Summary
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
editAs 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]
Together with Otto Forster he proved the Forster–Swan theorem.
Awards and honors
editIn 1970 Swan was awarded the American Mathematical Society's Cole Prize in Algebra.
Books
edit- 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
edit- ^ 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, 2001 (537): 165–234, doi:10.1515/crll.2001.063, MR 1856262.
- ^ "Putnam Competition Individual and Team Winners". Mathematical Association of America. Retrieved December 10, 2021.
- ^ a b 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.
External links
edit- Swan's homepage at Chicago.