Conference on Stark's Conjectures and Related Topics, August 4 - 9, 2002, The Johns Hopkins University

Johns Hopkins University, Baltimore MD

Investigators

Abstract

Originating in the mid-1970's, Stark's Conjecture remains one of the deepest unsolved problems in number theory. Tate's 1984 book on the sub- ject provided a generation of researchers with a solid exposition of the state of the conjecture at that time, and a foundation for further in- vestigation. Work related to the conjecture has recently grown to in- volve more and more number theorists, but there has never been a major conference on the subject. This NSF award will provide major funding for a conference dedicated to Stark's conjecture and its variations to be held at John's Hopkins University in Baltimore August 4-9, 2002. Plans include plenary talks devoted to background and current research in the mornings, followed by contributed talks in the afternoons. The gathering of researchers from various strands of inquiry should lead to insight into the links between various conjectures and provide an ideal platform for further research on all aspects of Stark's Conj- ecture. In particular, one would expect that this conference would lead to a number of new and fruitful collaborations, and to the greater in- volvement of graduate students in this research. Indeed, graduate stu- dents, junior faculty members, women, and members of traditionally under-represented minorities are especially encouraged to attend and to apply for funding. Stark's conjecture in number theory suggests that there is astonishing and useful structure waiting to be discovered behind the fundamental concepts of higher arithmetic. In higher arithmetic, one seeks to de- scribe the solutions of polynomial equations and their properties. This is the algebraic side of number theory. The conjecture states that the solutions of certain polynomial equations can be obtained from the values of specific limits and infinite sums which naturally involve the methods of calculus. This is the analytic side of number theory. Thus Stark's conjecture makes a striking connection between two branches of mathematics: algebra and analysis. Understanding this type of connection is just what leads to major breakthroughs. Indeed, the conjecture has already led to new and more efficient methods of performing certain computations.