Richard Gordon Swan (; born 1933) is an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

who is known for the

Serre–Swan theorem In the mathematical fields of topology and K-theory, the Serre–Swan theorem, also called Swan's theorem, relates the geometric notion of vector bundles to the algebraic concept of projective modules and gives rise to a common intuition throughout ...

relating the geometric notion of

vector bundle In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X (for example X could be a topological space, a manifold, or an algebraic variety): to every p ...

s to the algebraic concept of projective modules, and for the Swan representation, an ''l''-adic

projective representation In the field of representation theory in mathematics, a projective representation of a group ''G'' on a vector space ''V'' over a field ''F'' is a group homomorphism from ''G'' to the projective linear group \mathrm(V) = \mathrm(V) / F^*, where G ...

of a

Galois group In mathematics, in the area of abstract algebra known as Galois theory, the Galois group of a certain type of field extension is a specific group associated with the field extension. The study of field extensions and their relationship to the po ...

. His work has mainly been in the area of

algebraic K-theory Algebraic ''K''-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory. Geometric, algebraic, and arithmetic objects are assigned objects called ''K''-groups. These are groups in the sense ...

Education and career

As an undergraduate at

Princeton University Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ...

, Swan was one of five winners in the

William Lowell Putnam Mathematical Competition The William Lowell Putnam Mathematical Competition, often abbreviated to Putnam Competition, is an annual mathematics competition for undergraduate college students enrolled at institutions of higher learning in the United States and Canada (regar ...

in 1952. He earned his Ph.D. in 1957 from

under the supervision of

John Coleman Moore John Coleman Moore (May 27, 1923 – January 1, 2016) was an American mathematician. The Borel−Moore homology and Eilenberg–Moore spectral sequence are named after him. Early life and education Moore was born in 1923 in Staten Island, New ...

. In 1969 he proved in full generality what is now known as the Stallings-Swan theorem. He is the Louis Block Professor Emeritus of Mathematics at the

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chic ...

.. His doctoral students at Chicago include

Charles Weibel Charles Alexander Weibel (born October 28, 1950 in Terre Haute, Indiana) is an American mathematician working on algebraic K-theory, algebraic geometry and homological algebra. Weibel studied physics and mathematics at the University of Michigan, ...

, also known for his work in K-theory.

Awards and honors

In 1970 Swan was awarded the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

's Cole Prize in Algebra.

Books

* * *

References

External links

Swan's homepage at Chicago.
Year of birth missing (living people) Living people 20th-century American mathematicians 21st-century American mathematicians Princeton University alumni University of Chicago faculty Members of the United States National Academy of Sciences Putnam Fellows {{US-mathematician-stub