Mathematical Sciences: Center for Computation & Visualization of Geometric Structures

明尼苏达大学的这项提案要求资金， 建立计算科学技术中心， 几何结构的可视化。 中心主任 是阿尔伯特马尔登教授 该中心涉及18位数学家的合作 来自美国和欧洲的13个机构 在 除了来自明尼苏达大学的教师，该中心 将涉及来自杨百翰，康奈尔，柯朗 研究所，哈佛，普林斯顿，罗格斯，纽约州立大学斯托尼布鲁克， 加州大学圣地亚哥分校以及Ecole Normale 贝尔、巴黎、沃里克大学和AT T贝尔 Laboratories. 在几何超级计算机的支持下 在明尼苏达州的项目，这些研究人员一直在合作， 近三年 通过这次合作，他们 证明了他们有能力建造这样一个分布式中心 功能 数学是一门极其丰富多样的学科， 有分裂成许多分支学科的趋势， 他们之间的沟通很少，或者他们密切相关的领域， 比如计算机科学。 该中心的目标是将这些 在统一的主题下， 几何学和计算机上的几何表示。 的 中心的科学计划是基于科学的核心， 起源于“纯”数学的研究， 物理现象的模型。 它分为五组： 拓扑学;几何与对称动力学;几何优化; 计算、几何和图形;以及分形几何。 的 拟议的研究包括一系列高层次的数学 以几何学为中心， 在高质量的实验室环境中， 计算、图形和可视化。 通过共同 以可视化为主线，研究形成一个连贯的整体。 该中心将在打字的不同领域提供领导， 数学和计算机科学结合在一起， 领域之间的知识转移。 此外， 提出的一些问题将需要制定 可以超越基本数学领域的软件工具 参与并在其他领域的研究中有重要的应用 科学领域，如分子生物学，其中可视化 建模是必不可少的。 该中心将刺激增强活动在学前教育 教育和人力资源开发。//

This proposal from the University of Minnesota, requests funds to establish a Science and Technology Center for Computation and Visualization of Geometric Structures. The Director of the Center will be Professor Albert Marden. The Center involves collaboration among eighteen mathematicians from thirteen institutions throughout the U.S. and Europe. In addition to faculty from the University of Minnesota, the Center will involve participants from Brigham Young, Cornell, Courant Institute, Harvard, Princeton, Rutgers, SUNY Stony Brook, University of California, San Diego, as well as Ecole Normale Superieur, Paris, the University of Warwick, and AT&T Bell Laboratories. Under the aegis of the Geometry Supercomputer Project at Minnesota, these researchers have been collaborating for the past three years. Through this collaboration they have demonstrated their ability to make such a distributed Center function. The subject of mathematics, an extremely rich and varied territory, has had a tendency to fragment into many subdisciplines, with little communication between them, or their closely related fields, such as computer science. The goal of the Center is to tie these differently perceived fields together under the unifying topic of geometry and geometric representation on the computer. The Center's scientific program is based on a core of scientific investigations whose origins are in "pure" mathematics as well as models of physical phenomenon. It is organized into five groups: topology; geometry and symmetry dynamics; geometric optimization; computation, geometry and graphics; and fractal geometry. The proposed research includes a range of high-level mathematics centered on geometry utilizing high-level computer science centered on geometry, in the environment of a high-quality laboratory for computation, graphics, and visualization. Through the common thread of visualization, the research forms a coherent body. The Center will provide leadership in typing diverse fields of mathematics and computer science together and will facilitate knowledge transfer between fields. In addition, the solutions of some of the proposed problems will require the development of software tools that could reach beyond the basic mathematical areas involved and have important applications to research in other scientific fields, such as molecular biology, where visualization modeling are essential. This Center will stimulate enhanced activity in precollege education and in the development of human resource.//