Studies in Automorphic Representations

9401466罗加夫斯基该奖项资助乔纳森·罗加夫斯基教授在自同构表示理论及其与数论的关系方面的研究。这项工作有三个目标：第一，构造具有特定权重的Hilbert模形式的动机；第二，证明一个将Heisenberg模型的存在与多重配对联系起来的猜想；最后，在酉群的某些表示与一般线性群的表示之间建立对应关系。这项研究是数论的一部分，通常被称为朗兰计划。数论是研究全体数的性质的学科，是数学中最古老的分支。从一开始，数论中的问题就为在该学科的其他不同部分创造新的数学提供了动力。朗兰德的计划是一种将数论与微积分联系起来的一般哲学；它体现了研究整数的现代方法。现代数论是非常技术性和深刻性的，但它在理论计算机科学和编码理论等领域有着惊人的应用。

9401466 Rogawski This award funds the investigations of Professor Jonathan Rogawski in the theory of automorphic representations and its relations with number theory. The work has three objectives; first to construct motives for Hilbert modular forms of a particular weight, second to prove a conjecture relating the existence of Heisenberg models to the multiplicity pairing, and finally to construct a correspondence between certain representations of unitary groups with representations of the general linear group. This research is in a part of number theory generally known as the Langland's program. Number theory is the study of the properties of the whole numbers and is the oldest branch of mathematics. From the beginning problems in number theory have furnished a driving force in creating new mathematics in other diverse parts of the discipline. The Langland's program is a general philosophy that connects number theory with calculus; it embodies the modern approach to the study of whole numbers. Modern number theory is very technical and deep, but it has had astonishing applications in areas like theoretical computer science and coding theory.