Mathematical Sciences: Analytic and Algebraic Methods in Geometry and Number Theory

该奖项支持普林斯顿大学志村吾郎教授对自同构形式和表征的研究。志村博士的工作将主要涉及以下主题：算术类型的自同构形式的周期；对称空间上的微分算子；以及各种ζ函数和爱森斯坦级数的特殊值。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。这个领域主要关注关于整数的问题，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 and representations of Professor Goro Shimura of Princeton University. Dr. Shimura's work will be concerned principally with the topics of: the periods of automorphic forms of arithmetic type; differential operators on symmetric spaces; and the special values of various zeta functions and Eisenstein series. 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.