Mathematical Sciences: Dedekind's Eta-function, Combinatorics, Congruences and Approximations

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This grant supports the research of Professor F. Garvan to work on problems in additive number theory. In particular he will concentrate on various conjectures arising from the connection between Dedekind's eta function and partition theory. He also hopes to continue working on the Macdonald root system conjectures. 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.