Algebra, Number Theory and Algebraic Geometry

代数、数论和代数几何

• 批准号: 9700477
• 负责人: Benedict Gross
• 金额: $ 47.51万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-07-01 至 2002-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9700477&HistoricalAwards=false
• 关键词: Algebra; Number; Theory; Algebraic; Geometry

9700477 Gross This award supports research of Pavel Etingof, David Kazhdan and Benedict Gross in several areas of the theory of quantization, quantum groups, special functions, representation theory and number theory. Etingof will work on the new theory of dynamical quantum groups and special functions, and continue the joint work with Kazhdan on quantization and the theory of quantum groups. Kazhdan will continue his work on the discrete series for GL(n) and on minimal representations over local fields and will work on the theory of algebraic integration. Gross will continue his work on a construction of motives with Galois gpoup G2, via an exceptional theta correspondence, and will study Galois representations associated to "algebraic" automorphic forms. This project involves research in Algebra and Number Theory. Algebra can be though of as the study of symmetry in the abstract. As such, Algebra has direct applications to areas of physics and chemistry. In particular, the modern theory of gauge fields in physics uses algebra extensively. Number Theory has its historical roots in the study of the whole numbers, addressing such questions as those dealing with the divisibility of one whole number by another. It is among the oldest branches of mathematics and was pursued for many centuries for purely aesthetic reasons. Modern Number Theory and Algebra are very technical and deep. However, within the last half century, they have become indispensable tools in diverse applications in areas such as data transmission and processing, and communication systems.

9700477 Gross 该奖项支持 Pavel Etingof、David Kazhdan 和 Benedict Gross 在量子化理论、量子群、特殊函数、表示论和数论等多个领域的研究。 Etingof将致力于新的动态量子群和特殊函数理论的研究，并继续与Kazhdan在量子化和量子群理论方面的合作。 Kazhdan 将继续研究 GL(n) 的离散级数和局部域的最小表示，并将研究代数积分理论。 格罗斯将继续通过特殊的 theta 对应，利用 Galois gpoup G2 构建动机，并将研究与“代数”自守形式相关的 Galois 表示。 该项目涉及代数和数论的研究。代数可以被认为是抽象的对称性研究。因此，代数可以直接应用于物理和化学领域。特别是，现代物理学中的规范场理论广泛使用了代数。 数论的历史根源在于对整数的研究，解决诸如一个整数能否被另一个整数整除等问题。它是数学最古老的分支之一，几个世纪以来纯粹出于美学原因而被人们所追求。现代数论和代数非常技术性和深度。然而，在过去的半个世纪中，它们已成为数据传输和处理以及通信系统等领域的各种应用中不可或缺的工具。