By Alfred Geroldinger
Additive combinatorics is a comparatively contemporary time period coined to realize the advancements of the extra classical additive quantity concept, often focussed on difficulties on the topic of 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 sector. one of many good points of up to date additive combinatorics is the interaction of a superb number of mathematical strategies, together with combinatorics, harmonic research, convex geometry, graph concept, chance conception, algebraic geometry or ergodic thought.
This ebook gathers the contributions of the various best researchers within the zone and is split into 3 components. the 2 first elements correspond to the cloth of the most classes added, Additive combinatorics and non-unique factorizations, via 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 disguise a fairly large a part of the tools, thoughts and difficulties of up to date additive combinatorics.