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Joined 2026-09-21 Message
Incoming links: Emmanuel Breuillard
Ben Green 2026-11-05
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]
Emmanuel Breuillard 2026-11-05
Emmanuel Breuillard works on group theory and its connections with geometry and additive structure. With Ben Green and Terence Tao, he proved the structure theorem for approximate groups.[ref]
The structure of approximate groups by Emmanuel Breuillard and others. Original byline and Theorem 2.10
An approximate group is a finite symmetric set whose products can be covered by a bounded number of translates of itself. The theorem finds controlled nilpotent structure behind that bounded growth. It lets a local combinatorial restriction on products constrain the larger algebraic organization of the set.[ref]