Mathematical Sciences: Relative Regulators and Divisor ClassGroups

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This award supports the research in Algebraic and Analytic Number Theory of Professor Eduardo Friedman of the University of Pennsylvania. Dr. Friedman's project involves using analytic methods to investigate the behavior of the ratio of the regulators in an extension of number fields. Also, in the related geometric situation, the function field case, Professor Friedman will be examining the distribution of divisor class groups of curves over a function field. The subject of Analytic Number Theory applies to the discrete realm of the whole numbers the techniques of Analysis, dependent on the notions of continuity and limit, originating in Calculus. The idea of using continuous methods to investigate the discrete is two centuries old, but with the work of the modern analytic number theorists such as Professor Friedman, the field has had a new rebirth.