Lie Groups, Representations and Discrete Mathematics

李群、表示和离散数学

• 批准号: 0542278
• 负责人: Avi Wigderson
• 金额: $ 2万
• 依托单位: Institute For Advanced Study
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-02-15 至 2007-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0542278&HistoricalAwards=false
• 关键词: Lie; Groups; Representations; Discrete; Mathematics

Abstract for Lie Groups, Representations and Discrete Mathematics ConferenceFebruary 6-10, 2006The conference is part of a year-long program at the Institute for Advanced Study in Princeton, New Jersey on Lie Groups, Representations and Discrete Mathematics. The last two decades show some deep and surprising connections between questions and results in number theory in general, automorphic forms in particular and seemingly unrelated problems in discrete mathematics and computer science. These developments led to the constructions of Ramanujan graphs and complexes and to the solution of several long-standing problems. Many of these questions are related to the notion of expanders. This is a basic concept in combinatorics and computer science which found its way to the representation theory and the theory of discrete subgroups of Lie groups. Recently, it also found its use in 3-dimensional hyperbolic geometry.The goal of the conference is to bring together experts from these quite different areas of mathematics and computer science to present their work and to strengthen the potential cooperation between these scientists who usually do not meet or attend the same conferences.

李群、表示和离散数学会议摘要该会议是新泽西州普林斯顿高等研究院为期一年的李群、表示和离散数学项目的一部分。在过去的二十年中，数论中的问题和结果之间存在着深刻而令人惊讶的联系，特别是自同态形式，以及离散数学和计算机科学中看似无关的问题。这些发展导致了拉马努金图和复体的构造，并解决了几个长期存在的问题。其中许多问题都与扩展器的概念有关。这是组合学和计算机科学中的一个基本概念，它在李群的表示理论和离散子群理论中得到了应用。最近，它也在三维双曲几何中得到了应用。会议的目标是汇集来自这些完全不同的数学和计算机科学领域的专家来展示他们的工作，并加强这些科学家之间的潜在合作，这些科学家通常不会见面或参加相同的会议。