RUI: A High Performance Computing Environment at Smith College

由于高性能符号计算的出现，数学正在发生变化。这笔拨款将资助一个高性能计算集群，以满足史密斯学院各种教师的研究需求。符号计算和代数的一个项目将使用高性能的计算来证明关于特殊Weyl群的猜想，这些猜想需要大量的计算，并致力于为Weyl群和对称空间开发一个新的专门的计算机代数包。计算几何的研究人员将使用聚类来搜索蛋白质主链多边形链的特殊构型，并在R2和R3中生成随机几何对象。图论学家将使用并行计算来确定图的代数、几何和组合参数，以便找到表明特定边界是尖锐的例子。动力系统和数学生物学的一个项目涉及复杂的图像处理数据收集，计算昂贵的高维动力系统的探索，以及优化这些模型对大数据集的拟合。统计学家将使用高性能计算来开发回归模型中不完整数据的似然方法。一个计算几何、刚性和运动模拟的项目将利用生物物理学家和计算化学家在跨学科项目中的并行处理来实验和开发分子模拟的新工具。这项拨款将为研究项目提供计算能力，这些研究项目涵盖广泛的数学领域，包括图论、统计学、计算几何和符号计算。它们既是理论的又是应用的。其中一些项目涉及生物学家、物理学家、化学家和计算机科学家的跨学科工作。使用高性能计算机系统的可能性使我们能够提出不同的问题并设计不同的技术，从而从本质上改变我们的研究过程。提高史密斯学院的计算能力为教师创造了更好的研究环境。这是一所以吸引本科女性从事研究并将她们送到数学科学研究生院的能力而闻名的学院。因此，这项拨款将使那些复杂的、高计算性的、但又便于学生工作的项目得以实现。这将使史密斯大学的本科生（所有女性）和史密斯大学新成立的女性数学中心的学生能够以一种重要的方式参与到与史密斯大学教师合作的严肃研究项目中。

Mathematics is changing due to the advent of high-powered symbolic computation. This grant will fund a high performance computational cluster to serve the research needs of a variety of faculty at Smith College. A project in symbolic computation and algebra will use high powered computation to prove conjectures about exceptional Weyl Groups which require significant computation as well as working toward developing a new specialized computer algebra package for Weyl Groups and symmetric spaces. A researcher in computational geometry will use the cluster to search for special configurations of protein backbone polygonal chains, and to generate random geometric objects, in both R2 and R3. A graph theorist will use parallel computing to determine algebraic, geometric, and combinatorial parameters of graphs in order to find examples that show that particular bounds are sharp. A project in dynamical systems and mathematical biology involves intricate image processing for data collecting, computationally costly exploration of high dimensional dynamical systems, as well as optimization of the fit of these models to large data sets. A statistician will use high powered computation to develop likelihood methods for incomplete data in regression models. A project in computational geometry, rigidity and motion simulation will take advantage of parallel processing in an interdisciplinary project with bio-physicists and computational chemists for experimenting with and developing new tools for molecular simulations.This grant will provide computing power for research projects that span a broad spectrum of mathematics including graph theory, statistics, computational geometry, and symbolic computation. They are both theoretical and applied. Several of the projects involve interdisciplinary work with biologist, physicists, chemists and computer scientists. The possibility of using high-powered computer systems allows us to ask different questions and devise different techniques, thus inherently changing the course of our research. Improving the computational capabilities at Smith College creates a better research environment for the faculty. This is a College known for its ability to engage undergraduate women in research and to send them to graduate school in the mathematical sciences. Thus this grant will enable projects that are sophisticated, highly computational and yet accessible for student work. This will enable Smith undergraduate students (all women), and students at the new Center for Women in Mathematics at Smith to participate in a significant way in a serious research projects in collaboration with Smith faculty.