Mathematical Sciences: Geometry Supercomputer Project

该奖项将为一群 数学家和计算机科学家致力于 与几何学有关。 总体目标：（一）发展和 理解几何和几何算法，以及（ii） 开展几何结构计算工作， 这些结构的图像合成与分析。 的 计算机在这一努力中的作用既是为了解释， 也是推进研究的实验工具。 该项目的新颖性来自于使用一个 超级计算机在几何图形生成和显示中的应用 构造，如分形集，Dehn手术空间，Julia集 曼德尔布罗特集和褶皱表面。 一个焊接的 Kleinian群的数学理论，Teichmuller理论， 分析动力学、组合群论和三维流形 理论是这个项目的基础。 此外它 这将标志着数学研究人员第一次 不同的大学和几个国家将结合 他们的才能在这么大的项目上 大规模通信 在这一共同努力中将广泛使用链接。 目前可用的算法用于设想的目的 但这是不够。 除了理论上的计划外， 和图形实验，工作将在开发 解决组合问题的高级算法 复杂性和更通用的语言设计来建立可移植的 软件和对基本数据深入了解 结构. 经过一段时间的初步设置，研究生和 博士后研究员将被纳入该项目。 跨学科的研究经验将提供一个模式 为未来数学科学的大规模创新做准备。

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.