Ian Macdonald

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Ian Grant Macdonald (born October 11, 1928 in London ) is an English mathematician.

Ian Macdonald in Oberwolfach 1977

life and work

Macdonald went to Winchester College and then studied mathematics at Trinity College , Cambridge with a bachelor's degree in 1952. He then went five years in the public service (Ministry of Supply). In 1957 he became an assistant lecturer at the University of Manchester with Max Newman . In 1960 he went to the University of Exeter and in 1963 became a Fellow of Magdalen College, Oxford. In 1972 he became “Fielden Professor” at Manchester University, succeeding Frank Adams . In 1976 he became a professor at Queen Mary and Westfield College, University of London .

Macdonald first worked on algebraic geometry and Jordan algebras , then on symmetric functions , orthogonal polynomials , representation theory. His book Symmetric functions and Hall polynomials (1978) was influential and is both a synopsis and a research report. He became known for the Macdonald identities, which extend the Jacobian triple product identity of formal power series and relate it to the root systems of affine Lie algebras . The precise understanding of these identities was an important driver in the development of the representation theory of the Kac-Moody algebras (infinitely dimensional Lie algebras). Some of the conjectures he made about the combinatorial properties of root systems, the Macdonald conjectures , which generalize the conjectures of Freeman Dyson (1962, in connection with the theory of random matrices), were also influential . They were proven by Ivan Cherednik in 1995 . Around 1987 he introduced new symmetric functions related to the root systems of Lie algebras, the Macdonald polynomials .

In 1979 he was elected to the Royal Society . In 1991 he received the Pólya Prize from the London Mathematical Society . In 2009 he received the Leroy P. Steele Prize . Macdonald gave a plenary lecture at the ICM in Berlin in 1998 ( Constant term identities, orthogonal polynomials and affine Hecke algebras ) and was invited speaker at the ICM in Nice in 1970 ( Harmonic analysis on semi-simple groups ). He is a fellow of the American Mathematical Society .

Fonts

  • With Michael Atiyah : Introduction to commutative algebra , Addison-Wesley 1969
  • Algebraic geometry - introduction to schemes , Benjamin 1968
  • Spherical functions on a group of p-adic type , Publications of the Ramanujan Institute, Madras 1971
  • Notes on Schubert Polynomials , Montreal 1991
  • Affine Hecke algebras and orthogonal polynomials , Cambridge Tracts in Mathematics, Vol. 157. Cambridge University Press, Cambridge, 2003
  • With Roger Carter , Graeme Segal : Lectures on Lie groups and Lie algebras , London Mathematical Society Student Texts, Cambridge University Press 1995
  • Symmetric functions and Hall polynomials , 1978, 2nd edition, The Clarendon Press, Oxford University Press, New York, 1995
  • Symmetric functions and orthogonal polynomials , American Mathematical Society, Providence, RI, 1998
  • Affine Hecke Algebras and orthogonal polynomials , Cambridge University Press 2003
  • Affine Root Systems and Dedekind's η-Function , Inventiones Mathematicae, Vol. 15, 1972, pp. 91-143, online

literature

  • Alun Morris: "Ian Macdonald", in: Vadim B. Kuznetsov, Siddhartha Sahi (Eds.), Jack, Hall-Littlewood and Macdonald Polynomials, Contemporary Mathematics, Volume 417, 2006

Web links

Individual evidence

  1. ^ Macdonald: Affine root systems and Dedekind functions. In: Inventiones Mathematicae Volume 15, 1972, pages 91-143.
  2. ^ Macdonald: Some conjectures for root systems. In: SIAM Journal Mathematical Analysis Volume 13, 1982, pages 988-1007.
personal data
SURNAME Macdonald, Ian
ALTERNATIVE NAMES Macdonald, Ian Grant
BRIEF DESCRIPTION English mathematician and university professor
DATE OF BIRTH October 11, 1928
PLACE OF BIRTH London