A counterexample to a strong variant of the Polynomial Freiman-Ruzsa conjecture in Euclidean space
arXiv: Number Theory, 2017.
The Polynomial Freiman-Ruzsa conjecture is one of the central open problems in additive combinatorics. If true, it would give tight quantitative bounds relating combinatorial and algebraic notions of approximate subgroups. In this note, we restrict our attention to subsets of Euclidean space. In this regime, the original conjecture consid...More
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