Algebra, Number Theory and Algebraic Geometry

9700477毛额 该奖项支持研究的帕维尔Etingof，大卫Kazhdan和本尼迪克特格罗斯在几个领域的理论量子化，量子群，特殊功能，表示论和数论。 Etingof将工作的新理论的动态量子群和特殊功能，并继续联合工作与Kazhdan量子化和理论的量子群。 Kazhdan将继续他的工作离散系列GL（n）和最小的代表性在当地领域，并将工作理论的代数整合。 格罗斯将继续他的工作建设的动机与伽罗瓦gpoup G2，通过一个特殊的θ对应，并将研究伽罗瓦表示相关的“代数”自守形式。 该项目涉及代数和数论的研究。代数学可以看作是抽象的对称性研究。因此，代数直接应用于物理和化学领域。特别是，现代物理学规范场理论广泛使用代数。 数论有其历史根源，在研究整个数字，解决这样的问题，如那些处理整除一个整数由另一个。它是数学中最古老的分支之一，几个世纪以来，人们纯粹出于美学的原因而追求它。现代数论和代数是非常技术性和深刻的。然而，在过去的半个世纪，它们已经成为在诸如数据传输和处理以及通信系统等领域中的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.