W. T. Gowers
Published 2008-11-19Version 1
This paper is partly a survey of certain kinds of results and proofs in additive combinatorics, and partly a discussion of how useful the finite-dimensional Hahn-Banach theorem can be. The most interesting single result is probably a simpler proof of a key step in the proof of the Green-Tao theorem, but several other applications of the method are given. A similarly simplified proof of the Green-Tao transference principle was obtained independently (and expressed in a rather different language) by Reingold, Trevisan, Tulsiani and Vadhan.
Intervals of Antichains and Their Decompositions
Decompositions of even hypercubes into cycles whose length is a power of two
What is the number of decompositions of torus into given number of regions by unions of geodesics?
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