Reg Wood (University of Manchester)
reg@ma.man.ac.uk
The Steenrod algebra remains one of the most powerful tools for attacking problems in algebraic topology, and in spite of having been discovered about fifty years ago, relatively straightforward problems concerning its structure are still unsolved. Although these are algebraic, they have a combinatorial flavour, and remain of interest to geometric topologists for several different reasons. The hit problem arose originally arose for projective spaces, where some simple instances have been given beautiful solutions. The problem has since been extended to more general spaces, where the underlying geometry is more subtle, and answers are much more difficult to obtain. The talk will outline the geometric background, and proceed at a leisurely pace to recent work by Grant Walker and the speaker.