Mathematical Sciences: Integral Quadratic and Hermitian Forms

数学科学：二次积分和厄米形式

• 批准号: 8902227
• 负责人: Donald James
• 金额: $ 4.49万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-07-15 至 1992-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8902227&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Integral; Quadratic; Hermitian

This award supports the research in quadratic forms of Professor Donald James of the Pennsylvania State University. Dr. James's project is to study quadratic and Hermitian forms over integer rings of number fields, with special emphasis on the theory of classification, diagonalization, and representation. 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. The theory of quadratic forms is an aspect of number theory that is almost as ancient as the whole field itself, and was advanced especially far by the great nineteenth-century mathematician C.F. Gauss. This subfield of number theory retains its vitality even today, and has proved to have applications both in physics and in many branches of mathematics.

该奖项支持宾夕法尼亚州立大学唐纳德·詹姆斯教授以二次形式进行的研究。詹姆斯博士的项目是研究数域的整数环上的二次型和厄米特型，特别强调分类、对角化和表示理论。除计数外，数论是数学中最古老的分支，它研究整体数的性质。在现代，数论中的问题提供了在纯代数、分析和几何领域创造新数学的动力；一些最新和最令人惊讶的数论应用出现在理论计算机科学和编码理论中。二次型理论是数论的一个方面，它几乎和整个领域本身一样古老，特别是由19世纪伟大的数学家C.F.高斯提出的。数论的这个子领域直到今天仍然保持着它的活力，并被证明在物理学和数学的许多分支中都有应用。