## Student Number Theory Seminar 2019-20

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4/27/20: Trevor Karn -- *Three proofs of the Cauchy-Davenport inequality*

**Abstract:** First discovered by A.L. Cauchy, forgotten about for a century, and rediscovered by H. Davenport, the Cauchy-Davenport inequality gives a bound on the size of a sum of additive sets, modulo a prime $p$. In this expository talk, we discuss (at least) three proofs of the inequality by combinatorial means, by algebraic means, and by Fourier analytic means.