Mathematical Sciences: Results from the Monodromy Method

这个奖项支持弗里德教授的研究工作 在数论中，特别是在应用 单值法 monodromy方法采用以下形式。 一个关于丢番图方程的精确陈述S可以转化为 这：某些品种上的理性点产生了一个理想的 伽罗瓦理论的情况“g”。 忘记了伽罗瓦 理论出现时，我们得到一个群论情形G。 述的方法 应用群论求解G. 然后消除 在“g”的列表中的几何情况不对应于 剩下的是G。 这就留下了一个更难的问题， 几何学上的剩余产生了算术上的情形， 在研究中 这是数论领域的研究。 Number 理论从整数和问题开始，例如 一个整数被另一个整数整除。 它是其中的 最古老的数学领域，它最初是追求 纯粹的美学原因。 然而，在过去的半个世纪里， 它已经成为开发新算法的重要工具， 计算机科学和新的电子纠错码。

This award supports the research of Professor Fried to work in number theory, specifically, in the application of the monodromy method. The monodromy method takes the following form. A precise statement S about Diophantine equations translates to this: Rational points on certain varieties produce a desired Galois theory situation "g". By forgetting where the Galois theory arises, we get a group theory situation G. The method applies the group theory to solve G. It then eliminates geometric situations in the list of "g" that don't correspond to what remains of G. This leaves the harder problem of deciding if what geometrically remains produces the arithmetic situation under investigation. 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.