Workshop: Analytic Number Theory and Diophantine Approximation

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Abstract: This grant will help fund American students to attend a summer school in Analytic number theory and Diophantine Analysis held at the University of Ottawa, June 30-July 11, 2008. The object of the summer school is to expose young researchers to some of the latest results and techniques in analytic number theory and diophantine analysis. These areas have seen a lot of progress in recent years, with some highlights being the work of Goldston, Pintz and Yildirim on small gaps between prime numbers, and the work of Rivoal on irrationality of odd values of the Riemann zeta-function. Further, other breakthroughs such as Green and Tao's theorem on long arithmetic progressions of prime numbers relied on advances in the area of analytic number theory. The first week of the summer school will offer several introductory courses as background for beginning graduate students. The second week will then offer more advanced courses on recent developments. It is also hoped that researchers in these different, but related fields would be able to combine their ideas and insights, leading to further breakthroughs.The summer school immediately precedes a large international conference (the tenth meeting of the Canadian Number Theory Association) to be held in nearby Waterloo, Ontario. The training at the summer school should help graduate students benefit more fully from this research conference as well.The summer school supported by this NSF grant is in the area of number theory. Number theory is an area of mathematics with very old and easy-to-state problems whose solutions lie very deep, and connect very many disparate areas of mathematics. Progress in number theory has sometimes led to practical applications, such as in cryptography and in coding theory.