Bulletin of the American Mathematical Society

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MR: 1631259 (2000d:11019)
W. T. Gowers
A new proof of Szemerédi’s theorem for arithmetic progressions of length four.
Geometric and Functional Analysis 8, (1998), no. 3, 529–551
Reviewed by: D. R. Heath-Brown

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MR: 2150389 (2007b:37004)
Bernard Host and Bryna Kra
Nonconventional ergodic averages and nilmanifolds.
Annals of Mathematics. Second Series 161, (2005), no. 1, 397–488
Reviewed by: Randall McCutcheon

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MR: 2289012 (2008a:11002)
Terence Tao and Van Vu
Additive combinatorics.
Cambridge Studies in Advanced Mathematics, 105, Cambridge University Press, Cambridge, 2006, xviii+512 pp., ISBN 978-0-521-85386-6; 0-521-85386-9, $85.00
Reviewed by: Sergeĭ V. Konyagin and Ilya D. Shkredov

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MR: 2680398 (2011j:11177)
Benjamin Green and Terence Tao
Linear equations in primes.
Annals of Mathematics. Second Series 171, (2010), no. 3, 1753–1850
Reviewed by: Tamar Ziegler

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MR: 2912706
D. H. J. Polymath
A new proof of the density Hales-Jewett theorem.
Annals of Mathematics. Second Series 175, (2012), no. 3, 1283–1327
Reviewed by: T. C. Brown

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MR: 2931680
Terence Tao
Higher order Fourier analysis.
Graduate Studies in Mathematics, 142, American Mathematical Society, Providence, RI, 2012, x+187 pp., ISBN 978-0-8218-8986-2
Reviewed by: David Conlon