Mathematical Sciences: Arithmetical Algebraic Geometry

这个奖支持里贝特教授在数论方面的研究。自1986年以来，Ribet一直在研究Serre的猜想，这些猜想涉及有理的代数闭包的伽罗瓦群的模p模形式和模p二维表示。Ribet还建议继续他对涉及志村变量的变异体的兴趣，除了p的有理数和表示模幂之外的基域。这是数论领域的研究。数论从整数和诸如整数能被整数整除之类的问题开始。它是数学中最古老的领域之一，最初纯粹出于审美原因而追求它。然而，在过去的半个世纪里，它已经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。

This award supports the research of Professor Ribet to work in number theory. Since 1986, Ribet has been working on Serre's conjectures which relate mod p modular forms and mod p two dimensional representations of the Galois group of an algebraic closure of the rationals. Ribet also proposes to continue his interests in variants involving Shimura varieties, base fields other than the rationals and representation modulo powers of p. 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.