Discrete Groups, Expanding Graphs and Pro-P Methods

离散群、展开图和 Pro-P 方法

• 批准号: 0101174
• 负责人: Alexander Lubotzky
• 金额: $ 9万
• 依托单位: Yale University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-07-01 至 2004-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0101174&HistoricalAwards=false
• 关键词: Discrete; Groups; Expanding; Graphs; Pro

The project looks at several seemingly unrelated problems from a unified perspective. It deals with questions of expansion of Cayley graphs of finite groups, eigenvalues of Riemannian manifolds and pro-p groups. Somewhat unexpectedly, methods and results from one field shed a new light on the other areas. The work is promising to be very interdisciplinary and should have, if successful, a serious impact on several mathematical fields, pure and applied. On the pure side, it is expected to have a completely new approach toward the Thurston conjecture on three-dimensional manifolds. On the applied side, it will bring a better understanding of expanding graphs, graphs which serve as basic building blocks for various communication networks.

这个项目从一个统一的角度看待几个看似无关的问题。 它涉及有限群的凯莱图的展开、黎曼流形的特征值和pro-p群的问题。 有些出乎意料的是，一个领域的方法和结果为其他领域带来了新的启示。 这项工作是有希望的是非常跨学科的，应该有，如果成功的话，严重影响几个数学领域，纯和应用。 在纯粹的方面，它有望对三维流形上的Thurston猜想有一个全新的方法。 在应用方面，它将带来对扩展图的更好理解，这些图作为各种通信网络的基本构建块。