John H. Coates

John Henry Coates, FRS[5] (born 26 January 1945) is a mathematician who was the Sadleirian Professor of Pure Mathematics at the University of Cambridge in the United Kingdom from 1986 to 2012.[2][6][7][8][9][10]

John Coates
John H. Coates
Born	John Henry Coates 26 January 1945[1] New South Wales, Australia
Nationality	Australian
Alma mater	Australian National University (BSc) Trinity College, Cambridge (PhD)
Known for	Iwasawa theory p-adic L-functions
Spouse(s)	Julie Turner[1]
Awards	FRS (1985) Senior Whitehead Prize (1997)
Scientific career
Fields	Mathematics
Institutions	University of Cambridge Harvard University Université de Paris, Orsay École Normale Supérieure Stanford University[1]
Thesis	The Effective Solution of Some Diophantine Equations (1969)
Doctoral advisor	Alan Baker[2]
Doctoral students	Pierre Colmez Matthias Flach Catherine Goldstein Anupam Saikia Susan Howson Jacques Tilouine Andrew Wiles[2]
Influences	Kurt Mahler[3] John Tate[4]
Website	dpmms.cam.ac.uk/people/jhc13

Early life and education

Coates studied Mathematics and was born the son of J. H. Coates and B. L. Lee[1] and grew up in Possum Brush (near Taree) in New South Wales, Australia. Coates Road in Possum Brush is named after the family farm on which he grew up.[11] Before university he spent a summer working for BHP Billiton in Newcastle, New South Wales, though he was not successful in gaining a university scholarship with the company. Coates attended Australian National University on scholarship as one of the first undergraduates, from which he gained a BSc degree. He then moved to France, doing further study at the École Normale Supérieure in Paris, before moving again to England.

Career

In England he did postgraduate research at the University of Cambridge, his doctoral dissertation being on p-adic analogues of Baker's method. In 1969, Coates was appointed assistant professor of mathematics at Harvard University in the United States, before moving again in 1972 to Stanford University where he became an associate professor.

In 1975, he returned to England where he was made a fellow of Emmanuel College, and took up a lectureship. Here he supervised the PhD of Andrew Wiles, and together they proved a partial case of the Birch and Swinnerton-Dyer conjecture for elliptic curves with complex multiplication.[12]

In 1977, Coates moved back to Australia, becoming a professor at the Australian National University, where he had been an undergraduate. The following year, he moved back to France, taking up a professorship at the University of Paris XI at Orsay. In 1985, he returned to the École Normale Supérieure, this time as professor and director of mathematics.

Since 1986 Coates has worked in the Department of Pure Mathematics and Mathematical Statistics (DPMMS) of the University of Cambridge. He was head of DPMMS for several years. He played a role in new appointments in number theory and geometry in University of Cambridge.

In the last ten years Coates studied some aspects of non-commutative Iwasawa theory.

Awards and honours

Coates was elected a fellow of the Royal Society of London in 1985, and was President of the London Mathematical Society from 1988 to 1990. The latter organisation awarded him the Senior Whitehead Prize in 1997, for "his fundamental research in number theory and for his many contributions to mathematical life both in the UK and internationally". His nomination for the Royal Society reads:

Distinguished for his contributions to the theory of numbers, in particular to the study of transcendence, cyclotomic fields and elliptic curves. In addition to his own important contributions he has been a stimulating influence on colleagues and students. Together with his pupil A. Wiles he achieved the first major breakthrough towards a proof of the Birch-Swinnerton-Dyer conjectures.[5]

Personal life

Coates married Julie Turner in 1966, with whom he had three sons.[1] He collects Japanese pottery and porcelain.[4]

References

1. "COATES, Prof. John Henry". Who's Who 2014, A & C Black, an imprint of Bloomsbury Publishing plc, 2014; online edn, Oxford University Press.(subscription required)
2. John H. Coates at the Mathematics Genealogy Project
3. Moore, Susan, "Cambridge Blue and White", Apollo, November 2020, pp 56-62 at p 58.
4. John Coates interviewed by Alan Macfarlane, 15 February 2008, retrieved 30 March 2009
5. "EC/1985/08: Coates, John Henry". London: The Royal Society. Archived from the original on 8 July 2019.
6. O'Connor, John J.; Robertson, Edmund F., "John H. Coates", MacTutor History of Mathematics archive, University of St Andrews.
7. Emmanuel College profile: Professor John Coates
8. interviewed by Alan Macfarlane 25th February 2008 (video)
9. John H. Coates's publications indexed by the Scopus bibliographic database. (subscription required)
10. Coates, J.; Fukaya, T.; Kato, K.; Sujatha, R.; Venjakob, O. (2005). "The GL2 Main Conjecture for Elliptic Curves without Complex Multiplication". Publications mathématiques de l'IHÉS. 101: 163–208. arXiv:math/0404297. doi:10.1007/s10240-004-0029-3. S2CID 13996298.
11. "Whereis: Possum Brush".
12. Coates, J.; Wiles, A. (1977). "On the conjecture of Birch and Swinnerton-Dyer". Inventiones Mathematicae. 39 (3): 223. Bibcode:1977InMat..39..223C. doi:10.1007/bf01402975. S2CID 189832636.