Mathematical Sciences: Toric Geometry, Lattice Points in Polytopes, and Zeta Functions

数学科学：环面几何、多面体中的格点和 Zeta 函数

• 批准号: 9404627
• 负责人: Robert Morelli
• 金额: $ 8.07万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1997-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9404627&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Toric; Geometry; Lattice

Morelli This award funds the research of Professor Robert Morelli into toric varieties and lattice point counting. The work is a combination of ideas from several parts of number theory and combinatorics. The work includes developing general techniques for counting points in convex polytopes. The investigator also intends to explore connections between these problems and problems involving zeta functions and modular forms. This work falls into the general areas of Number Theory and Combinatorics. Number Theory is the study of properties of the whole numbers and is the oldest branch of systematic mathematics. Combinatorics is the study of problems involving the counting of complex collections. The research involves establishing general methods for counting regularly distributed points within regular boundaries. This has important application in many different areas of mathematics and science. Recently both Number Theory and Combinatorics have found applications in theoretical computer science and modern communication. ***

这个奖项资助了罗伯特·莫雷利教授在环簇和格点计算方面的研究。这项工作融合了数论和组合学的几个部分的思想。这项工作包括开发计算凸多面体中的点的一般技术。研究人员还打算探索这些问题与涉及Zeta函数和模形式的问题之间的联系。这项工作属于数论和组合学的一般领域。数论是研究整体数的性质的学科，是系统数学中最古老的分支。组合学是研究复杂集合的计数问题的学科。这项研究涉及建立计算规则边界内规则分布点数的一般方法。这在数学和科学的许多不同领域都有重要的应用。近年来，数论和组合学都在理论计算机科学和现代通信中得到了应用。***