On a conjecture of Marton

Ben Green; Freddie Manners; Terence Tao; W. T. Gowers

On a conjecture of Marton

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arxiv 2311.05762 v2 pith:SYVVR5I2 submitted 2023-11-09 math.NT math.CO

W. T. Gowers , Ben Green , Freddie Manners , Terence Tao This is my paper · ORCID

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keywords conjecturecharacteristicmartonargumentdetailsextendsfollowfreiman--ruzsa

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abstract

We prove a conjecture of K. Marton, widely known as the polynomial Freiman--Ruzsa conjecture, in characteristic $2$. The argument extends to odd characteristic, with details to follow in a subsequent paper.

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Stabilizers and NIP arithmetic regularity
math.CO 2025-09 conditional novelty 7.0 of 10

NIP sets in finite groups admit arithmetic regularity through stabilizers, with a new proof and polynomial bounds in the bounded-tripling case.

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