Paul A. Schweitzer
Paul Alexander Schweitzer SJ (born July 21, 1937) is an American mathematician specializing in differential topology, geometric topology, and algebraic topology.[1]
Paul A. Schweitzer | |
|---|---|
| Born | Paul Alexander Schweitzer July 21, 1937 Yonkers, New York, U.S. |
| Nationality | American |
| Alma mater | College of the Holy Cross (BS) Princeton University (PhD) Weston College (PhL, BDiv) |
| Scientific career | |
| Fields | Topology |
| Institutions | Pontifical Catholic University of Rio de Janeiro |
| Thesis | Secondary cohomology operations induced by the diagonal mapping (1962) |
| Doctoral advisor | Norman Steenrod |
| Doctoral students | Suely Druck |
Schweitzer has done research on foliations, knot theory, and 3-manifolds. In 1974 he found a counterexample to the Seifert conjecture that every non-vanishing vector field on the 3-sphere has a closed integral curve.[2] In 1995 he demonstrated that Sergei Novikov's compact leaf theorem cannot be generalized to manifolds with dimension greater than 3. Specifically, Schweitzer proved that a smooth, compact, connected manifold with Euler characteristic zero and dimension > 3 has a C1 codimension-one foliation that has no compact leaf.[3]
Education and career
Schweitzer studied at the College of the Holy Cross in Worcester, Massachusetts, with a B.S. in 1958 and then received his Ph.D. in 1962 at Princeton University under Norman Steenrod with thesis Secondary cohomology operations induced by the diagonal mapping.[4][5]
He received a degree in philosophy (Ph.L.) in 1966 from Weston College in Weston, Massachusetts, and a bachelor's degree in 1970 in theology (B. Div.) from the Weston Jesuit School of Theology in Cambridge, Massachusetts and was ordained in 1970 as a Catholic priest. In 1963 he became a member of the Jesuits. He became in 1971 a professor extraordinarius and in 1980 a professor ordinarius at the Pontifical Catholic University of Rio de Janeiro.
Schweitzer has been a visiting professor at the University of Notre Dame, the Fairfield University, Northwestern University, Boston College, Harvard University, and the University of Strasbourg. For the academic years 1970–1971 and 1981–1982 he was at the Institute for Advanced Study.
Since 1978 he has been on the board of the Brazilian Mathematical Society.
He was elected a Fellow of the American Mathematical Society in 2012. He was an Invited Speaker at the ICM in 1974 in Vancouver.[6]
References
- Saldanha, Nicolau C., ed. (2009). Foliations, geometry, and topology : Paul Schweitzer festschrift: conference in honor of the 70th birthday of Paul Schweitzer, S.J., August 6–10, 2007, PUC-Rio, Rio de Janeiro, Brazil. American Mathematical Society. ISBN 9780821846285.
- Schweitzer, P. A. (1974). "Counterexamples to the Seifert conjecture and opening closed leaves of foliations". Annals of Mathematics. 100 (2): 386–400. doi:10.2307/1971077. JSTOR 1971077.
- Schweitzer, Paul A. (1995). "Codimension one foliations without compact leaves". Commentarii Mathematici Helvetici. 70 (1): 171–209. doi:10.1007/BF02566004. S2CID 120853552.
- Paul Alexander Schweitzer at the Mathematics Genealogy Project
- Schweitzer, Paul A. (1965). "Secondary cohomology operations induced by the diagonal mapping". Topology. 3 (4): 337–355. doi:10.1016/0040-9383(65)90002-9. MR 0182969.
- Schweitzer, P. A. (1975). "Compact leaves of foliations". Proc. Int. Congr. Math., Vancouver, 1974. Vol. 1. pp. 543–546.