Peter Swinnerton-Dyer

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Peter Swinnerton-Dyer at the workshop “Explicit methods in number theory” in Oberwolfach , 2007

Sir Henry Peter Francis Swinnerton-Dyer, 16th Baronet KBE FRS (born August 2, 1927 in Ponteland , Northumberland - † December 26, 2018 ) was an English mathematician who worked in the field of number theory and algebraic geometry.

life and work

Swinnerton-Dyer wrote his first work (on number theory) at the age of 15. He studied at Cambridge with John Edensor Littlewood and initially dealt with nonlinear differential equations ( Van der Pol equations ), which Littlewood had previously investigated with Mary Cartwright . He received a Junior Research Fellowship from Trinity College (which made a doctorate common in other countries superfluous) and went to Chicago on a scholarship in 1954 to study with the specialist in harmonic analysis Antoni Zygmund . The acquaintance with André Weil changed his research interests and he turned to number theory. After returning to Cambridge in 1955, he initially devoted himself to the current geometry of numbers, partly in collaboration with Eric Barnes and John Cassels . He was later Dean of Trinity College, 1973-1983 Masters of St. Catherine College and 1979-1981 Vice Chancellor of the University. From 1983 to 1989 he was also active in education policy: he was Chairman of the Commission (UGC or UFC, University Grants Committee) that regulated the allocation of state research funds to universities. At that time he criticized the University of London and advocated the award according to the quality of research. He was also active in various British state investigative commissions. He was active as professor emeritus at the university until his death.

Swinnerton-Dyer specialized in number theory and is best known for the conjecture by Birch and Swinnerton-Dyer , on which he worked with Bryan Birch in the 1960s for computer calculations of the number of points of elliptical curves over finite fields (modulo a prime number p ) arrived. The conjecture makes a statement about the asymptotic behavior of the number of solutions for large prime numbers. Usually the assumption is formulated as a statement about the behavior of the zeta function Z (s) belonging to the elliptic curve at the pole point s = 1. The conjecture 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 number theory of higher-dimensional algebraic varieties ( algebraic surfaces ), e.g. B. on the validity (for special areas) or obstructions to the Hasse principle (local-global principle) , where he found the first counterexamples in cubic areas, and about the density and number of rational points on special areas.

In the 1970s, he dealt with modular forms (and their p-adic properties, Antwerp conferences), the arithmetic of Weil curves (elliptic curves parameterized by modular forms, with Barry Mazur ), the proof of the Tate-Shafarevich conjectures for special K3 areas (with Michael Artin ). He also continued numerical work on elliptic curves (tables of elliptic curves with a small guide) and was still active in the theory of differential equations.

Swinnerton-Dyer was a very accomplished programmer. For the computer calculations in Cambridge in the 1960s on their in-house computer "Titan", he wrote the operating system and created his own programming language "Autocode".

In 1967 he was elected as a member (" Fellow ") in the Royal Society , which in 2006 awarded him the Sylvester Medal " for his fundamental work on arithmetic geometry and his many contributions to the theory of ordinary differential equations ". Since 1989 he was a member of the Academia Europaea .

He came from a noble family and inherited from his father in 1975 the title of Baronet of Tottenham in the County of Middlesex, created in the Baronetage of England in 1678 . In 1987 he was inducted into the Order of the British Empire as Knight Commander .

Swinnerton-Dyer was also an accomplished chess and bridge player who represented the United Kingdom in bridge in the 1953 European Championship and in 1963 won the English Gold Cup with his team.

He was married to the archaeologist Harriet Crawford ( who specializes in Sumer and Dilmun ) .

Fonts

  • with Bryan J. Birch : Notes on elliptic curves. I. In: Journal for pure and applied mathematics . Volume 212, 1963, pp. 7-25 .
  • with Bryan J. Birch: Notes on elliptic curves. II. In: Journal for pure and applied mathematics. Volume 218, 1965, pp. 79-108 , (Birch / Swinnerton-Dyer presumption).
  • with Michael Artin : The Shafarevich-Tate conjecture for pencils of elliptic curves on 3 surfaces. In: Inventiones Mathematicae . Volume 20, 1973, pp. 249-266 .
  • Analytic theory of Abelian varieties (= London Mathematical Society. Lecture Notes Series. 14). Cambridge University Press, Cambridge et al. 1974, ISBN 0-521-20526-3 .
  • with Barry Mazur : Arithmetic of Weil curves. In: Inventiones Mathematicae. Volume 25, 1974, pp. 1-61 .
  • with Bryan J. Birch: The Hasse problem for rational surfaces. In: Journal for pure and applied mathematics. Volume 274/275, 1975, pp. 164-174 .
  • A brief guide to algebraic number theory (= London Mathematical Society Student Texts. 50). Cambridge University Press, Cambridge et al. 2001, ISBN 0-521-00423-3 .

literature

  • Barry Mazur, John Tate , Jeremy Teitelbaum : On- adic analogues of the conjectures of Birch and Swinnerton-Dyer. In: Inventiones Mathematicae. Volume 84, 1986, pp. 1-48 .

Web links

supporting documents

  1. Entry prabook.com, accessed on January 1, 2019
  2. The New Year's Eve Medal of the Royal Society ( Memento from November 12, 2007 in the Internet Archive ) on royalsoc.ac.uk, as of: November 12, 2007, in the Internet Archive at archive.org, viewed August 7, 2011 (English)
  3. ^ London Gazette  (Supplement). No. 50764, HMSO, London, December 31, 1986, p. 7 ( PDF , accessed August 7, 2011, English).