Richard Swan

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.

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).

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. 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. 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. "Putnam Competition Individual and Team Winners". Mathematical Association of America. Retrieved December 10, 2021.
  4. Richard Gordon Swan at the Mathematics Genealogy Project
  5. Weigel, Thomas; Zalesskii, Pavel (2016). "Virtually free pro-p products". arXiv:1305.4887 [math.GR].
  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. University of Chicago Mathematics Faculty Listing, retrieved 2015-08-31.


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