Mathematical Sciences: Automorphic L-Functions and Representation Theory

该奖项支持普渡大学弗雷登·沙希迪教授在自同构形式和表征理论方面的研究。沙希迪博士的项目之一是研究数域上拟分裂群上的尖点形式，在极大幂零子群的一般特征标上具有非零的傅立叶系数与到处具有一般局部分量之间的可能等价性。另一个相关的项目是证明某些与调和表示有关的局部L函数的全纯。非欧几里得平面几何始于十九世纪初，最初是一种数学奇闻，但到那个世纪末，数学家们已经意识到许多具有根本重要性的物体本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已经产生了现代数学的几个分支，其中模和自同构形的研究是最活跃的之一。这一领域主要涉及关于整数的问题，但在几何和分析的使用中，它保留了与其历史根源的联系。

This award supports the research in automorphic forms and representation theory of Professor Freydoon Shahidi of Purdue University. One of Dr. Shahidi's projects is to study the possible equivalence, for a cusp form on a quasi-split group over a number field, between having a non-zero Fourier coefficient with respect to a generic character of a maximal unipotent subgroup, and having generic local components everywhere. Another related project is to prove the holomorphy of certain local L- functions related to tempered representations. 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.