

Paul A. Schweitzer, S.J.
Full Professor
Department
of Mathematics
PUCRio
(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 PUCRio 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 19701971 and 19811982 and have been a shorttime 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 nonexistence of compact leaves and Reeb components in codimension one foliations
 Foliations whose leaves are 3dimensional 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
 Threedimensional 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 quasiisometric to leaves in codimension one (Preprint number MAT 04/2008 of the Dept. of Mathematics, PUCRio, 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 volumepreserving 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), 2135, with P. Walczak
 A note on actions of the cylinder S^1 x R, Topology and Its Appls. 123 (2002),533535, with J. L. Arraut
 Surfaces not quasiisometric to leaves of foliations of compact 3manifolds, 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), 223238.
 Codimension one foliations without compact leaves, Comm. Math. Helv. 70 (1995), 171209.
 On foliations, concordance spaces, and the Smale conjecture, Amer. Math. Soc., Contemp. Math. Vol.161 (1994), 235258, with D. Randall.
 Existence of codimension one foliations with minimal leaves, Ann. Global Anal. Geom. 9 (1991), 6771.
 Stability of compact leaves with trivial linear holonomy, Topology 27 (1988), 3756.
 Théorème de Thurston établi au moyen de l’analyse non standard, Differential Topology, Foliations and GelfandFuks Cohomology (Proceedings, PUCRio de Janeiro, 1976), Springer Lect. Notes in Math. 652 (1978), 138.
 Pontryagin polynomial residues of isolated foliation singularities, Differential Topology, Foliations and GelfandFuks Cohomology (Proceedings, PUCRio de Janeiro, 1976), Springer Lect. Notes in Math. 652 (1978), 95103, with A.P. Whitman.
 Axioms for characteristic classes of manifolds, Proc. Symp. Pure Math. 26, Part I (1975), 349356, with J. Blanton.
 Compact leaves of foliations, Proc. Intern. Cong. of Mathematicians (invited talk, Vancouver, 1974), vol. 1(19750, 543546.
 Counterexamples to the Seifert Conjecture and opening closed leaves of foliations, Annals of Math. 100 (1974), 386400.
 Joint cobordism of immersions, The Steenrod Algebra and Its Applications, Springer Lect. Notes in Math. 168 (1971), 268282.
 Secondary cohomology operations induced by the diagonal mapping, Topology 3 (1965), 337355
Recent Participation in
Organization of Meetings
 Organizer of the UFFPUC 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, PUCRio, August 2004.
 Organizer and Member of the Scientific Committee, Foliations and Geometry 2001, PUCRio, August 2001.
 Participant and coorganizer 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), BuressurYvette, France (Annual Meeting of the Clavius Group, IHES, July 2003), Kyoto (Geometry and FoliationsKyoto 2003, Ryukoku Univ., Sept. 2003), Tokyo (BGamma 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 ScienceA 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).
Address
Pontifícia
Universidade Católica do Rio de Janeiro
Departamento de Matemática
Rua Marquês de São Vicente, 225, Gávea
Rio de Janeiro, RJ 22.453900, Brazil
Tel:
55 + 21 + 3527  1736
Fax: 55 + 21 + 3537  1282
email: paul@mat.pucrio.br, paul37sj@gmail.com