Representation theory of wreath products

The wreath product of a finite group, or more generally an algebra, with a symmetric group is a familiar and important construction in representation theory and other areas of Mathematics. I shall present some highlights from my work on the representation theory of wreath products. These will include both structural properties (for example, that the wreath product of a cellular algebra with a symmetric group is again a cellular algebra) and cohomological ones (one 
particular point of interest being a generalisation of the result of Hemmer and Nakano on filtration multiplicities to the wreath product of two symmetric groups). I will also give an outline of some potential applications of this and related theory to important open  problems in algebraic combinatorics.