Mathematical Sciences: Research in Number Theory and Automorphic Forms

该奖项支持布兰代斯大学迈克尔·哈里斯教授对自同构形式的研究。Harris博士的研究项目是研究全纯和非全纯自同构形式的数论性质，以及与l函数特殊值的关系。他用来解决所选问题的主要工具是志村变种的环面紧化的上同调。非欧几里得平面几何开始于19世纪初，当时只是数学上的一种好奇，但到19世纪末，数学家们已经意识到，许多具有根本重要性的物体在其基本性质上都是非欧几里得的。对非欧几里得平面几何的详细研究产生了现代数学的几个分支，其中模和自同构形式的研究是最活跃的分支之一。这个领域主要是关于整数的问题，但在使用几何和分析时，它保留了与历史根源的联系。

This award supports the research in Automorphic Forms of Professor Michael Harris of Brandeis University. Dr. Harris's research project is to study the number-theoretic properties of holomorphic and nonholomorphic automorphic forms, and relations with special values of L-functions. His principal tool for attack of his chosen problems will be the cohomology of the toroidal compactification of Shimura varieties. Non-Euclidean plane geometry began in the early nineteenth century as a mathematical curiosity, but by the end of that century, mathematicians had realized that many objects of fundamental importance are non-Euclidean in their basic nature. The detailed study of non-Euclidean plane geometries has given rise to several branches of modern mathematics, of which the study of Modular and Automorphic Forms is one of the most active. This field is principally concerned with questions about the whole numbers, but in its use of Geometry and Analysis, it retains connection to its historical roots.