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Difference sets and nonnegative exponential sums

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Given a prescribed subset R of some Abelian group, what is the maximal cardinality of a set A such that the difference set A-A lies in R? Several problems from strikingly different parts of mathematics fit into this general setting, including sphere-packings, number theoretical problems and mutually unbiased bases. In this talk I will describe a general method (due to Delsarte) involving nonnegative exponential sums which leads to upper bounds on the cardinality (or density) of such sets A. Possible applications will be mentioned. Some of the material is joint work with Imre Z. Ruzsa.

This talk is part of the Discrete Analysis Seminar series.

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