Near optimal bounds in Freiman's theorem

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Some new inequalities in additive combinatorics (2012, methodology): “E(A,B) ≪ MlogM|A||B|3/2 . 4 Weighted Katz–Koester transform In the section we have deal with so–called Katz–Koester trick [11] based on inequality (3), which has recently found many applications, see [10, 14, 15, 17, 18, 19, 20, 21, 24]. We collect all required tools in the section. First of all let”
On the Bogolyubov–Ruzsa lemma (2010, methodology): “With this in mind the extension from Z to arbitrary abelian groups is due to Green and Ruzsa [GR07], and the first good bounds to Schoen [Sch10] for certain classes of groups.”
The structure theory of set addition revisited (2012, methodology): “For example, Gowers himself used it to spectacularly improve the bounds in Szemerédi’s theorem; Szemerédi and Vu used it to investigate long arithmetic progressions in [SV06]; Tao and Vu used it to investigate random matrices in [TV07]; Schoen records many shorter consequences at the end of his pape”