Ian G. Macdonald
Encyclopedia
Ian Grant Macdonald is a British
mathematician
known for his contributions to symmetric function
s, special functions, Lie algebra
theory and other aspects of algebraic combinatorics
(see also combinatorics
).
He was educated at Winchester College
and Trinity College, Cambridge
, graduating in 1952. He then spent five years as a civil servant. He was offered a position at Manchester University in 1957 by Max Newman
, on the basis of work he had done while outside academia. In 1960 he moved to the University of Exeter
, and in 1963 became a Fellow of Magdalen College, Oxford
. He became Fielden Professor
at Manchester in 1972, and professor at Queen Mary and Westfield College, London
in 1976.
He worked on symmetric products of algebraic curves, Jordan algebra
s, representation theory
of groups over local field
s. In 1972 he proved the Macdonald identities
, after a pattern known to Freeman Dyson
. His 1979 book Symmetric Functions and Hall Polynomials has become a classic. Symmetric functions are an old theory, part of the theory of equations
, to which both K-theory
and representation theory
lead. His was the first text to integrate much classical theory, such as Hall polynomial
s, Schur functions, the Littlewood-Richardson rule, with the abstract algebra
approach. It was both an expository work and, in part, a research monograph, and had a major impact in the field. The Macdonald polynomial
s are now named for him. The Macdonald conjectures from 1982 also proved most influential.
Macdonald was awarded the 2009 Steele Prize for Mathematical Exposition.
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
known for his contributions to symmetric function
Symmetric function
In algebra and in particular in algebraic combinatorics, the ring of symmetric functions, is a specific limit of the rings of symmetric polynomials in n indeterminates, as n goes to infinity...
s, special functions, Lie algebra
Lie algebra
In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. Lie algebras were introduced to study the concept of infinitesimal transformations. The term "Lie algebra" was introduced by Hermann Weyl in the...
theory and other aspects of algebraic combinatorics
Algebraic combinatorics
Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algebra....
(see also combinatorics
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
).
He was educated at Winchester College
Winchester College
Winchester College is an independent school for boys in the British public school tradition, situated in Winchester, Hampshire, the former capital of England. It has existed in its present location for over 600 years and claims the longest unbroken history of any school in England...
and Trinity College, Cambridge
Trinity College, Cambridge
Trinity College is a constituent college of the University of Cambridge. Trinity has more members than any other college in Cambridge or Oxford, with around 700 undergraduates, 430 graduates, and over 170 Fellows...
, graduating in 1952. He then spent five years as a civil servant. He was offered a position at Manchester University in 1957 by Max Newman
Max Newman
Maxwell Herman Alexander "Max" Newman, FRS was a British mathematician and codebreaker.-Pre–World War II:Max Newman was born Maxwell Neumann in Chelsea, London, England, on 7 February 1897...
, on the basis of work he had done while outside academia. In 1960 he moved to the University of Exeter
University of Exeter
The University of Exeter is a public university in South West England. It belongs to the 1994 Group, an association of 19 of the United Kingdom's smaller research-intensive universities....
, and in 1963 became a Fellow of Magdalen College, Oxford
Magdalen College, Oxford
Magdalen College is one of the constituent colleges of the University of Oxford in England. As of 2006 the college had an estimated financial endowment of £153 million. Magdalen is currently top of the Norrington Table after over half of its 2010 finalists received first-class degrees, a record...
. He became Fielden Professor
Fielden Chair of Pure Mathematics
The Fielden Chair of Pure Mathematics is an endowed professorial position in the School of Mathematics, University of Manchester, England.In 1870 Samuel Fielden, a wealthy mill owner from Todmorden, donated £150 to Owens College for the teaching of evening classes and a further £3000 for the...
at Manchester in 1972, and professor at Queen Mary and Westfield College, London
Queen Mary, University of London
Queen Mary, University of London is a public research university located in London, United Kingdom and a constituent college of the federal University of London...
in 1976.
He worked on symmetric products of algebraic curves, Jordan algebra
Jordan algebra
In abstract algebra, a Jordan algebra is an algebra over a field whose multiplication satisfies the following axioms:# xy = yx # = x ....
s, representation theory
Representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studiesmodules over these abstract algebraic structures...
of groups over local field
Local field
In mathematics, a local field is a special type of field that is a locally compact topological field with respect to a non-discrete topology.Given such a field, an absolute value can be defined on it. There are two basic types of local field: those in which the absolute value is archimedean and...
s. In 1972 he proved the Macdonald identities
Macdonald identities
In mathematics, the Macdonald identities are some infinite product identities associated to affine root systems, introduced by . They include as special cases the Jacobi triple product identity, Watson's quintuple product identity, several identities found by , and a 10-fold product identity found...
, after a pattern known to Freeman Dyson
Freeman Dyson
Freeman John Dyson FRS is a British-born American theoretical physicist and mathematician, famous for his work in quantum field theory, solid-state physics, astronomy and nuclear engineering. Dyson is a member of the Board of Sponsors of the Bulletin of the Atomic Scientists...
. His 1979 book Symmetric Functions and Hall Polynomials has become a classic. Symmetric functions are an old theory, part of the theory of equations
Theory of equations
In mathematics, the theory of equations comprises a major part of traditional algebra. Topics include polynomials, algebraic equations, separation of roots including Sturm's theorem, approximation of roots, and the application of matrices and determinants to the solving of equations.From the point...
, to which both K-theory
K-theory
In mathematics, K-theory originated as the study of a ring generated by vector bundles over a topological space or scheme. In algebraic topology, it is an extraordinary cohomology theory known as topological K-theory. In algebra and algebraic geometry, it is referred to as algebraic K-theory. It...
and representation theory
Representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studiesmodules over these abstract algebraic structures...
lead. His was the first text to integrate much classical theory, such as Hall polynomial
Hall polynomial
In mathematics the Hall algebra is an associative algebra with a basis corresponding to isomorphism classes of finite abelian p-groups. It was first discussed by E. but forgotten until it was rediscovered by , both of whom published no more than brief summaries of their work. The Hall polynomials...
s, Schur functions, the Littlewood-Richardson rule, with the abstract algebra
Abstract algebra
Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras...
approach. It was both an expository work and, in part, a research monograph, and had a major impact in the field. The Macdonald polynomial
Macdonald polynomial
In mathematics, Macdonald polynomials Pλ are a family of orthogonal polynomials in several variables, introduced by...
s are now named for him. The Macdonald conjectures from 1982 also proved most influential.
Macdonald was awarded the 2009 Steele Prize for Mathematical Exposition.
Selected publications
- Macdonald, I. G. Affine Hecke algebras and orthogonal polynomials. Cambridge Tracts in Mathematics, 157. Cambridge University Press, Cambridge, 2003. x+175 pp. ISBN 0-521-82472-9
- Macdonald, I. G. Symmetric functions and Hall polynomials. Second edition. Oxford Mathematical Monographs. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1995. x+475 pp. ISBN 0-19-853489-2
- Macdonald, I. G. Symmetric functions and orthogonal polynomials. Dean Jacqueline B. Lewis Memorial Lectures presented at Rutgers University, New Brunswick, NJ. University Lecture Series, 12. American Mathematical Society, Providence, RI, 1998. xvi+53 pp. ISBN 0-8218-0770-6