Reg Wood

Mathematics Department

Manchester University

Oxford Road

Manchester

M13 9PL

England

reg@ma.man.ac.uk

0161 275 5849

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In recent years my interests have been in a branch of topology
concerned mainly with the action of the Steenrod
algebra *A* on polynomials. From the topological point of view *A*
is the algebra of universal stable operations in ordinary cohomology theory and has been of fundamental importance in the development of algebraic topology since the first publication on the subject by Steenrod in 1947. The action of *A* on polynomials arises from the cohomology of certain particular spaces, namely products of infinite projective spaces. However, these examples are in a sense universal and determine the algebra itself. They also provide the launching pad for a purely algebraic development of the Steenrod algebra, which has led to many interconnections with such subjects as modular representation theory of matrix semigroups, invariant theory, differential operators and the combinatorics of symmetric functions, see Problems in the Steenrod algebra . There are many unsolved problems concerned both with the internal structure of *A* as well as its action on polynomials. Many of these questions go under the umbrella title of `hit problems' and are concerned with the general question in algebra of finding minimal generating sets for modules over rings, see Ioannina article .

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