, R.I. April 17, 1998.; The geometry surrounding the Arnold-Liouville theorem;

31. Bronks Community College, Bronks, N.Y. April 1, 1998.; The geometry of transformation groups , or the Erlanger Program revisited;

30. Emory University, Atlanta, GA, March 26,1998 ; The geometry surrounding the Arnold-Liouville theorem;

29. International Colloquium on Infinite dimensional Lie groups and algebras , Marseille, Sept 15-19, 1997 ; On Poisson diffeomorphisms;

28. Stefan Banach International Mathematical Center, Warsaw, Poland Workshop on Lie group and Lie algebras in infinite dimension.8-18 Sept. 1997 ; The gemetry of the classical diffeomorphism groups;

27. University of Benin. IMSP ; Un nouvel invariant conforme des variétés riemanniennes;  June 1997

26. University of Benin, IMSP ; Series of lectures on ; The Dirac operators; June 3- July 3, 1997.

25. University of Benin; Leafwise constructions in Poisson Geometry; Dec. 1996

24. Howard University, Complete integrability in Contact Geometry , Nov. 1996

23. University of Benin, IMSP :  Sur le programme d'Erlanger, July 17,1996

22 .University of Benin, IMSP   Complete integrabilite en geometrie de contact, July 12, 9996

21. University of Benin, IMSP, Series of lectures on ;SPMquot;introduction to Seiberg-Witten equations and a series of lectures on the introduction to symplectic geometry, July-Agust 1996

20. University of Aix-en-Provence : La complete integrabilite en geometrie de contact ,I,II , june 1996

19. Stanford University; Complete integrability in Contact Geometry, Feb.8 1996

18. Stanford University : Hypercontact Geometry and Gauge Theory, Feb.5,1996

17. Howard University, : Hypercontact Geometry and Gauge Theory, Nov.17, 1995

16. SUNY Geneseo (MAA Lectures Series), : Euclidean and Non-Euclidean Geometry, Nov. 1 , 1995

15.Fourth African Mathematical Union Pan-African Congress of Mathematics, Ifrane, Morocco, Plennary invited address: Invariants of contact structures,symplectic structures and transversally oriented foliations, Sept. 1995

14.Workshop on Geometry, Topology and Dynamics,CRM, Montreal ,Canada.  Instantons and hypercontact structures.June 1995.

13.University of Marseille, Les structures d'hypercontact et les instantons, June 1995

12.University of Montpellier, Instantons et les structures d'hypercontact, June 1995

11.University of Cambridge,UK , Instantons and Hypercontact structures, May 1995

10. Howard University : Instantons and Hypercontact structures, Nov 94

9.Forstburg State University (MAA Lecture Series ):A Panorama of Euclidean and Non-Euclidean Geometries , Oct.94

8.University of Marseille : Quelques nouveaux invariants en Geometrie de Contact, July 94

7.Institut Henri Poincare (Paris) : Some contact geometry invariants. June 94

6.University of Strasbourg: Invariants de Geometrie de Contact, May 94

5.University of Strasbourg:Le Programme d'Erlanger . June 94

4.University of Florida Gainsville: New Contact Geometry invariants,April 94

3.Howard University : Series of Lectures on: The topology of Torus Actions on Symplectic Manifolds, Jan.-May 93

2.International Center for Pure and Applied Mathematics (CIMPA) ,Lectures Series at the Summer School on Symplectic Geometry,pseudo-holomorphic curves and applications. Nice (France) : Introduction to symplectic geometry. July,92

1.University of Geneva (Switzerland) : Formes normales de diffeomorphismes de contact au voisinage de points fixes hyperboliques. June 92
 
 

Research areas

Symplectic, Contact Geometry and Topology

Research Summary

My longtime interest has been in the study of the algebra, the geometry, the topology and the dynamics of symplectic, contact, volume preserving, and measure preseving diffeomorphisms of smooth manifolds. My work has been qualified by Sternberg in his review of Abraham-Marsden  Foundation of Mechanics as one of the best achievement of the last decade on the subject.

Over the last ten years, I have made contributions to the century old Klein's Program by proving that the symplectic, unimodular, and contact categories are determined by their automorphism groups.

The main results obtained in the above areas have been gathered in my book The structure of classical diffeomorphism groups, published by Kluwer Academic Publishers (1997). This momograph is a unique treatise presenting the state-of-the art in the domain.

Since 1989, I have been interested in the Weinstein conjecture on the existence of periodic orbits of the contact flow on a compact contact manifold. I have developped new contact-riemanian geometry machinery which allowed me to prove the existence of periodic orbits in some particular ( important ) cases.

I am coming back to the subject armed with new machineries including Gromov's pseudoholomorphic curves, and gauge theory.

I have done research on normal forms of contact diffeomorphisms near hyperbolic fixed points and extended Sternberg geometric linearization theorems using cohomology equations. My approach works when Sternberg's does not, i.e. when we have non-resonnance conditions. The work was carried out in collaboration with R. de La Llave and E.C.Wayne.

In collaboration with Pierre Molino, I have worked out a theory of  Complete Integrability  in Contact Geometry. This is an integrated and uniform formulation of the generalization to contact geometry of the classical Arnold-Liouville theorem, Duistermaat theory of Lagrangian fibrations, the famous Atiyah-Guillen-Sternberg convexity theorem for the moment map , and Delzant realization theorem.

I have worked on the connection between Gauge Theory and Contact Geometry. I proved that the components of any self or anti self dual connection ( along the Pauli matrices) of any SU(2)-connection on the SU(2) tautological bundle over S4, form a hypercontact structure on S7.

Right now, I am working on the Floer homotopy type, a concept invented by Cohen, Segal and Jones. I work on the so-called Cohen-Segal-Jones conjecture which claims that a function defining the Floer homology can be used todefine some homotopical theoretical object ( an inverse system of spectrum) from which the Floer groups can be recovered. This leads me to study the Gromov-Witten invariants and Quantum cohomology.

This loops back to my traditional interests ; diffeomorphism groups. On one hand, recent work of Seidel, and Lalonde-Polterovich-Mac-Duff show a link between quantum cohomology and hamiltonnian loops. I am trying to find a geometric meaning to the extensions of hamiltonnian diffeomorphisms arising from Seilel and Mac-Duff's works.

On the other hands, this leads to an interest in the geometry of gauge fields, especially the study of the structure of symplectic diffeomorphisms of the moduli space of flat connections on S0(3) bundles over surfaces. I am trying to understand how much contribute the mapping class group of the surface to the group of symplectic diffeomorphism of the moduli space.

Finally, I have been working on conformal geometry: I found a conformal invariant characterising the standard sphere and have studied the group of automorphisms of locally conformal symplectic structure. I also keep working on the theory of complete integrability in Contact Geometry. Using my work with Molino, I try to construct a combinatorial approach to Contact geometry, like Guillemin, using my generalization to Contact Geometry of Delzant realisation theorem.
 
 

1. Sur le groupe des diffeomorphismes symplectiques.

C.R.Acad.Sc.Paris t.278(1974) serie A,1343-1344.

2. Sur le groupe des diffeomorphismes qui preservent une forme de contact reguliere.

C.R.Acad.Sc.Paris t.281(1975) serie A 707-709.

3. Sur la structure du groupe de diffeomorphismes.

Publ.Dept.Math.Lyon,13(1976)no3 ,57-61.

4. Sur le groupe des automorphismes d'un Tn-fibre principal.

C.R.Acad.Sc.Paris t.284(1977) serie A 619-622.

5. On the structure of equivariant diffeomorphisms.

Topology,vol 16 no 3 (1977)279-283.

6. Sur le groupe des diffeomorphismes symplectiques.

Springer Lecture Note in Math.Vol 484,pp 50-56.

7. Formes-volume sur les varietes a bord.

Enseig.Math. 20 (1974)127-131

8. On the automorphism groups of a toral action.

Hadronic Journal,2(1979)296-320

9. Sur la structure du groupe des diffeomorphismes qui

preservent une forme symplectique.

Comment.Math.Helv.53(1978)174-227.

10. The group of diffeomorphisms preserving a regular contact form.

In Topology and Algebra, Enseig.Math. (1979) 47-53.

11.(with J.Pulido) On the group of contact diffeomorphisms of ...

Bol.Soc.Mat.Mexicana,vol 23 no2(1978)43-47 .

12. On fixed points of symplectic maps.

Inventiones Math.56(1980) 215-229.

13. On the group of diffeomorphisms preserving an exact symplectic form.

In Differential Topology. V.Villani ed.CIME(1976),Varenna,Italy,pp 7-9.

14. (with R.W.Urwin) Sur la cohomologie du groupe des diffeomorphismes .

C.R.Acad.Sc.Paris t.294(1982) 625-627 .

15.(with R.W.Urwin) On the cohomology of the diffeomorphism group.

Atti della Acad.Sc.di Torino,Suppl.Vol 117(1983) 7-34.

16. The mass-flow homomorphisms and extension of certain groups of homeomorphisms.

Atti della Acad.Sc.di Torino,Suppl.Vol 117(1983) 35-38

17. Sur la geometrie de l'homomorphisme flux.

C.R.Acad.Sc.Paris t.296(1983) 725-727.

18. The Calabi Invariant and the Gauge Group.

In Geometrie Symplectique et Mecanique. J.P.Dufour,Ed.

Travaux en Cours,Hermann,Paris (1985) 3-11.

19. On isomorphic classical diffeomorphism groups I.

Proceed.Amer.Math.Soc. vol98 no1 (1986) 113-118.

20. On isomorphic classical diffeomorphism groups II.

J.Differ.Geom. 28(1988) 93-114.

21. (with De la Llave R. and Wayne E.) Cohomology equations and commutators of germs of contact diffeomorphisms.

Trans.Amer.Math.Soc. vol 312 no 2 (1989) 755-778.

22. A note on Weinstein conjecture.

Proceed.Amer.Math.Soc. vol 109 no3 (1990) 855-858.

23. (with Molino P.) Geometrie des formes de contact completement integrables de type torique.

In Sém.G.Darboux Geom.Top.Diff.Univ.Montpellier 1991-92 ,1-25

24. On characteristics of hypersurfaces in symplectic manifolds.

Symposia in Pure Math.Amer.Math.Soc. Vol 54 Part 2 (1993) 9-17.

25. (with Gole C.) A Remark on a conjecture of Arnold:linking of spheres and fixed points.

In Hamiltonian Systems and Celestrial Mechanics,Lacomba E.A. and Llibre J.Ed.World Scientific(1993) 23-30.

26. An introduction to symplectic geometry.

In Holomorphic curves in symplectic geometry. Audin M.

and Lafontaine J. Ed. Progress in Math.Birkhauser,(1994) 17-40.

27. Quelques invariants de la geometrie de contact.

C.R.Acad.Sc.Paris,t.318 serie I (1994) 671-674.

28. (with Rukimbira P.) Weak stability of almost contact foliations.

Journal of Geometry, Vol.50 (1994) 16-27.

29. The cohomology class of the action functional.

Expo.Math.12(1994) 371-379.

30. (with McInerney A.) On isomorphic classical diffeomorphism groups III.

Annals of Global Analysis and Geometry 13 (1995) pp 117-127

31. (with Rukimbira P.) On characteristics of circle invariant presymplectic forms.

Proceed.Amer.Math.Soc.Vol 123 no 12(1995) pp 3901-3906

32. Instantons and hypercontact structures.

J.of Geometry and Physics, 19(1996) 267-276

33. (with Donato P) Some remarks on the integration of the Poisson algebra.

J.Geometry and Physics , 19(1996) 368-378.

34. Invariants of contact structures and transversally oriented foliations.

Annals of Global Analysis and Geometry 14 (1996) 427-441

35. Instantons and hypercontact structures ,Part II

J.Geometry and Physics 21 (1997) 136-148

36. (with C.Torre) A symplectic structure on coadjoint orbits of diffeomorphism groups.

Cienc.Tecn 17(1993) no 2 ,1-14(1995)

37. (with C.Torre) A characterisation of some coadjoint orbits of diffeomorphism groups.

Cienc.Tecn 17(1993) no 2, 15-38(1995)

38. (with de la Llave R. and Wayne E.) Cohomology equations near hyperbolic points and geometric versions of Sternberg's linearization theorems.

The Journal of Geometric Analysis 6 no 4 (1997) , 613-649

39. K-contact flows,

Encyclopedia of Mathematics, Supplement Volume 1 (1997) , 325-326

Kluwer Academic Publishers.

40.Isomorphism between classical diffeomorphism groups .

In  Geometry, Topology, and Dynamics, Francois Lalonde, Ed.

CRM Proceed.and Lecture Notes, Vol. 15(1998) 1-15 .

41. The Geometry surrounding the Arnold-Liouville theorem

Advances in Geometry, Progress in Math no 172. Birkhauser(1999) pp 53-69.

42. On Poisson Diffeomorphisms.

Analysis on infinite dimensional Lie groups and algebras, H. Heyer and J.Marion, Ed, World Scientific Publishers (1999) pp 1-8.

43.(with J.P.Ezin) A conformal invariant characterizing the standard sphere

Topics in Low-Dimensional Topology, A. Banyaga, H.Movahedi-Lankarani, R.Wells Ed., World Scientific Publishers (1999) pp 93-97

44. Some geometrical structures underlying mechanics

Contemporary Problems in Mathematical Physics.

J.Govaerts, M.N.Hounkonnou, W.A.Lester,Jr. Ed., World Scientific (2000) pp 109- 117

45. On essential conformal groups and a conformal invariant

Journal of Geometry 68 (2000) pp 10-15

46.(with P.Molino ) Complete integrability in Contact Geometry.

Preprint 1996

47.(With P.Donato) A Leafwise construction in Poisson Geometry.

Preprint (1997)

48. (with P.Donato) On equivalence of Poisson structures.

Preprint

49. (with D.Hurtbise) On quantum cohomology and Floer homotopy type

Preprint

50. (with Hee-Jung Kim) Some characteristic classes of contact structures.

preprint.

51. A geometric integration of the extended Lee homomorphism.

J. of Geometry and Physics, In press.

52. Quelques invariants des structures localement conformement symplectiques.

C..R.Acad. Sc.i. Paris, t 332 Seriies I (2001) 29-32

53. Remarks on locally conformal symplectic symplectic structures,

Preprint, 2001

534 (with Chaiyasena P. Sibul .Flower M.) Wavelet transforms and signal ambiguity functions.

In Proc. 24th annual Asilomar Conf. Signal and Computers (1990) Pacific Grove,CA.

55. (with Chaiyasena P. Sibul L.) The relationship between narrow band and wide band ambiguity function,volume preserving properties ,a group contraction approach,

In Proceed Conf.on Information Science and Systems.John Hopkins University.MD (1991).

56. (with Chaiyasena P and Sibul L.) Radar and sonar ambiguity functions and group theory.

Applied Research Lab.Technical Report.Penn State University.
 

Books

57. The structure of Classical Diffeomorphism Groups.

Mathematics and Its Applications,(208 pages), Vol 400

Kluwer Academic Publishers (1997)

58 .Topics in Low-Dimensional Topology,

A. Banyaga, H.Movahedi-Lankarani, R.Wells Editors,

World Scientific Publishers (1999)

59. Lectures on Differential Topology.

Preprint.

60.. (with Rukimbira P) An invitation to Contact Geometry.

Preprint.

61.  (with P. Molino) Complete integrability in Contact Geometry. ( in preparation )