Mathematical Sciences: Problems in Arithmetic Geometry and Complexity Theory

数学科学：算术几何和复杂性理论问题

• 批准号: 9204265
• 负责人: Jeremy Teitelbaum
• 金额: $ 7.49万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1995-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9204265&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Arithmetic; Geometry

Professor Teitelbaum will work on the p-adic analytic theory of modular curves and its arithmetic implications. He will study higher weight invariants of modular forms, the arithmetic of Shimura varieties and the arithmetic of Drinfeld modular curves. This project falls into the general area of arithmetic geometry - a subject that blends two of the oldest areas of mathematics: number theory and geometry. This combination has proved extraordinarily fruitful - having recently solved problems that withstood generations. Among its many consequences are new error correcting codes. Such codes are essential for both modern computers (hard disks) and compact disks.

泰特尔鲍姆教授将致力于p-adic分析理论 及其算术含义。 他将研究 模形式的更高权重的不变量， Shimura簇与Drinfeld模曲线的算法。 这个项目福尔斯属于算术的一般范畴 几何学-一个融合了两个最古老的领域的主题， 数学：数论和几何。 这种组合有 被证明是非常富有成效的-最近解决了一些问题 经受住了几代人的考验 在其众多后果中， 纠错码 这些准则对现代和 计算机（硬盘）和光盘。