Mathematical Sciences: Cohomology of Arithmetic Groups

数学科学：算术群的上同调

• 批准号: 8919696
• 负责人: Avner Ash
• 金额: --
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-01 至 1994-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8919696&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Cohomology; Arithmetic; Groups

This award supports the research in number theory, arithmetic groups, and automorphic forms of Professor Avner Ash of Ohio State University. Dr. Ash's project centers on the cohomology of the group of n-by-n integral matrices with determinant 1, and will follow two main paths. These are the study of the structure of the cohomology as a module for the Hecke algebra, and computer-aided calculation of cohomology groups in the case where n is 3. Except for counting, number theory, which is the study of the properties of the whole numbers, is the oldest branch of mathematics. In modern days, problems in number theory have furnished the driving force to creation of new mathematics in the fields of pure algebra, analysis, and geometry; some of the most recent and most astonishing applications of number theory have appeared in theoretical computer science and coding theory.

该奖项支持俄亥俄州立大学 Avner Ash 教授在数论、算术群和自守形式方面的研究。 Ash 博士的项目以行列式 1 的 n×n 积分矩阵群的上同调为中心，并将遵循两条主要路径。这些是作为赫克代数模块的上同调结构的研究，以及 n 为 3 的情况下上同调群的计算机辅助计算。除了计数之外，数论是研究整数，是数学最古老的分支。如今，数论中的问题为纯代数、分析和几何领域的新数学创造提供了动力。数论的一些最新且最令人惊讶的应用出现在理论计算机科学和编码理论中。