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]
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