Frank Wilson Warner III (born March 2 1938 in Pittsfield, Massachusetts)[1] is an American mathematician, specializing in differential geometry.

Education and career

Warner graduated in 1959 with a bachelor's degree from Pennsylvania State University and in 1963 with a Ph.D. in mathematics from the Massachusetts Institute of Technology. His thesis, written under the supervision of Isadore M. Singer, is entitled Conjugate Locus of a Riemannian Manifold.[2] At the University of California, Berkeley, Warner was an assistant professor from 1965 to 1968. At the University of Pennsylvania, he became an associate professor in 1968 and a full professor in 1973. He was from 1995 to 1997 the deputy dean of the University of Pennsylvania School of Arts and Sciences. In 2000, he retired as professor emeritus.[3]

In the 1970s he and Jerry Kazdan, as collaborators, made important contributions to the theory of Riemannian manifolds with prescribed scalar curvature. They proved in 1975 that any smooth function can be realized as a scalar curvature if it becomes negative somewhere on the manifold. Their further research dealt with conjugate points on Riemannian manifolds.

Warner was a Guggenheim Fellow for the academic year 1976–1977.[4] He was elected in 1994 a Fellow of the American Association for the Advancement of Science.[5]

Selected publications

Articles

Books

  • Foundations of differentiable manifolds and Lie groups (1st ed.). Scott, Foresman and Co. 1971.
  • Foundations of Differentiable Manifolds and Lie Groups. Graduate Texts in Mathematics. Springer-Verlag. 1983.
    • Warner, Frank W. (1983). "Chapter 1. Manifolds". Foundations of Differentiable Manifolds and Lie Groups. Graduate Texts in Mathematics. Vol. 94. pp. 1–52. doi:10.1007/978-1-4757-1799-0_1. ISBN 978-1-4419-2820-7.
    • Warner, Frank W. (1983). "Chapter 2. Tensors and Differential Forms". Foundations of Differentiable Manifolds and Lie Groups. Graduate Texts in Mathematics. Vol. 94. pp. 53–80. doi:10.1007/978-1-4757-1799-0_2. ISBN 978-1-4419-2820-7.
    • Warner, Frank W. (1983). "Chapter 3. Lie Groups". Foundations of Differentiable Manifolds and Lie Groups. Graduate Texts in Mathematics. Vol. 94. pp. 81–136. doi:10.1007/978-1-4757-1799-0_3. ISBN 978-1-4419-2820-7.
    • Warner, Frank W. (1983). "Chapter 4. Integration on Manifolds". Foundations of Differentiable Manifolds and Lie Groups. Graduate Texts in Mathematics. Vol. 94. pp. 137–160. doi:10.1007/978-1-4757-1799-0_4. ISBN 978-1-4419-2820-7.
    • Warner, Frank W. (1983). "Chapter 5. Sheaves, Cohomology, and the de Rham Theorem". Foundations of Differentiable Manifolds and Lie Groups. Graduate Texts in Mathematics. Vol. 94. pp. 161–217. doi:10.1007/978-1-4757-1799-0_5. ISBN 978-1-4419-2820-7.
    • Warner, Frank W. (1983). "The Hodge Theorem". Chapter 6. Foundations of Differentiable Manifolds and Lie Groups. Graduate Texts in Mathematics. Vol. 94. pp. 219–258. doi:10.1007/978-1-4757-1799-0_6. ISBN 978-1-4419-2820-7.
  • Warner, Frank W. (11 November 2013). Foundations of Differentiable Manifolds and Lie Groups (softcover reprint of Springer-Verlag's hardcover ed.). ISBN 9781475717990.

References

  1. ↑ biographical information from American Men and Women of Science, Thomson Gale 2004
  2. ↑ Frank Wilson WarnerIII at the Mathematics Genealogy Project
  3. ↑ "Tenured Faculty History". Department of Mathematics, University of Pennsylvania.
  4. ↑ "Frank W. Warner". John Simon Guggenheim Memorial Foundation.
  5. ↑ "Historic Fellows". American Association for the Advancement of Science.
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