Mathematical Sciences: Stark's Conjectures on Number Fields and Theory Fields

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This award supports the research of Professor Hayes to work in number theory. Professor Hayes will be addressing Stark's conjectures in class field theory. These conjectures are an ingenious and highly original answer to the questions raised by the famous 12 problem of Hilbert. Professor Hayes has given constructed proofs of the abelian Stark conjectures in function fields and he now hopes to apply his insights to the number field case. 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.