Mathematical Sciences: The Structure of Polynomials in Several Variables and Hilbert Identities

数学科学：多变量多项式的结构和希尔伯特恒等式

• 批准号: 9500507
• 负责人: Bruce Reznick
• 金额: $ 7.5万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-05-15 至 1998-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500507&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Structure; Polynomials; Several

Polynomials in several variables are important and ubiquitous. The principal investigator will work on the creation of new Hilbert Identities; the further analysis of spherical designs; the development of a theory of blenders; the representation of forms as sums of powers of linear forms; and the continuing explorations of sums of powers of rational functions over fields. These studies touch many areas of mathematics including algebra, number theory, combinatorics, algebric geometry, harmonic analysis and functional analysis. 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. The study of quadratic forms has deep interrelations with algebraic geometry and algebraic K-theory.

多元多项式是重要且普遍存在的。 首席研究员将致力于创造新的希尔伯特恒等式;进一步分析球形设计;发展一个理论的搅拌机;表示形式的权力总和的线性形式;和不断探索的权力总和的合理职能领域。 这些研究涉及数学的许多领域，包括代数、数论、组合学、代数几何、调和分析和泛函分析。 支持的研究涉及二次型理论。 最简单的形式是研究二次多项式形式。 等价地，它是一个分析类型的内积，可以定义度量几何的n维向量空间。 二次型的研究与代数几何和代数K-理论有着深刻的相互关系。