Mathematical Sciences: Arithmetical Algebraic Geometry

点击翻译按钮获取中文摘要

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.