Mathematical Sciences: Relative Regulators and Divisor ClassGroups

该奖项支持宾夕法尼亚大学Eduardo Friedman教授在代数和解析数论方面的研究。弗里德曼博士的项目涉及使用分析方法来研究在数字领域的扩展中监管者的比率的行为。同样，在相关的几何情况下，函数场的情况下，弗里德曼教授将研究函数场上曲线的除数类群的分布。解析数论的主题应用于整数的离散领域的分析技术，依赖于连续性和极限的概念，起源于微积分。用连续方法研究离散问题的想法已有两个世纪的历史，但随着弗里德曼教授等现代分析数论家的工作，这一领域获得了新生。

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.