Martin Liebeck
(Imperial College, London)
Word Maps on Finite Groups

A word map on a group G is a map sending (g1,...,gk) to w(g1,...,gk), where w is a fixed word in k variables. For example, the commutator map and power maps are word maps. I shall discuss various questions about word maps, such as surjectivity and distribution of values, with particular emphasis on simple groups.