Mathematical Sciences: Geometry Supercomputer Project

数学科学：几何超级计算机项目

• 批准号: 8619562
• 负责人: Albert Marden
• 金额: $ 237.73万
• 依托单位: University of Minnesota Saint Paul
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-09-01 至 1993-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8619562&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometry; Supercomputer; Project

This award will provide support for a group of mathematicians and computer scientists working on problems related to geometry. The broad objectives (i) to develop and understanding of geometry and algorithms in geometry, and (ii) to carry out work on the computation of geometric structures and on the sythesis and analysis of images of these structures. The role of the computer in this effort is both for explication as well as an experimental tool to advance the research. The novelty of this project derives from the use of a supercomputer in the generation and display of geometric constructs such as fractal sets, Dehn surgery space, Julia sets Mandelbrot sets and pleated surfaces. A welding of the mathematical theories of Kleinian groups, Teichmuller theory, analytic dynamics, combinatorial group theory and 3-manifold theory lies at the foundation of this project. In addition it will mark the first time that mathematical researchers located at diverse universities and in several countries will be combining their talents on such a large project. Large scale communication links will be used extensively in this joint effort. Currently available algorithms for the purposes envisioned here are insufficient. In addition to the planned theoretical and graphical experimentation, work will be done in developing advanced algorithms addressing problems of combinatorial complexity and more general language design to establish portable software and advance understanding of fundamental data structures. After an initial set-up period, graduate students and postdoctoral associates will be incorporated into the project. The interdisciplinary research experience will provide a model for future large-scale initiatives in the mathematical sciences.

该奖项将为一组研究几何相关问题的数学家和计算机科学家提供支持。广泛的目标(i)发展和理解几何和几何算法，以及（ii）开展几何结构计算和这些结构图像的合成和分析工作。在这项工作中，计算机的作用既是为了解释，也是为了推进研究的实验工具。这个项目的新颖之处在于使用超级计算机来生成和显示几何结构，如分形集、Dehn手术空间、Julia集、Mandelbrot集和褶皱表面。结合Kleinian群的数学理论、Teichmuller理论、解析动力学、组合群论和3流形理论是本项目的基础。此外，这将标志着来自不同大学和几个国家的数学研究人员将首次在如此大的项目上结合他们的才能。在这一共同努力中，将广泛使用大规模通信链路。目前可用的算法在这里设想的目的是不够的。除了计划中的理论和图形实验外，还将开发先进的算法来解决组合复杂性和更通用的语言设计问题，以建立可移植的软件和提高对基本数据结构的理解。在初始设置期后，研究生和博士后将被纳入该项目。跨学科的研究经验将为未来数学科学的大规模倡议提供一个模型。