Yet another proof of Szemeredi's theorem

TL;DR

This paper proves Szemeredi's theorem on arithmetic progressions by leveraging the inverse conjectures for Gowers norms, building on the density-increment strategy of Roth and Gowers.

Contribution

It establishes Szemeredi's theorem from the inverse Gowers norm conjectures, which were recently proven by the authors and Ziegler, providing a new proof approach.

Findings

Szemeredi's theorem derived from inverse Gowers norm conjectures

Verification of inverse Gowers conjectures for s

Connection between density-increment strategy and Gowers norms

Abstract

Using the density-increment strategy of Roth and Gowers, we derive Szemeredi's theorem on arithmetic progressions from the inverse conjectures GI(s) for the Gowers norms, recently established by the authors and Ziegler.