Mathematical Sciences: Stark's Conjectures in Function Fields and Number Fields

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This award supports the research in number theory and arithmetic algebraic geometry of Professor David R. Hayes of the University of Massachusetts at Amherst. One of Dr. Hayes's projects is to carry out a high-precision verification of the Refined Stark Conjecture for special values of a p-adic zeta function defined from a real quadratic field. Another project, more geometric in nature, is to settle completely a Goldbach-like problem in function fields over finite fields. As with the Stark- Conjecture problem, Dr. Hayes will make extensive use of supercomputers in these investigations. Except for counting, number theory, which is the study of the properties of the whole numbers, is the oldest branch of mathematics. In modern days, problems in number theory have furnished the driving force to creation of new mathematics in the fields of pure algebra, analysis, and geometry; some of the most recent and most astonishing applications of number theory have appeared in theoretical computer science and coding theory.