Professor Robert A Wilson
Address :	School of Mathematical Sciences Queen Mary, University of London Mile End Road London E1 4NS
Office :	none
Telephone :	none
School Fax :	+44 (0)20 7882 7684
Email Address :	R.A.Wilson [add AT qmul DOT ac DOT uk]
Blog :	http://robwilson1.wordpress.com

Research

• In recent years my research has been mainly in applications of group theory and representation theory in fundamental physics, where it seems to me the algebra is widely misunderstood, and badly applied. One result of this is that there is no consistent definition of mass in physics, which leads to problems both on the large scale (measuring the mass of a galaxy in order to understand its dynamics) and the small scale (understanding how the mass of a proton relates to the mass of its constituents). Group theory explains where this problem comes from, and suggests possible ways to overcome it.
• Prior to that, my research was 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. A specialism is the sporadic simple groups, especially the MONSTER, a group with
  808017424794512875886459904961710757005754368000000000
  elements. More details can be found on my research page.
• You can find the web-based Atlas of Group Representations (version 3) at brauer.maths.qmul.ac.uk/Atlas/v3/.
• A list of possible research problems.

Research seminars

The following notes and/or slides are from a few of my talks given in a variety of places during the last 20 or so years.

• Umbral groups. LMS-EPSRC Durham Symposium on New moonshines, mock modular forms and string theory. 04/08/15.
• Simple groups of Lie type without Lie theory. Bielefeld, 12/3/12 (conference in honour of Bernd Fischer's 75th birthday)
• A quaternionic approach to E7 (London Algebra Colloquium, 01/12/11; Bristol, 01/02/12; Birmingham, 16/02/12).
• The Suzuki groups (York, 03/02/10; Birmingham, 23/03/11; revised, Manchester 19/02/13).
• A new approach to the Leech lattice (Cambridge, 21/10/09).
• 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.

Recent Publications and Preprints

My publication list according to MathSciNet.

My recent work in groups applied to physics is described in the following places:

• Preprints on the arXiv:
  • Integer versions of Yang-Mills theory. (2202.08263)
  • Possible uses of the binary icosahedral group in grand unified theories. (2109.06626)
  • Comparison of group-theoretical strategies for unification of 3+1 structures in physics. (2108.04675)
  • Potential applications of modular representation theory to quantum mechanics. (2106.00550)
  • Options for a finite group model of quantum mechanics. (2104.10165)
  • Finite symmetry groups in physics. (2102.02817)
  • Subgroups of Clifford algebras. (2011.05171. Published in Advances in Applied Clifford Algebras, under a more specific title.)
  • A group-theorist's perspective on symmetry groups in physics. (2009.14613)
• Preprints at the Isaac Newton Institute:
  • Potential uses of representations of SL(4,R) in particle physics. (no.19014)
  • Possible emergence of fundamental constants from a generally covariant model of quantum mechanics. (no.19013)
  • A 2020 vision for a new theory of physics. (no. 19012)
  • Remarks on the group-theoretical foundations of particle physics. (no.19011)
• Preprints on my blog:
  • Remarks on the group-theoretical foundations of particle physics (revised version).
  • Quaternionic reflections and (non)locality.
  • Towards a discrete model of physics.

Translations

• Sylow's original paper proving the Sylow theorems. Translated from the original French, with annotations. Sylow, L. (1872), "Théorèmes sur les groupes de substitutions", Mathematische Annalen 5: 584–594, doi:10.1007/BF01442913

Grant reports

• Grant reports. New report added 26/7/07.

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.
	Graphs, colourings and the four-colour theorem
	Oxford University Press, 2002.
	Published on the 150th anniversary of the first recorded statement of the four-colour problem.
	Webpage (not yet available).
	Linear algebra
	by Richard Kaye and Robert Wilson
	Oxford University Press, 1998.
	Webpage with corrections.
	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.

Ancient wisdom

Socrates on innovation in teaching (Xenophon, Memoirs of Socrates, 4.4):
"Of course," Hippias said, "I always try to say something new."
"Even about facts that you know? I mean, if somebody asks you how many letters there are in 'Socrates', and what they are, do you try to say something different now from what you said before? Or if somebody asked about numbers, whether twice five is ten, don't you give the same answer now as before?"

An archive of past teaching is kept here. However, not all links are guaranteed to work (e.g. to model solutions, or to College information pages).

Lecture notes

• Finite simple groups . Expanded notes of an MSci course given in Birmingham in 2003-4 by Chris Parker and myself.
• On the O'Nan--Scott Theorem (QMUL, November 2005)
  Some notes on the proof of this theorem are available in dvi format or in ps format or in pdf format.
• Introductory mathematics for civil engineers. A course I taught in Birmingham in 2001.
• Introductory mathematics for computer scientists. A course I taught in Birmingham in 1997.

Postgraduate 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 - 2011). PhD thesis: Some computations in the Monster group and related topics
• Johanna Rämö (QMUL, 2006 - 2010). PhD thesis: On structural aspects of finite simple groups of Lie type
• Colin Reid (QMUL, 2006 - 2009). PhD thesis: Finiteness properties of profinite groups
• Gregor Dick (QMUL, 2010 - 2014). PhD thesis: Constructive recognition of black-box \(F_4(q)\) in odd characteristic
• Stefanos Aivazidis (QMUL, 2011 - 2015). PhD thesis: On the subgroup permutability degree of some finite simple groups
• Yegor Stepanov (QMUL, 2015 - 2020).

About me

• Current position. At the end of 2016 I took early retirement from my position as Professor of Mathematics in the School of Mathematical Sciences at Queen Mary, University of London, which I had held since September 2004.
  My inaugural lecture took place on 2/4/8 (aka Wednesday 2nd April 2008), at 5.30 pm in the Mathematics Lecture Theatre. You can view the invitation, the slides and the prepared text of the talk (not quite the same as what I actually said), and listen to the musical interlude (aka the first movement of the Moonshine Sonata by Beethoven).
• Brief CV.
  • Professor in Algebra and Combimatorics, Queen Mary University of London, 2004-2016.
  • Lecturer, Senior Lecturer, Reader and Professor, The University of Birmingham. 1987-2004.
  • Official Fellow and College Lecturer, Girton College, Cambridge. 1986-7.
  • Research Fellow, Jesus College, Cambridge, 1983-6.
  • BA, Part 3, MA, PhD, and Rouse Ball Student, Trinity College, Cambridge, 1975-83.

Other Activities

• LMS Council. I was elected to the LMS Council as a Member-at-large, for a term of two years, at the AGM on 20th November 2009. My election statement is archived here. Appointed to the Programme Committee, and co-opted onto the Working Group for the new LMS web-site. Also appointed Council Diarist from November 2010, to November 2011. Elected as Programme Secretary, for one year, on 18th November 2011. Re-elected 2012 and 2013. Resigned 2014.

Personal

• I was principal viola in the Sinfonia of Birmingham for many years, but now sometimes play violin instead. Here is a poster advertising one of our previous concerts. I also play in the Birmingham Philharmonic Orchestra, and in other orchestras and chamber music ensembles from time to time.
• I play the piano occasionally, but with more enthusiasm than accuracy.
• Due to a damaged finger, I was unable to play violin/viola/piano for a while, and took up the kora as it does not require the use of that particular finger. The Kora workshop have supplied me with new strings, and video tutorials.