Mathematical Sciences: Combinatorics and Number Theory

数学科学：组合数学和数论

• 批准号: 9001677
• 负责人: Marvin Wunderlich
• 金额: --
• 依托单位: National Security Agency
• 依托单位国家: 美国
• 项目类别: Interagency Agreement
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1992-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001677&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Combinatorics; Number; Theory

This award supports the research in combinatorics and number theory of Professor Wen-Ching Li of The Pennsylvania State University. Dr. Li's project is centered on questions relating modular forms to graph theory. Among the questions she will investigate are: to realize certain Ramanujan graphs as quotients of trees associated to projective linear groups over p-adic fields; to continue her collaboration with Dr. F.K. Hwang of Bell Laboratories on generalized double loop networks; and to study the Galois structure of p-Sylow subgroups of ideal class groups. Non-Euclidean plane geometry began in the early nineteenth century as a mathematical curiosity, but by the end of that century, mathematicians had realized that many objects of fundamental importance are non-Euclidean in their basic nature. The detailed study of non-Euclidean plane geometries has given rise to several branches of modern mathematics, of which the study of modular and automorphic forms is one of the most active. This field is principally concerned with questions about the whole numbers, but in its use of geometry and analysis, it retains connection to its historical roots. The work of Professor Li is in this tradition, but extends beyond the traditional boundaries of the theory of modular forms in a particularly interdisciplinary thrust.

该奖项支持宾夕法尼亚州立大学李文清教授在组合学和数论方面的研究。李博士的项目集中在与模块化形式图论相关的问题上。她将研究的问题包括：实现某些Ramanujan图作为与p进域上的投影线性群相关的树的子图;继续与F.K.博士合作。Hwang的关于广义双环网络的研究，并研究了理想类群的p-Sylow子群的Galois结构。非欧平面几何开始于19世纪早期，当时它只是一种数学上的好奇心，但到了那个世纪末，数学家们已经认识到，许多具有根本重要性的物体在其基本性质上都是非欧的。对非欧平面几何的详细研究产生了现代数学的几个分支，其中模形式和自守形式的研究是最活跃的分支之一。该领域主要关注有关整数的问题，但在几何和分析的使用中，它保留了与其历史根源的联系。李教授的工作是在这一传统，但超出了传统的边界理论的模块形式在一个特别的跨学科的推力。