Mathematical Sciences Computing Research Environments

该奖项将为数论、代数和代数几何方面的几个正在进行的研究项目提供必要的计算资源。这些项目涵盖了表示理论、模形式和椭圆曲线、代数簇的拓扑和Picard-Fuchs、微分方程、以及Arakelov理论、K理论和算术几何等相关领域。研究人员计划以不同的方式应用符号代数程序，如Reduce，Maple，Macaulay，来解决这些问题；用这些语言开发程序包；用FORTRAN和C等低级语言开发程序。此外，这些设备将用于支持在这些领域工作的研究生。

This award will provide essential computational resources, to several on-going research projects in number theory, algebra, and algebraic geometry. These projects cover the related areas of representation theory; modular forms and elliptic curves; the topology of algebraic varieties and Picard-Fuchs, differential equations; and Arakelov theory, K-theory, and arithmetic geometry. The investigators plan variously to apply symbolic algebra programs, such as REDUCE, Maple, Macaulay, to these problems; to develop packages of procedures in these languages; and to develop programs in lower level languages such as FORTRAN and C. In addition, the equipment will be used to support graduate students working in these areas.