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SUMMARY:Generalized sum-product phenomenon and group configurations - Emma
 nuel Breuillard (University of Cambridge)
DTSTART:20180301T143000Z
DTEND:20180301T153000Z
UID:TALK96862@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:A large finite set of numbers must grow under either\naddition
  or multiplication (sum-product phenomenon) and more generally under any p
 olynomial map which is not of a special form coming either from addition o
 nly or from multiplication only. Several years ago Elekes and Szabo have s
 hown more generally that if an algebraic constraint is satisfied by too ma
 ny triples of numbers from the same\nfinite set\, then this algebraic cons
 traint must come from the graph of a group operation. In joint work with M
 artin Bays (Muenster) we present a new approach to this problem which enab
 les us to completely classify the type of constraints that can arise in al
 l dimensions and all arities.\n
LOCATION:MR12
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