Mathematical Sciences: An Investigation of Relations Between Permutation Representations and Trace Forms of FieldExtensions

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This research planning grant will enable the researcher to continue her investigation into the relationship between permutation representations and the trace form in number fields. The idea is to study how the trace form varies in a family of Galois extensions of number fields. 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.