Mathematical Sciences: Mathematical Science: Modular forms, Elliptic curves and galois reprentations"

数学科学：数学科学：模形式、椭圆曲线和伽罗瓦表示"

• 批准号: 9224925
• 负责人: Andrew Wiles
• 金额: $ 27.01万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-05-01 至 1997-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9224925&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Science; Modular; forms

This award supports the research of Professor Wiles to work in number theory. The aim of this project is to try to prove that certain families of elliptic curves over the field of rationals is modular, the famous conjecture of Shimura-Taniyama-Weil. The approach will be to prove in general that suitable Galois representations with values in the two by two matrices , with entries in the field with three elements, always arise from modular forms. This is research in the field of number theory. Number theory starts with the whole numbers and questions such as the divisibility of one whole number by another. It is among the oldest fields of mathematics and it was originally pursued for purely aesthetic reasons. However, within the last half century, it has become an essential tool in developing new algorithms for computer science and new error correcting codes for electronics.

该奖项支持怀尔斯教授在数论方面的研究。 该项目的目的是试图证明有理数域上的某些椭圆曲线族是模的，即志村谷山韦尔的著名猜想。 该方法将证明一般情况下，具有二乘二矩阵中的值的合适的伽罗瓦表示，以及具有三个元素的字段中的条目，总是从模形式中产生。 这是数论领域的研究。 数论从整数和诸如一个整数能否被另一个整数整除之类的问题开始。 它是最古老的数学领域之一，最初纯粹出于美学原因而追求它。 然而，在过去的半个世纪中，它已成为开发计算机科学新算法和电子学新纠错码的重要工具。