Robert Wilson's Research Page

RESEARCH | Seminars | Papers | Books || Grant reports | Postgraduate Students

Research

My research is mainly in finite group theory, and related areas such as representation theory, some aspects of combinatorics, and computational techniques and algorithms applicable to finite groups. Some particular aspects that interest me as listed below.

The sporadic simple groups, especially the MONSTER, a group with
808017424794512875886459904961710757005754368000000000
elements. A recent highlight is a construction of the Leech lattice and Conway's group in terms of 3 by 3 octonion matrices.
Simple constructions of exceptional groups of Lie type. A recent highlight is the first really elementary existence proof for the Ree groups of type F₄. A consequence of this is a construction of the Suzuki groups which is easy enough to be presented to undergraduates.
Algorithms for computing with matrix groups. A recent highlight is the publication of a paper jointly with Chris Parker, giving estimates for the complexity of a whole range of algorithms involving involution centralisers in groups of Lie type. This paper has been in preparation for ten years, and the ideas in it underpin much of current algorithm development in the area.

Some links:

You can find the web-based Atlas of Group Representations (version 3) at brauer.maths.qmul.ac.uk/Atlas/v3/, or if that does not work, try the old version 2 in Birmingham.
A list of possible research problems.
A link to the Representation theory across the Channel website.

Research seminars

The following notes and/or slides are from a few of my talks given in a variety of places during recent years.

Five lectures on exceptional structures and simple groups
- E₈ (QMUL, 17/11/08).
- Octonions (QMUL, 24/11/08).
- The Golay code (QMUL, 01/12/08).
- The Leech lattice (QMUL, 08/12/08).
- An octonionic Leech lattice (QMUL, 15/12/08).
248 and all that (Birmingham, 60th birthday conference for Professor Robert Curtis, 21/09/07; updated: QMUL, 15/10/07; ICMS, Edinburgh, 20/11/07).
Involution centralizers in matrix group algorithms (QMUL, 14/11/05; Warwick 17/2/06) Text also available as: dvi or ps.
Finite groups with small automorphism groups (QMUL, 7/10/04; Manchester, 30/11/04; Cambridge, 9/2/05; City, 23/1/06) Text also available as: dvi or ps.
The weird and wonderful world of octonions (QMUL, 13/12/04; Birmingham, 15/2/06). The text of the talk, plus a bit more, is also available in dvi format or in ps format.
Taming the Monster (Plenary talk at New Zealand Mathematics Colloquium, Auckland, 4/12/02)
Slides also available as : dvi or ps.

Papers and Preprints

My publication list according to MathSciNet.
For preprints and other information see separate publications page.

Research-level books

	The finite simple groups
	Springer, 2009.
	Webpage with corrections and additional material.
	The various old versions are no longer available.
	Atlas of finite groups
	by JHConway, RTCurtis, SPNorton, RAParker and RAWilson
	Oxford University Press, 1985. Reprint with corrections, 2004
	Webpage (not yet available).
	The Atlas of Finite Groups: Ten Years On
	edited by Robert Curtis and Robert Wilson
	Cambridge University Press, 1998.
	LMS Lecture Notes.
	An Atlas of Brauer Characters
	by CJansen, KLux, RParker and RWilson
	Oxford University Press, 1995. Out of print.
	Webpage (not yet available). One day the contents of the book may be available here.

Grant reports

A world-wide-web Atlas of group representations EPSRC grant GR/S41319 ran from 1st May 2004 to 30th April 2007. [GR/S41319/01 from 1/05/04 - 31/08/04 at the University of Birmingham; GR/S41319/02 from 1/09/04 - 30/04/07 at Queen Mary, University of London.]
Computing in the Fischer-Griess Monster EPSRC grant GR/R95265/01 ran from 1st May 2002 to 30th April 2004.

Postgraduate Students

Current and recently graduated students:

Richard Barraclough (Birmingham, 2001 - 2005). PhD thesis: Some calculations related to the Monster group
Simon Nickerson (Birmingham, 2002 - 2005). PhD thesis: An Atlas of Characteristic Zero Representations
Jonathan Ward (QMUL, 2004 - 2009). PhD thesis: Generation of simple groups by conjugate involutions
Adeel Farooq (QMUL, 2005 - )
Johanna Rämö (QMUL, 2006 - )
Colin Reid (QMUL, 2006 - 2009)
Nicholas Krempel (QMUL, 2007 - )

This page is maintained by Robert Wilson. The views and opinions expressed in these pages are mine. The contents of these pages have not been reviewed or approved by Queen Mary, University of London.