Ben Green works on additive combinatorics and number theory. With Emmanuel Breuillard and Terence Tao, he proved a structure theorem for approximate groups, extending the study of sets with small product growth beyond commutative groups.[ref]
The structure of approximate groups by Emmanuel Breuillard and others. Original byline and Theorem 2.10
He also coauthored the characteristic-two proof of the polynomial Freiman–Ruzsa conjecture with Timothy Gowers, Freddie Manners and Terence Tao. Both projects turn limited growth under addition or multiplication into structural information; the later proof makes entropy a central quantitative tool.[ref]
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