Algebra, Number Theory and Algebraic Geometry

9700477格罗斯该奖项支持帕维尔·埃廷奥夫、大卫·卡什丹和本尼迪克特·格罗斯在量子化理论、量子群、特殊函数、表示理论和数论等多个领域的研究。Etingof将致力于动力学量子群和特殊函数的新理论，并继续与Kazhdan在量子化和量子群理论方面的合作。Kazhdan将继续他在GL(N)的离散级数和局部域上的极小表示方面的工作，并将致力于代数积分理论。格罗斯将继续他与伽罗瓦gpoup G2通过一种特殊的theta通信来构建动机的工作，并将研究与“代数”自构形式相关的伽罗瓦表示。这个项目涉及到代数和数论的研究。代数可以看作是对抽象对称性的研究。因此，代数在物理和化学领域有直接的应用。特别是，现代物理学中的规范场理论广泛地使用了代数。数论的历史根源在于对整数的研究，它解决了一些问题，比如一个整数被另一个整数整除的问题。它是数学中最古老的分支之一，出于纯粹的美学原因，人们追寻了许多个世纪。现代数论和代数是非常技术性和深刻性的。然而，在过去的半个世纪里，它们已经成为数据传输和处理以及通信系统等领域中各种应用中不可或缺的工具。

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.