By Sarah Peluse
In this talk, I will define the Gowers uniformity norms, discuss the role they play in Gowers's proof of Szemerédi's theorem, and state a couple of versions of the inverse theorem for these norms, including the “local” version used in Gowers's proof. As a warm-up for thinking about the inverse theory of the Gowers norms, I will also present a proof of the “99% inverse theorem”, which concerns a model case of the inverse problem.
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