Aner Shalev (Hebrew University Jerusalem): Quantitative
repreresentation theory, Waring problems, and the product replacement
algorithm
Quantitative representation theory deals with counting irreducible
representations of various (finite and infinite) groups and bounding the
values of the associated characters. In recent years there is growing
interest in this subject with diverse applications to other fields;
these include random walks, commutator maps, algorithmic questions,
and Waring type problems (establishing non-commutative analogues of the
celebrated Waring problem in number thoery). I will present some new
results in some of these fields, and outline the role of representation
theory in the proofs.