Title:  The non-commutative Waring problem
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Abstract:
The classical Waring problem deals with expressing every natural number as a sum of g(k) k-th powers. Recently there has been considerable interest in non-commutative versions of this problem for non-abelian groups, and simple groups in particular. Here the k-th power word can be replaced by an arbitrary nontrivial group word w, and the goal is to express group elements as short products of values of w. I will discuss my recent joint work with M. Larsen and A. Shalev on this non-commutative Waring problem.