Computational Initiative in Core Mathematics

密歇根大学数学系将雇用一名技术程序员，其职责是协助教师和研究生完成与数学兴趣有关的研究相关的编程任务，并为SUN和APOLLO计算机执行日常的系统管理任务。此外，该部将为其核心SUN系统购买维修合同。主要研究人员的研究总结如下：组合组将使用SUN工作站研究经典群及其Weyl群。方向将包括对Sn上的Kazhdan-Lusztig表示的研究以及操纵经典群表示的算法的比较。非线性波动组将进行几个以研究与波传播相关的偏微分方程为中心的项目。此外，计算机代数程序将用于协助进行矩阵值代数函数的计算，这是解决大量差分方程所必需的。数论组将使用计算设备在数值上近似p进l函数的特殊值，通过符号处理来解决平面曲线的奇异性，并将有理点的倍数的坐标计算为2属曲线的雅可比矩阵。

The Department of Mathematics at the University of Michigan will hire a technical programmer whose responsibilities will be to assist faculty members and graduate students in research- related programming tasks which are special to mathematical interests, and to perform routine system administration tasks for the SUN and APOLLO computers. In addition, the Department will purchase a maintenance contract for its core SUN system. The research of the principal investigators is summarized below: The combinatorics group will use SUN work-stations to study classical groups and their Weyl groups. Directions will include a study of the Kazhdan-Lusztig representations on Sn and a comparison of algorithms for manipulating representations of classical groups. The nonlinear wave motion group will pursue several projects centered on the study of partial diffferential equations that are associated with wave propagation. In addition, a computer algebra program will be used to assist in doing computations with matrix-valued algebraic functions which are necessary to solve a large set of difference equations. The number theory group will use computing equipment to numerically approximate the special values of p-adic L-functions, resolve plane curve singularities by symbolic manipulation and calculate the coordinates of multiples of rational points as Jacobians of curves of genus two.