Peter Swinnerton-Dyer

Sir Henry Peter Francis Swinnerton - Dyer ( born August 2, 1927) is an English mathematician who works in the field of number theory and algebraic geometry.

Life and work

Swinnerton - Dyer wrote his first work ( number theory ) already with 15, he studied at Cambridge with John Edensor Littlewood and was first engaged in non-linear differential equations ( van der Pol equation), the Littlewood had earlier studied with Mary Cartwright. He received a Junior Research Fellowship at Trinity College (which is a standard in other countries Promotion made ​​redundant ) and went on a scholarship in 1954 to Chicago to study at the specialist for harmonic analysis Antoni Zygmund. But acquaintance with André Weil changed his research interests, and he turned to the theory of numbers. After returning to Cambridge in 1955 he devoted himself at first there just the current geometry of numbers, partly in collaboration with Eric Barnes and John Cassels. Later, he was Dean of Trinity College, 1973-1983 Master of St. Catherine College and from 1979 to 1981 Vice- Chancellor of the University. 1983 to 1989 he was also active in education policy: he was Chairman of the Commission ( UGC or UFC, University Grants Committee), which governed the allocation of public research funds to universities. At that time, he criticized the University of London and campaigned for the award based on the quality of research. He was also active in various state commissions of English. He is still active as a professor emeritus of the University.

Swinnerton - Dyer, specializing in number theory and is especially known for the conjecture of Birch and Swinnerton - Dyer, on which he in the 1960s with Bryan Birch in computer calculations of the number of points on elliptic curves over finite fields ( modulo a prime p ) arrived. The conjecture makes a statement about the asymptotic behavior of the solution for large number of primes. Usually, the assumption is formulated as a statement about the behavior of the elliptic curve associated with the zeta function Z ( s ) at the pole s = 1. The assumption plays a central role in number theory and is one of the Millennium Problems of the Clay Mathematics Institute. Swinnerton - Dyer also dealt with the theory of numbers higher dimensional algebraic varieties ( algebraic surfaces ), eg on the validity (for special areas ) or obstruction to the Hasse principle ( local-global principle), where he found first counter-examples for cubic surfaces, and the density and number of rational points on specific areas.

In the 1970s he worked on, among others, with modular forms (and their p- adic properties, Antwerp conferences), the arithmetic of Weil curves ( parameterized by modular forms elliptic curves, with Barry Mazur ), the proof of the Tate - Shafarevich conjecture for special K3 surfaces ( with Michael Artin ). He sat and numerical work on elliptic curves away (tables of elliptic curves with small guide) and was still in the theory of differential equations active.

Swinnerton - Dyer is a very experienced programmer. For the computer calculations in the 1960s in Cambridge on their own home computer "Titan" he wrote the operating system, creating its own programming language "Auto Code".

In 1967 he was elected as a member ( "Fellow" ) to the Royal Society, in 2006, the Sylvester Medal "for his fundamental work on arithmetic geometry and his many contributions to the theory of ordinary differential equations " gave him.

He comes from a noble family and inherited the title of Baron by his father (16th Baron Swinnerton - Dyer ), but he was also knighted and appointed KBE.

Swinnerton - Dyer is also an accomplished chess and bridge players, who represented the United Kingdom at the Bridge in 1953 in the European Championship and 1963 his team won the English Gold Cup.

He is married to the (on Sumer and Dilmun specialized ) archaeologist Harriet Crawford.

Writings

  • Analytic theory of Abelian varieties, London Mathematical Society (LMS ) Lecture Notes 14, Cambridge University Press 1974 ISBN 0-521-20526-3
  • A brief guide to algebraic number theory, LMS Student Text, Cambridge University Press, 2001 ISBN 0-521-00423-3
  • Swinnerton - Dyer, Arithmetic of Weil curves Mazur, Inv.Math.1974
  • Swinnerton - Dyer, Notes on elliptic curves I, Birch, Crelle J.1963
  • Swinnerton - Dyer, Notes on elliptic curves II Birch, Crelle J.1963, Birch / Swinnerton - Dyer conjecture
  • Swinnerton - Dyer, The Hasse Birch trouble for rational surfaces, J. 1975 Crelle
Birch and Swinnerton-Dyer conjecture Bryan John Birch Name Authority File
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