Minimal Representations and Functoriality

最小表示和函数性

• 批准号: 0138604
• 负责人: Gordan Savin
• 金额: --
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-07-01 至 2007-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0138604&HistoricalAwards=false
• 关键词: Minimal; Representations; Functoriality

Abstract: SavinGordan Savin is continuing his work on minimal representations, with applications to and explicit constructions of some cases of Langlands functoriality which can not be obtained by any other method. The subject of automorphic forms is a crossroad of analysis, algebra, and number theory. It is a subject with roots in indispensable mathematical theories such as Fourier Analysis which impact our everyday lives in many ways. Telecommunications, data transmission, and modern instruments of radiology would not be possible without Fourier Analysis. A purpose of this research is to use tools of analysis (calculus) to answer some questions in number theory, such as to get a better understanding of zeroes of polynomials. Almost everybody knows how to solve a quadratic equation. It is also possible, although it is less known, to find zeroes of any polynomial of degree 3 or 4. A higher degree polynomial, in general, cannot be solved, but can be studied using some special functions of complex variable (called modular forms). This circle of ideas, which surprisingly relates mathematical theories which at first glance do not appear related, is about 30 years old, and called the Langlands Program, after Robert P. Langlands of the Institute of Advanced Sciences in Princeton.

摘要：Saverordan Savin正在继续他的作品最少的表示，并在某些Langlands功能的情况下进行了应用和明确的构造，这些构建方式无法通过任何其他方法获得。 自动形式的主题是分析，代数和数理论的十字路口。这是一个根源在必不可少的数学理论中的主题，例如傅立叶分析，以许多方式影响我们的日常生活。如果没有傅立叶分析，则无法进行电信，数据传输和现代放射学工具。这项研究的目的是使用分析工具（微积分）来回答数字理论中的一些问题，以便更好地了解多项式的零。几乎每个人都知道如何解决二次方程式。尽管鲜为人知，但也有可能找到第3度或4个多项式的零。通常无法解决较高的多项式，但可以使用复杂变量的某些特殊功能（称为模块化形式）来研究）。 这一思想循环令人惊讶地将数学理论乍一看与数学理论无关，大约30岁，并称为兰兰兹计划，在普林斯顿州高级科学研究所的罗伯特·P·兰兰兹（Robert P. Langlands）之后。