Selections Reprinted from Mathematical Reviews

Review information:

Journal:
Bull. Amer. Math. Soc. **54** (2017), 123-134

Published electronically:
October 11, 2016

Full text:
PDF

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

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

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

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

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

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

Journal: Bull. Amer. Math. Soc.

**54**(2017), 123-134

Article copyright: © Copyright 2016 American Mathematical Society