Approximate groups

Approximate groups

Tue, 02/06/2009
14:30 		Ben Green (Cambridge) Combinatorial Theory Seminar Add to calendar L3
Approximate groups
Let $ A $ be a finite set in some ambient group. We say that $ A $ is a $ K $-approximate group if $ A $ is symmetric and if the set $ A.A $ (the set of all $ xy $, where $ x $, $ y $ lie in $ A $) is covered by $ K $ translates of $ A $. I will illustrate this notion by example, and will go on to discuss progress on the "rough classification" of approximate groups in various settings: abelian groups, nilpotent groups and matrix groups of fixed dimension. Joint work with E. Breuillard.