Mathematical Sciences: Quadratic Forms and Related Topics

数学科学：二次形式及相关主题

• 批准号: 9107707
• 负责人: Tsit-Yuen Lam
• 金额: $ 18.81万
• 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: 1991
• 资助国家: 美国
• 起止时间: 1991-06-01 至 1996-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9107707&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Quadratic; Forms; Related

This project is concerned with research on Witt rings and quadratic forms. The principal investigator will focus on the computation of Witt kernels for algebraic and transcendental field extensions. He will also continue his work on the theory of semidefinite polynomials and sums of even powers in rational function fields over a real-closed field, with particular attention to quantitative questions on the higher pythagoras numbers of such fields. In another direction, he will carry out further investigations on Ore extensions over division rings, in the hope that this will shed some light on the structure of division rings themselves. The research supported involves the theory of quadratic forms. This, in its simplest form, is the study of polynomial forms of degree two. Equivalently, it is an analysis of the types of inner products that can define the metric geometry of an n-dimensional vector space.

该项目涉及Witt环的研究， 二次型 首席研究员将专注于 代数域和超越域Witt核计算 extensions. 他还将继续他的理论工作， 有理半定多项式与偶次幂和 在实闭域上的函数域，特别注意 关于这些的更高的毕达哥拉斯数的定量问题 领域的 在另一个方向，他将进一步开展 研究了Ore在分割环上的扩张，希望 这将有助于我们了解分裂环的结构 自己 支持的研究涉及二次型理论 forms.最简单的形式就是研究多项式形式 2度。 等价地，它是对 内积可以定义度量几何， n维向量空间