Mathematical Sciences: Diophantine Geometry and Differential Algebraic Geometry

数学科学：丢番图几何和微分代数几何

• 批准号: 9500331
• 负责人: Alexandru Buium
• 金额: $ 6.09万
• 依托单位: University of New Mexico
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500331&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Diophantine; Geometry; Differential

9500331 Buium Professor Buium will work in arithmetic geometry specifically problems in Diophantine geometry. He will use techniques from differential algebraic geometry to study Lang's conjecture, the semi-abelian case of Mazur's conjecture as well as relationships between the abc conjecture and logarithmic Kodaira dimension. 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. Professor Buium's research even includes a component coming from classical analysis. 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.

小行星9500331 教授Buium将工作在算术几何特别是丢番图几何问题。他将使用技术从微分代数几何研究郎的猜想，半阿贝尔案件马祖尔的猜想以及之间的关系的abc猜想和对数科代拉维。 这个项目福尔斯属于算术几何的一般领域-一个融合了两个最古老的数学领域：数论和几何的主题。 Buium教授的研究甚至包括来自经典分析的一个组成部分。事实证明，这种结合非常富有成效--最近解决了几代人都无法解决的问题。 在它的许多后果是新的纠错码。 这种代码对于现代计算机（硬盘）和光盘都是必不可少的。