Mathematical Sciences Research Equipment

这个项目是数学科学计划科学计算研究设备活动补助金下的一项设备赠款。该项目涉及购买专门用于支持数学科学研究的特殊用途设备。一般来说，这种设备是几个研究项目共同需要的，很难单独在一个项目上证明是合理的。来自国家科学基金会的这项研究设备支持，加上制造商提供的设备折扣和捐款，以及提交机构的重大费用分摊。该项目为大学、产业界和政府合作支持数学科学的基础研究提供了一个很好的范例。该设备将用于几个研究项目，包括：(1)开发交互图形例程，利用该例程将实现用于计算紧致Shimura曲面上的Hirzebruch-Zagier圈的两两交的重数的算法，(2)油藏模拟、地球物理和生物学中各种参数识别问题的近似解的数值方法；(3)建立一个自动搜索李代数表示的无穷小变形的符号计算环境；(4)计算作用在李群齐次空间上的有限子群。

This project is an equipment grant under the activity Grants For Scientific Computing Research Equipment For The Mathematical Sciences program. The project involves the purchase of special purpose equipment dedicated to the support of research in the mathematical sciences. In general, this equipment is required jointly by several research projects and would be difficult to justify on one project alone. This research equipment support from the National Science Foundation is coupled with discounts and contributions of equipment from manufacturers and significant cost-sharing from the submitting institution. This project provides a good example of university, industrial, and government cooperation in the support of basic research in the mathematical sciences. This equipment will be used for several research projects including: (1) development of interactive graphics routines with which algorithms for computing the pairwise intersection multiplicities of Hirzebruch-Zagier cycles in a compact Shimura surface will be implemented, (2) numerical methods for approximate solutions for various identification of parameters problems appearing in reservoir simulation, geophysics and biology, (3) creation of a symbolic computational environment in which the search for infinitesimal deformations of Lie algebra representations will be implemented automatically, (4) computation of finite subgroups acting on homogeneous spaces of a Lie group.