John Coates - Biography#

John Coates was born in 1945 in New South Wales, Australia.

He studied at the Australian National University. He then moved to France, doing further study at the Ecole Normale Supérieure in Paris, before moving again to England, where Coates received Ph.D from the University of Cambridge in 1969 on the subject "p—adic analogues of Baker's method".

He held positions at Harvard University, Stanford University, Cambridge University as Fellow of Emmanuel College, the Australian National University in Canberra, the Université Paris-sud at Orsay, the Ecole Normale Supérieure in Paris. Since 1986, he holds the position of Sadleirian Professor of Pure Mathematics at the University of Cambridge.

He was elected a Fellow of the Royal Society of London in 1985. He received the Senior Whitehead Prize of the London Mathematical Society in 1997. Coates was President of the London Mathematical Society from 1988 to 1990, and vice-president of the international Mathematical Union from 1991 to 1994. He holds a Doctor honoris cause of the Ecole Normale Supérieure in Paris.

ln a joint work with his student Andrew Wites, he proved a partial case of the Birch and Swinnerton—Dyer conjecture for elliptic curves with complex multiplication. More recently he has focused on the study of various aspects of non-commutative Iwasawa theory, for instance, the study of the arithmetic of elliptic curves in nonabelian infinite extensions. Coates's insights into the iwasawa theory of the symmetric square of an elliptic curve were instrumental in the proof of the Shimura-Taniyama conjecture for semi-stable elliptic curves over Q, a wide generalisation of Fermat’s last theorem.

He had 19 doctoral students, among which some outstanding ones such as Pierre Cotivuaz, Andrew Wltes, Otmar Venjakov.

He has been for several years editor-in—chief of lnventiones Mathematicae, and serves on the editorial board of several major journals.

Detailed biography