Mathematical Sciences: Cohomology of Arithmetic Groups

该奖项支持数论研究， 算术群，和教授阿夫纳阿什自守形式 来自俄亥俄州州立大学。阿什博士的项目集中在 n阶整矩阵群的上同调 第一步，走两条主要的路。这些都是 上同调模的结构研究 Hecke代数，及计算机辅助上同调计算 在n为3的情况下， 除了计数，数论，这是研究 整数的性质，是最古老的分支， 数学在现代，数论中的问题 为新数学的产生提供了动力， 纯代数，分析和几何领域;一些最重要的 数论最近最令人惊讶的应用是 出现在理论计算机科学和编码理论中。

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.