Workshop on Graphs and Arithmetic

图表与算术研讨会

• 批准号: 1007973
• 负责人: Wen-Ching Li
• 金额: $ 2.5万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-03-01 至 2012-02-29
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1007973&HistoricalAwards=false
• 关键词: Workshop; Graphs; Arithmetic

There is a long history of interaction between number theory and combinatorics. In the past two decades, deep results in automorphic forms and number theory were used to construct (optimal) expanders, which are known to have wide applications in computer science and communication networks. These techniques were generalized to construct higher dimensional analogues. Very recently, zeta functions for graphs have been extended to complexes. They contain topological and spectral information of the combinatorial objects so that the Riemann hypothesis is satisfied if and only if the object is spectrally extremal. Furthermore, exciting developments in arithmetic combinatorics in recent years provide new tools to construct families of good expanders, which in turn are used to obtain deep number theoretic results. At the same time, the concept of expansion is extended in group theory and computer science to a different new context.A workshop on graphs and arithmetic will take place March 8-12, 2010, at CRM,Montreal, Canada, to review recent exciting developments in expanders and number theory. The focus will be on the interconnections between combinatorics, group theory and number theory. Both theories and applications will be emphasized. Seventeen invited speakers are from the US. To cover the expenses of the invited speakers and partially support graduate students and recent doctorates, support from the NSF is sought to supplement the fundscommitted by the CRM.

数论和组合数学之间的相互作用有着悠久的历史。在过去的二十年中，自同构形式和数论的深入成果被用来构造（最优）扩展器，众所周知，它们在计算机科学和通信网络中具有广泛的应用。这些技术被推广到构建更高维度的类似物。最近，图的 zeta 函数已扩展到复形。它们包含组合对象的拓扑和光谱信息，因此当且仅当对象是光谱极值时黎曼假设才得到满足。此外，近年来算术组合学的令人兴奋的发展提供了构建良好扩展器族的新工具，而这些扩展器又可用于获得深入的数论结果。与此同时，展开式的概念在群论和计算机科学中扩展到了不同的新背景。图形和算术研讨会将于 2010 年 3 月 8 日至 12 日在加拿大蒙特利尔的 CRM 举行，回顾展开器和数论方面最近令人兴奋的发展。重点将放在组合数学、群论和数论之间的相互联系。理论和应用都会得到强调。十七位受邀演讲者来自美国。为了支付受邀演讲者的费用并部分支持研究生和最近的博士学位，寻求 NSF 的支持来补充 CRM 承诺的资金。