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, mathematical structure, structure, space, Mathematica ...

who is known for the Serre–Swan theorem 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 eve ...

s to the algebraic concept of

projective module In mathematics, particularly in algebra, the class of projective modules enlarges the class of free modules (that is, modules with basis vectors) over a ring, keeping some of the main properties of free modules. Various equivalent characterizati ...

s, 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 pol ...

. 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 sens ...

Education and career

As an undergraduate at

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

, 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 list of mathematics competitions, mathematics competition for undergraduate college students enrolled at institutions of higher learning in th ...

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, Ne ...

. 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, or UChi) is a Private university, private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park, Chicago, Hyde Park neighborhood on Chicago's South Side, 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 Michiga ...

, also known for his work in K-theory. Together with

Otto Forster Otto Forster (born 8 July 1937 in Munich) is a German mathematician. Education and career Forster received his ''Diplom'' in 1960 from Ludwig Maximilian University of Munich. There he received in 1961 his doctorate. His thesis ''Banachalgebren st ...

he proved the

Forster–Swan theorem The Forster–Swan theorem is a result from commutative algebra that states an upper bound for the minimal number of generators of a finitely generated module M over a commutative Noetherian ring. The usefulness of the theorem stems from the fact, ...

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, ...

Cole Prize The Frank Nelson Cole Prize, or Cole Prize for short, is one of twenty-two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to numbe ...

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