# 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.

## Education and career

As an undergraduate at Princeton University, Swan was in 1952 one of five winners in the William Lowell Putnam Mathematical Competition. He earned his Ph.D. in 1957 from Princeton University under the supervision of John Coleman Moore.[3] In 1969 he proved in full generality what is now known as the Stallings-Swan theorem.[4][5] He is the Louis Block Professor Emeritus of Mathematics at the University of Chicago.[6] His doctoral students at Chicago include Charles Weibel, also known for his work in K-theory.[3]

## 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.**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.**149**. Notes by E. Graham Evans. Berlin, New York: Springer-Verlag. doi:10.1007/BFb0059150. ISBN 978-3-540-04938-8. MR 0308195.

## References

- 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. - Huber, R. (2001), "Swan representations associated with rigid analytic curves",
*Journal für die Reine und Angewandte Mathematik*,**537**(537): 165–234, doi:10.1515/crll.2001.063, MR 1856262. - Richard Gordon Swan at the Mathematics Genealogy Project
- Weigel, Thomas; Zalesskii, Pavel (2016). "Virtually free pro-p products". arXiv:1305.4887 [math.GR].
- Swan, R. G. (1969). "Groups of cohomological dimension one".
*Journal of Algebra*.**12**(4): 585–610. doi:10.1016/0021-8693(69)90030-1. -
*University of Chicago Mathematics Faculty Listing*, retrieved 2015-08-31.