Paul A. Schweitzer, S.J.

Full Professor
Department of Mathematics
PUC-Rio (2022)

Biographical Information

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., Boston College, Northwestern Univ., Harvard 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 countries. I have been a Brazilian citizen since 2004 and an emeritus professor since 2010.

Research Interests


  • Foliation Theory
    • 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 leaves
  • Other Areas of Differential Topology and Geometry and Algebraic Topology
  • Three-dimensional manifolds and knots, asymptotic linking
  • Interaction of Christian faith with contemporary science and mathematics
  • Mathematics,Reality, and God Paul A. Schweitzer, S.J.


Former Doctoral Students


  • Carlos Frederico B. Palmeira - 1976
  • Maria de Socorro de O. Pereira - 1982
  • Suely Druck - 1984
  • Sebastião Firmo - 1984
  • Plácido Francisco de Assis Andrade - 1985 (codirected by Sue Goodman)
  • Ricardo Sá Earp - 1986
  •  Alberto Sarmiento Vera - 1994 (codirected by Sebastião Firmo)
  • Leonardo Navarro de Carvalho - 2002 (codirected by Ulrich Oertel)
  • Luis Fernando Crocco Afonso - 2003 (codirected by Nicolai Goussevsky)
  • José Luis Lizarbe Chira - 2005 PhD Thesis
  • Fábio Silva de Souza
  • Inês da Silva


Former Masters Students

  • Iaci Malta – 1976
  • Leonardo Navarro de Carvalho – 1966
  • Adriana Chaves – 1999
  • Vladimir Caetano de Olivera Contreras – 2001
  • Sérgio de Moura Almaraz – 2003
  • Fábio Silva de Souza – 2007
  • Raquel Ribeiro Barroso Portela – 2007
  • José Lisboa Gondin Junior


Current Collaborators

  • Fernando Alcalde, Univ. de Santiago de Compostela, Spain
  • Gaël Meigniez, Univ. de Bretagne Sud, Vannes, France
  • Gilbert Hector, Univ. Claude Bernard, Lyon , France
  • José Luis Lizarbe Chira, UFF, Volta Redonda, RJ, Brazil
  • Pawel Walczak, Univ. de Lodz, Poland

Selected Papers

  • 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.
  • 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), 268-282.
  • 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 Investigaciónn del Instituto Politécnico Nacional of Mexico, Univ. of Notre Dame, Boston College, and others.


Recent Lectures and Participation in Meetings


            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 of 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).




Pontifícia Universidade Católica do Rio de Janeiro Departamento de Matemática


Rua Marquês de São Vicente, 225, Gávea

Rio de Janeiro, RJ 22.453-900, Brazil

Tel: 55 + 21 + 3527 - 1736

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