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John Henry Coates

John H. Coates
Born	January 26, 1945 New South Wales, Australia
Residence	England
Nationality	Australian
Field	Mathematician
Institution	Cambridge University
Alma mater	Australian National University
Academic advisor	Alan Baker
Notable students	Pierre Colmez, Matthias Flach, Jacques Tilouine, Andrew Wiles
Known for	Iwasawa theory p-adic L-functions

Professor John Henry Coates, FRS (born January 26, 1945) is a mathematician who holds (since 1986) the position of Sadleirian Professor (of pure mathematics) at the University of Cambridge in the United Kingdom.

Coates was born and grew up in Possum Brush in New South Wales, Australia, and studied at the Australian National University from which he gained a B.Sc. degree. He then moved to France, doing further study at the École Normale Superieure in Paris, before moving again to England. There 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, the mathematician who went on to find a proof of Fermat's last theorem - in which Coates's work on elliptic curves, Iwasawa theory, and p-adic L-functions helped greatly.

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 Superieure, this time as professor and director of mathematics.

He 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".

He now works in the Department of Pure Mathematics and Mathematical Statistics (DPMMS) of the University of Cambridge, where he specialises in number theory, arithmetical algebraic geometry, and Iwasawa theory. His current research focuses on the study of non-commutative Iwasawa theory, for instance, the study of the arithmetic of elliptic curves along -extensions.

• O'Connor, John J., and Edmund F. Robertson. "John Coates". MacTutor History of Mathematics archive.
• DPMMS profile