2 citations · 2 across the 3 of their papers we have counts for
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Marton's Conjecture in abelian groups with bounded torsion
W. T. Gowers, Ben Green, Freddie Manners +1
We prove a Freiman--Ruzsa-type theorem with polynomial bounds in arbitrary abelian groups with bounded torsion, thereby proving (in full generality) a conjecture of Marton. Specifi…
On a conjecture of Marton
W. T. Gowers, Ben Green, Freddie Manners +1
We prove a conjecture of K. Marton, widely known as the polynomial Freiman--Ruzsa conjecture, in characteristic . The argument extends to odd characteristic, with details to fol…
Sumsets and entropy revisited
Ben Green, Freddie Manners, Terence Tao
The entropic doubling of a random variable taking values in an abelian group is a variant of the notion of the doubling constant of a fin…
True complexity and iterated Cauchy--Schwarz
Freddie Manners
We prove a polynomial bound in the "true complexity" problem of Gowers and Wolf. The proof uses only repeated applications of the Cauchy--Schwarz inequality, answering negatively a…
Formulations of the PFR Conjecture over
Freddie Manners
The polynomial Fre\uıman--Ruzsa conjecture is a fundamental open question in additive combinatorics. However, over the integers (or more generally or )…