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Additive combinatorics front page

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Additive combinatorics is a difficult area to define. The basic object of study could be said to be finite subsets of Abelian groups, but the subject is characterized more by its techniques than by its subject matter. These techniques are a blend of ideas from combinatorics, harmonic analysis, ergodic theory, and analytic number theory.

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If your problem can be expressed in terms of convolutions and inner products then take the Fourier transform

If a result is true for random-like sets and true for structured sets, then it may well be true for all sets

Important counterexamples in additive combinatorics