A new proof of Szemerédi's theorem

By William T. Gowers. 2001

935 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/3e47e427a64759a41e54dd60c27e5663068886ca

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

An improved point‐line incidence bound over arbitrary fields (2016, methodology): “Previous approaches to incidence problems over finite fields relied on techniques from additive combinatorics, and in particular the Balog–Szemerédi–Gowers (BSG) theorem [13].”
A relative Szemerédi theorem (2013, methodology): “2 follows from a direct application of the Gowers-Cauchy-Schwarz [17] inequality for hypergraphs (see [8]).”
Decompositions, approximate structure, transference, and the Hahn–Banach theorem (2008, background): “In [7], the following ‘weak inverse theorem’ was proved for all U-norms.”
Linear Forms and Higher-Degree Uniformity for Functions On $${\mathbb{F}^{n}_{p}}$$ (2010, result): “It was shown in [G01] that if ‖A− δ1‖Uk−1 is small, then A contains roughly the number of arithmetic progressions of length k that you would expect if the elements of A had been selected randomly and independently with probability δ.”
Recent progress on the Kakeya conjecture (2000, background): “The main breakthrough came from Gowers [10], who developed a quantitative version of the Balog-Szemerédi theorem while working on the apparently unrelated problem of locating arithmetic progressions of length 4.”
Near optimal bounds in Freiman's theorem (2011, background): “It is proved in [13] that for every k ∈ N the density of a subset of {1, .”
Montréal notes on quadratic Fourier analysis (2007, methodology): “To prove Proposition 2.2 we will essentially follow the approach of Gowers [8].”
Higher order Fourier analysis of multiplicative functions and applications (2014, methodology): “We recall the definition of the U s-Gowers uniformity norms from [13].”
Open problems in additive combinatorics (2007, positive): “and from the work of Gowers [43] we know that”
On the energy variant of the sum-product conjecture (2016, background): “In contrast, this section is about the Balog–Szemerédi– Gowers theorem [12], which our main proofs avoid.”
On exchangeable random variables and the statistics of large graphs and hypergraphs (2008, background): “3 in Host and Kra’s use in [43] of an infinitary analog of the related arithmetic Gowers norms (see [37, 64]), and the proof is exactly similar.”
The true complexity of a system of linear equations (2007, methodology): “The first steps were taken in [3, 4] for the group ZN in order to give an analytic proof of Szemerédi’s theorem.”