Generalized sum-product phenomenon and group configurations

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• Emmanuel Breuillard (University of Cambridge)
• Thursday 01 March 2018, 14:30-15:30
• MR12.

If you have a question about this talk, please contact Andrew Thomason.

A large finite set of numbers must grow under either addition or multiplication (sum-product phenomenon) and more generally under any polynomial map which is not of a special form coming either from addition only or from multiplication only. Several years ago Elekes and Szabo have shown more generally that if an algebraic constraint is satisfied by too many triples of numbers from the same finite set, then this algebraic constraint must come from the graph of a group operation. In joint work with Martin Bays (Muenster) we present a new approach to this problem which enables us to completely classify the type of constraints that can arise in all dimensions and all arities.

This talk is part of the Combinatorics Seminar series.

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