# Grant Walker's Home Page

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

### Research interests

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

#### MT3522 Knot Theory

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.

Course Notes for Chapter 1 (Postscript file)
Course Notes for Chapter 1 (PDF file)
Exercises for Chapter 1 (Knot Theory,
Examples 1 (Postscript file) Exercises for Chapter 1 (Knot Theory, Examples 1 (PDF file)
Solutions for Chapter 1 (Knot Theory, Solutions 1
(Postscript file) Solutions for Chapter 1 (Knot Theory, Solutions 1 (PDF file)
Course Notes for Chapter 2 (Knot Theory, Chapter
2 (Postscript file) Course Notes for Chapter 2 (Knot Theory, Chapter 2 (PDF file)
Exercises for Chapter 2 (Knot Theory, Examples 2
(Postscript file) Exercises for Chapter 2 (Knot Theory, Examples 2 (PDF file)
Solutions for Chapter 2 (Knot Theory, Solutions 2
(Postscript file) Solutions for Chapter 2 (Knot Theory, Solutions 2 (PDF file)
Course Notes for Chapter 3 (Knot Theory, Chapter 3
(Postscript file) Course Notes for Chapter 3 (Knot Theory, Chapter 3 (PDF file)
Exercises for Chapter 3 (Knot Theory, Examples 3
(Postscript file) Exercises for Chapter 3 (Knot Theory, Examples 3 (PDF file) Solutions for
Chapter 3 (Knot Theory, Solutions 3 (Postscript
file) Solutions for Chapter 3 (Knot
Theory, Solutions 3 (PDF file)
Course Notes for Chapter 4 (Knot Theory, Chapter 4
(Postscript file) Course Notes for Chapter 4 (Knot Theory, Chapter 4 (PDF file) Course
Notes for Chapter 5 (Knot Theory, Chapter 5
(Postscript file) Course Notes for Chapter 5 (Knot Theory, Chapter 5 (PDF file)
Exercises for Chapters 4/5 (Knot Theory, Examples 4
(Postscript file) Exercises for Chapters 4/5 (Knot Theory, Examples 4 (PDF file) Solutions for
Chapters 4/5 (Knot Theory, Solutions 4 (Postscript
file) Solutions for Chapter 4/5 (Knot
Theory, Solutions 4 (PDF file) Course Notes for Chapter 6 (Knot Theory, Chapter 6 (Postscript file)
Course Notes for Chapter 6 (Knot Theory, Chapter
6 (PDF file) Exercises for Chapter 6 (Knot Theory, Examples 5 (Postscript file)
Exercises for Chapter 6 (Knot Theory, Examples 5
(PDF file) Solutions for Chapter 6 (Knot
Theory, Solutions 5 (Postscript file) Solutions for Chapter 6 (Knot Theory, Solutions 5 (PDF file)
Menu Page for Knots
Exhibition Borromean rings The Knot Plot Site Knots on the Web Math Forum Library, Knot Theory
#### MT30512 Polynomials

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.

Course Notes for session 2006--2007 (PDF file)
Course Notes for session 2006--2007
(Postscript file) Examples 1, 2006--2007 Session , Polynomials Examples 1 (Postscript file)
Examples 1, 2006--2007 Session , Polynomials
Examples 1 (PDF file) Examples 2, 2006--2007 Session , Polynomials Examples 2 (Postscript file)
Examples 2, 2006--2007 Session , Polynomials
Examples 2 (PDF file) Examples 3, 2006--2007 Session , Polynomials Examples 3 (Postscript file)
Examples 3, 2006--2007 Session , Polynomials
Examples 3 (PDF file) Examples 4, 2006--2007 Session , Polynomials Examples 4 (Postscript file)
Examples 4, 2006--2007 Session , Polynomials
Examples 4 (PDF file) Examples 5, 2006--2007 Session , Polynomials Examples 5 (Postscript file)
Examples 5, 2006--2007 Session , Polynomials
Examples 5 (PDF file) Examples 6, 2006--2007 Session , Polynomials Examples 6 (Postscript file)
Examples 6, 2006--2007 Session , Polynomials
Examples 6 (PDF file) Examples 7, 2006--2007 Session , Polynomials Examples 7 (Postscript file)
Examples 7, 2006--2007 Session , Polynomials
Examples 7 (PDF file) Examples 8, 2006--2007 Session , Polynomials Examples 8 (Postscript file)
Examples 8, 2006--2007 Session , Polynomials
Examples 8 (PDF file)
### Recent papers and preprints

- (with Reg Wood) Flag modules and the hit problem for the Steenrod
algebra,
submitted to Math. Proc. Camb. Phil. Soc.
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
### Algebra Seminar, 14 December 2010

- 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