Mathematical Sciences: Results from the Monodromy Method

该奖项支持弗里德教授致力于数论的研究，特别是在单列方法的应用方面。Mondromy方法采用以下形式。S关于丢番图方程的精确表述可以翻译为：某些变种上的有理点产生所需的伽罗瓦理论情形“g”。通过忘记伽罗瓦理论出现在哪里，我们得到了一个群论情形G。该方法应用群论来求解G，然后它消除了“G”列表中与G的剩余部分不对应的几何情形。这就留下了一个更难的问题，即确定几何剩余部分是否会产生正在研究的算术情形。这是数论领域的研究。数论始于整数和问题，例如一个整数被另一个整数整除的问题。它是最古老的数学领域之一，最初是出于纯粹的美学原因。然而，在过去的半个世纪里，它已经成为开发计算机科学的新算法和电子产品的新纠错码的必要工具。

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.