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.
