9401391 Yukie This award funds the research of Professor Akihiko Yukie in number theory. Prof. Yukie will use the theory of prehomogeneous vector fields to attempt to compute the density of certain arithmetic objects. In particular, he believes that his techniques can be used on arithmetic aspects of quartic and quintic extensions of global fields. This is research in the branch of mathematics known as number theory. Number theory at its most basic is the study of whole numbers and their properties. This theory begins with the connections between whole numbers such as the divisibility of one number by another. In short order the theory includes some of the most profound problems in science. It is among the oldest fields of mathematics and 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.
