Grant Walker

School of Mathematics

University of Manchester

Oxford Road

Manchester M13 9PL

UK

Email address: grant@ma.man.ac.uk

Telephone: (+44)(0)161 275 5897

Fax: (+44)(0)161 275 5819

Algebraic topology; the structure of the Steenrod algebra,
the action of the Steenrod algebra on polynomials

Combinatorics; symmetric functions, Young diagrams and tableaux

Algebra; Modular representation theory of
general linear groups in the defining characteristic

This is a third level course unit which provides an introduction to knot
theory at an elementary level.

The central theme is polynomial invariants of knots and links.

This course aims to provide a concrete approach to standard topics in commutative algebra by focussing on polynomial algebras over a field of scalars. The topic up to Easter is Groebner bases for ideals. Results on factorisation and irreducible polynomials will be introduced as required. The topic after Easter is symmetric and alternating polynomials. Chapter 5 of the book "Concrete Abstract Algebra" by Niels Lauritzen (Cambridge University Press, 2003) follows a similar approach to Groebner bases to that given in the lectures, and is recommended.

- (with Reg Wood) Flag modules and the hit problem for the Steenrod algebra, Math. Proc. Camb. Phil. Soc. 147 (2009), 143--171. pdf
- (with Reg Wood) Young tableaux and the Steenrod algebra, Geometry and Topology Monographs,11 (2007), 379--398 pdf
- (with Reg Wood) Weyl modules and the mod 2 Steenrod algebra, Journal of Algebra 311 (2007), 840--858 pdf
- (with Pham Anh Minh) Linking first occurrence polynomials over F_p by Steenrod operations, Algebraic and Geometric Topology 2 (2002), 563--590 pdf
- (with Suo Xiao) A symmetric property of truncated Schur modules over fields of characteristic 2, Advances in Mathematics (China) 31 (2002), 549--559 ps
- (with Judith Silverman and Reg Wood) The elements chi(Sq^a).Sq^b and Sq^a.chi(Sq^b), preprint, University of Manchester 1995. pdf
- The elements chi(P^a).P^b and P^a.chi(P^b), preprint, University of Manchester 1996. pdf
- (with Reg Wood) Notes on the elements P^a.chi(P^b) in A_p, preprint, University of Manchester 2011. pdf
- Notes on representations of the simple group of order 168 pdf
### Ph.D Theses

- Toda brackets and the odd primary homotopy of complex Stiefel manifolds, Manchester Centre for Pure Mathematics, Preprint No 1994/02} pdf
- Applications of the twisted Steenrod action to the hit problem, (Helen Weaver, Ph.D. thesis, University of Manchester 2006) pdf
- Generating sets for polynomial rings as modules over the divided differential operator algebra D (Suo Xiao, Ph.D. thesis, University of Manchester 1999) pdf