Richard_G._Swan

Richard Swan

Richard Swan

American mathematician

This article is about the American mathematician. For the Scottish cricketer, see Richard Swan (cricketer). For the 15th-century English member of parliament, see Kingston upon Hull (UK Parliament constituency).

Richard Gordon Swan (/swɑːn/; born 1933) is an American mathematician who is known for the Serre–Swan theorem relating the geometric notion of vector bundles to the algebraic concept of projective modules,[1] and for the Swan representation, an l-adic projective representation of a Galois group.[2] His work has mainly been in the area of algebraic K-theory.

Education and career

As an undergraduate at Princeton University, Swan was one of five winners in the William Lowell Putnam Mathematical Competition in 1952.[3] He earned his Ph.D. in 1957 from Princeton University under the supervision of John Coleman Moore.[4]

In 1969 he proved in full generality what is now known as the Stallings–Swan theorem.[5][6] He is the Louis Block Professor Emeritus of Mathematics at the University of Chicago.[7]

His doctoral students at Chicago include Charles Weibel, also known for his work in K-theory.[4]

Awards and honors

In 1970 Swan was awarded the American Mathematical Society's Cole Prize in Algebra.

Books

  • Swan, R. G. (1964). The Theory of Sheaves. Chicago lectures in mathematics. Chicago: The University of Chicago Press.
  • Swan, R. G. (1968). Algebraic K-theory. Lecture Notes in Mathematics. Vol. 76. Berlin, New York: Springer-Verlag. doi:10.1007/BFb0080281. ISBN 978-3-540-04245-7. MR 0245634.
  • Swan, Richard G. (1970). K-theory of finite groups and orders. Lecture Notes in Mathematics. Vol. 149. Notes by E. Graham Evans. Berlin, New York: Springer-Verlag. doi:10.1007/BFb0059150. ISBN 978-3-540-04938-8. MR 0308195.

References

  1. [1]
    Manoharan, P. (1995), "Generalized Swan's Theorem and its Application", Proceedings of the American Mathematical Society, 123 (10): 3219–3223, doi:10.2307/2160685, JSTOR 2160685.
  2. [2]
    Huber, R. (2001), "Swan representations associated with rigid analytic curves", Journal für die Reine und Angewandte Mathematik, 2001 (537): 165–234, doi:10.1515/crll.2001.063, MR 1856262.
  3. [3]
    "Putnam Competition Individual and Team Winners". Mathematical Association of America. Retrieved December 10, 2021.
  4. [4]
    Richard Gordon Swan at the Mathematics Genealogy Project
  5. [5]
    Weigel, Thomas; Zalesskii, Pavel (2016). "Virtually free pro-p products". arXiv:1305.4887 [math.GR].
  6. [6]
    Swan, R. G. (1969). "Groups of cohomological dimension one". Journal of Algebra. 12 (4): 585–610. doi:10.1016/0021-8693(69)90030-1.
  7. [7]
    University of Chicago Mathematics Faculty Listing, retrieved 2015-08-31.


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