Paul A. Schweitzer, S.J.
Born in a suburb of New
York on July 21, 1937, I have been a professor at
the Pontifical Catholic University of Rio de Janeiro since August, 1971. I have
the following degrees: B.S. Mathematics (College of the Holy Cross, Worcester,
MA, USA, 1958), Ph.D. Mathematics (Princeton
Univ., Princeton, NJ, USA, 1962),
Phil.L. in philosophy (Weston College, Weston, MA, USA, 1966), and B.
Div. (Weston School of Theology, Cambridge, MA, USA, 1970). I am also a
Catholic priest (ordained May
30, 1970) and a member of the Society of Jesus (the Jesuit order, since Sept. 1, 1963).
I have been a Full Professor in the Department of Mathematics at PUC-Rio
since 1980. I have also taught at the Univ. of Notre Dame, Fairfield
Univ., and the Univ.
of Strasbourg. I was a member of the School
of Mathematics of the Institute for
Advanced Study in 1970-1971 and 1981-1982 and have been a short-time visitor at
about 20 other universities and research institutes in the United
States, England, France, Canada, Mexico, Spain, Germany, Austria, Poland, and Japan, among other
- Existence or non-existence of compact
leaves and Reeb components in codimension one foliations
- Foliations whose leaves are
3-dimensional and have Thurston model geometries
- Geometry of the leaves of foliations
- Manifolds which cannot be realized as
- Other Areas of Differential Topology
and Geometry and Algebraic Topology
- Three-dimensional manifolds and knots,
Fábio Silva de Souza (Ph.D.)
article (2009) “A variedade de
Ghys não é folha de folheações de Lie”
Inês da Silva (Ph.D)
José Lisboa Gondin Junior (M)
Former Doctoral Students
Frederico B. Palmeira – 1976
de Socorro de O. Pereira – 1982
Druck – 1984
Firmo – 1984
Francisco de Assis Andrade – 1985 (codirected by Sue Goodman)
Sá Earp – 1986
Sarmiento Vera – 1994 (codirected by Sebastião Firmo)
Navarro de Carvalho – 2002 (codirected by Ulrich Oertel)
Fernando Crocco Afonso – 2003 (codirected by Nicolai Goussevsky)
José Luis Lizarbe Chira
– 2005 PhD Thesis
Former Masters Students
- Iaci Malta – 1976
- Leonardo Navarro de
Carvalho – 1966
- Adriana Chaves –
- Vladimir Caetano de
Olivera Contreras – 2001
- Sérgio de Moura
Almaraz – 2003
- Fábio Silva de
Souza – 2007
- Raquel Ribeiro
Barroso Portela – 2007
- Fernando Alcalde,
Univ. de Santiago de Compostela, Spain
- Gaël Meigniez,
Univ. de Bretagne Sud, Vannes, France
- Gilbert Hector, Univ. Claude Bernard, Lyon,
- José Luis Lizarbe
Chira, UFF, Volta Redonda, RJ, Brazil
- Pawel Walczak,
Univ. de Lodz, Poland
- Riemannian manifolds not quasi-isometric to
leaves in codimension one (Preprint number MAT 04/2008 of the Dept.
of Mathematics, PUC-Rio, 2008) – DVI file
- The structure of Reeb components in codimension
one foliations, with F. Alcalde and G. Hector (Preprint being revised)
- (G,X)-structures in manifolds and foliations
(Preprint in preparation)
- Asymptotic linking of volume-preserving actions
of R^k, with J.L. Lizarbe Chira (Preprint in preparation, based on the
thesis of Lizarbe Chira)
- Prescribing mean curvature vectors for
foliations, Illinois J. Math. 48 (2004), 21-35, with P. Walczak
- A note on actions of the cylinder S^1 x R,
Topology and Its Appls. 123 (2002),533-535, with J. L. Arraut
- Surfaces not quasi-isometric to leaves of
foliations of compact 3-manifolds, Analysis and Geometry in Foliated
Manifolds (Proceedings of the Coloquio de Xeometria, Santiago de
Compostela, 1994), X. Masa, E. Macias, and J.A. Alvarez eds., World
Scientific (1995), 223-238.
- Codimension one foliations without compact
leaves, Comm. Math.
Helv. 70 (1995), 171-209.
- On foliations, concordance spaces, and the Smale
conjecture, Amer. Math.
Soc., Contemp. Math. Vol.161 (1994), 235-258, with D. Randall.
- Existence of codimension one foliations with
minimal leaves, Ann. Global Anal. Geom. 9 (1991), 67-71.
- Stability of compact leaves with trivial linear
holonomy, Topology 27 (1988), 37-56.
- Un théorème de Thurston établi au moyen de
l’analyse non standard, Differential Topology, Foliations and Gelfand-Fuks
Cohomology (Proceedings, PUC-Rio de Janeiro, 1976), Springer Lect. Notes
in Math. 652 (1978), 138.
- Pontryagin polynomial residues of isolated
foliation singularities, Differential Topology, Foliations and
Gelfand-Fuks Cohomology (Proceedings, PUC-Rio de Janeiro, 1976), Springer
Lect. Notes in Math. 652 (1978), 95-103, with A.P. Whitman.
- Axioms for characteristic classes of manifolds,
Proc. Symp. Pure Math. 26, Part I (1975), 349-356, with J. Blanton.
- Compact leaves of foliations, Proc. Intern. Cong.
of Mathematicians (invited talk, Vancouver,
1974), vol. 1(19750, 543-546.
- Counterexamples to the Seifert Conjecture and
opening closed leaves of foliations, Annals of Math. 100 (1974), 386-400.
- Joint cobordism of immersions, The Steenrod
Algebra and Its Applications, Springer Lect. Notes in Math. 168 (1971),
- Secondary cohomology operations induced by the
diagonal mapping, Topology 3 (1965), 337-355.
Recent Participation in
Organization of Meetings
- Organizer of the UFF-PUC Topology Seminar, First
semester of 2009.
- Member of the Scientific Committee, VIII
International Colloquium on Differential Geometry, Santiago de Compostela,
Spain, July, 2008.
- Member of the Scientific Committee of topology
and dynamics meetings in the Federal Fluminense University (UFF), in Feb.
2006, Feb. 2007, Feb. 2008, Feb. 2009, Feb. 2010.
- Organizer of the Clavius Symposium on Faith,
Mathematics and Science, Boston College (Boston, MA, USA), July 2007.
- Organizer and Member of the Scientific Committee,
Jornada de Topologia, PUC-Rio, August 2004.
- Organizer and Member of the Scientific Committee,
Foliations and Geometry 2001, PUC-Rio, August 2001.
- Participant and co-organizer of the Annual
Meetings of the Clavius Group of Mathematicians every year in July, since
1967, in various institutions: Institute for Advanced Study, IHES, Centro
de Investigación del Instituto Politécnico Nacional of Mexico, Univ. of Notre Dame, Boston College, and others.
Recent Lectures and Participation
I have given about 95 invited lectures in universities and institutes in 20
countries and all continents (except Australia),
and participated in about 85 international mathematics meetings, since 1962.
Invited lectures in the last few years: in Viena (Workshop on Geometry
and Foliations, Schrödinger Inst., Aug. 2002), Niteroi (Jornada de Topologia, UFF, Jan. 2003), Bures-sur-Yvette, France
(Annual Meeting of the Clavius Group, IHES, July 2003), Kyoto (Geometry and
Foliations—Kyoto 2003, Ryukoku Univ., Sept. 2003), Tokyo (B-Gamma School, Chuo
Univ., 2 lectures, Sept. and Oct. 2003), Lodz, Poland (Foliations—Lodz 2005,
Opening Lecture, Univ. of Lodz, June 2005), Notre Dame, IN, USA (Annual Meeting
of the Clavius Group, Univ. of Notre Dame, July 2005), Havana, Cuba (Simposium
Religion and Science—A Possible Dialogue?, May 2006), Worcester, MA, USA
(Annual Meeting of the Clavius Group, College of the Holy Cross, July 2006),
Campinas, SP, Brazil (Jornada em memória de James Eells, Unicamp, May 2007),
Boston, MA, USA (Annual Meeting of the Clavius Group, Boston College, July
2007), Worcester, MA, EUA (College of the Holy Cross, 2 lectures, March 2009).
Universidade Católica do Rio de Janeiro
Departamento de Matemática
Rua Marquês de São Vicente, 225, Gávea
Rio de Janeiro, RJ 22.453-900, Brazil
55 + 21 + 3527 - 1736
55 + 21 + 3537 - 1282
e-mail: email@example.com, firstname.lastname@example.org