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.

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]

Together with Otto Forster he proved the Forster–Swan theorem.

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

• 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.

• Swan's homepage at Chicago.

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