Henri Darmon of McGill University will receive the 2017 AMS Cole Prize in Number Theory. Darmon is honored "for his contributions to the arithmetic of elliptic curves and modular forms."
The work of Henri Darmon has centered on a major open problem in mathematics known as the Birch and Swinnerton-Dyer conjecture. It is one of the seven "Millennium Prize Problems," the solutions for which the Clay Mathematics Institute has offered prizes of US$1-million each.
The Birch and Swinnerton-Dyer conjecture suggests a connection between two mathematical objects that seem to come from different worlds: analytically defined objects called L-functions, and algebraically defined objects called elliptic curves. While the conjecture was first formulated in the 1960s, the mathematical world needed some time to understand the deep and fundamental nature of the question it poses. Since the 1970s, the conjecture has been a central occupation of number theory.
The Cole Prize honors two papers that Darmon wrote with co-authors: "Generalized Heegner cycles and p-adic Rankin L-series" (with Massimo Bertolini and Kartik Prasanna, and with an appendix by Brian Conrad), Duke Mathematical Journal, 2013; and "Diagonal cycles and Euler systems, II: the Birch and Swinnerton-Dyer conjecture for Hasse-Weil-Artin L-functions" (with Victor Rotger), Journal of the AMS, 2016. The two papers cast new light on the Birch and Swinnerton-Dyer conjecture and on possible extensions of the theory of complex multiplication. The latter was developed by mathematicians such as Gauss, Eisenstein, and Kronecker, and is a key ingredient in many of the most important advances on the Birch and Swinnerton-Dyer conjecture, including work of Coates and Wiles from the mid-1970s and of Gross-Zagier and Kolyvagin from the late 1980s.
Darmon is one of the world's leading number theorists. The prize citation notes that the two papers being honored are "only high points of a long sequence of influential papers" by Darmon.
Born in 1965 in Paris, France, Darmon moved to Canada in 1968. He received a bachelor's degree from McGill University in 1987 and a PhD in mathematics from Harvard University in 1991, under the supervision of Benedict Gross. He then held a postdoctoral position at Princeton University, under the mentorship of Andrew Wiles. It was around this time that Wiles gained worldwide fame for his proof of Fermat's Last Theorem.
In 1994, Darmon joined the faculty of McGill University, where he is currently a James McGill Professor in the Department of Mathematics and Statistics. His other honors include the André Aisenstadt Prize (1997), the Coxeter-James Prize of the Canadian Mathematical Society (1998), the Ribenboim Prize of the Canadian Number Theory Association (2002), and the John L. Synge Award of the Royal Society of Canada (2008). He was elected a Fellow of the Royal Society of Canada in 2003.
Presented every three years, the AMS Cole Prize in Number Theory recognizes a notable paper in number theory published during the preceding six years. The prize will be awarded Thursday, January 5, 2017, at the Joint Mathematics Meetings in Atlanta.
Find out more about AMS prizes and awards at http://www.ams.org/profession/prizes-awards/prizes.
Founded in 1888 to further mathematical research and scholarship, today the American Mathematical Society fulfills its mission through programs and services that promote mathematical research and its uses, strengthen mathematical education, and foster awareness and appreciation of mathematics and its connections to other disciplines and to everyday life.