Mathematical Sciences: Quadratic Forms and Ring Theory

数学科学：二次形式和环理论

• 批准号: 8805262
• 负责人: Tsit-Yuen Lam
• 金额: $ 19.72万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-05-15 至 1991-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8805262&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Quadratic; Forms; Ring

This project is concerned with field arithmetic and the algebraic theory of quadratic forms. The principal investigator has a long-term interest in the structure and classification of positive semi-definite polynomials and will continue working in this area. In relation to this work, the principal investigator will study the Hurwitz Problem on the composition of sums of squares by using the techniques of induced representations. The postdoctoral associate on this award will work on the theory of W-groups and will investigate the application of this theory to problems in quadratic forms and field invariants. The research supported involves the theory of quadratic forms which, in its simplest form, is a study of polynomial forms of degree two or equivalently, an analysis of the types of inner products that can define the metric geometry of an n-dimensional vector space. This is an important and difficult branch of mathematics which has attracted the attention of a number of notable mathematicians.

这个项目是关于域算术和 二次型的代数理论。主要研究者 长期以来，他一直对结构和分类感兴趣。 半正定多项式，并将继续工作， 这方面在这项工作中，首席研究员 将研究的赫维茨问题的总和的组成 平方米的使用技术的诱导表示。的 这个奖项的博士后助理将致力于理论， 群，并将研究这一理论的应用， 二次型和域不变量的问题。 支持的研究涉及二次型理论 形式，在其最简单的形式，是一个研究多项式形式 二度或等效，内部类型的分析 可以定义一个n维的度量几何的乘积 向量空间这是一个重要而困难的分支 数学吸引了许多人的注意力， 著名数学家