Additive Combinatorics: Contents

By Terence Tao, V. Vu. 2006

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A quantitative version of the idempotent theorem in harmonic analysis (2006, background): “It is by now described in several places, including the book [25].”
Inverse zero-sum problems II (2008, methodology): “We refer to the recent survey article [10], the lecture notes [14], the monographs [13], in particular Chapters 5 to 7, and [20], in particular Chapter 9, for detailed information on and applications of Davenport’s constant, e.”
On exchangeable random variables and the statistics of large graphs and hypergraphs (2008, background): “Before we leave this subsection, it is worth noting that it is (k + 1)-partite k-uniform hypergraphs, not just ordinary k-hypergraphs, that emerge naturally in the recent hypergraph regularity approaches to Szemerédi’s Theorem (see, for example, Nagle, Rödl and Schacht [53], Gowers [36] and Chapter ”
Uniform expansion bounds for Cayley graphs of SL2(Fp) (2008, methodology): “In particular, we make crucial use (see §3) of the noncommutative product set estimates, obtained by Tao [26], [27] (Theorems 4 and 5); and of the result of Helfgott [9], asserting that subsets of SL2(Fp) grow rapidly under multiplication (Theorem 6).”
The structure of approximate groups (2011, background): “The concept of a local homomorphism is closely related to that of a Freiman homomorphism in additive combinatorics, as discussed for example in [53].”