By Alfred Geroldinger

Additive combinatorics is a comparatively fresh time period coined to appreciate the advancements of the extra classical additive quantity conception, commonly focussed on difficulties concerning the addition of integers. a few classical difficulties just like the Waring challenge at the sum of k-th powers or the Goldbach conjecture are actual examples of the unique questions addressed within the quarter. one of many positive factors of up to date additive combinatorics is the interaction of an excellent number of mathematical thoughts, together with combinatorics, harmonic research, convex geometry, graph concept, chance conception, algebraic geometry or ergodic concept.

This publication gathers the contributions of some of the prime researchers within the quarter and is split into 3 elements. the 2 first elements correspond to the cloth of the most classes introduced, Additive combinatorics and non-unique factorizations, through Alfred Geroldinger, and Sumsets and structure, by means of Imre Z. Ruzsa. The 3rd half collects the notes of many of the seminars which followed the most courses, and which hide a fairly large a part of the tools, options and difficulties of up to date additive combinatorics.

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