Dr. Ben Fairbairn "The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful." Aristotle Postal address: School of Mathematics Watson Building University of Birmingham Edgbaston Birmingham B15 2TT UK Email address: fairbaib AT maths DOT bham DOT ac DOT uk

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Research

I am an Honorary Research Fellow at the University of Birmingham where I completed my PhD under the supervision of Professor Robert Curtis. My thesis can be found here. I study finite groups along with related geometric/combinatorial structures emphasising the Sporadic Simple Groups. I did my first degree at King's College of the University of Cambridge, home to the wonderful CMS. I also did Part III.

Preprints and Publications A short list:

• "Symmetric Representation of the Elements of the Conway group .0" with R.T. Curtis, Journal of Symbolic Computation 44 (2009) p.1044-1067 The suplimentary material is below.
  • The Main Program
  • The Program putting 24 by 24 Z/3Z matrices into standard form
  • The Program converting elements in near standard form into 24 by 24 Z/3Z matrices
• "Symmetric Generation of Coxeter Groups" with J Müller, Archiv der Mathematik 93 (2009) p.1-10 and available on the arxiv here.
• "A Note on Monomial Representation of Linear Groups", accepted by Communications in Algebra.
• "Some Design Theoretic Results on the Conway Group .0", accepted the Electronic Journal of Combinatorics.
• "Improved Upper Bounds on the Spreads of some Large Sporadic Groups", in preparation. An early version may be found on the arxiv here.
• "The exact spreed of M₁₂ is 9", prprint (2009) and on the arxiv here.
• "Symmetric Presentations of Coxeter Groups", submitted to the Proceedings of the Edinburgh Mathematical Society
• "Recent Progress in the Symmetric Generation of Groups", survey article in preparation for the conference proceedings of 'Groups St Andrews 2009'
• "Extensions of Symmetric Generating Sets" with RT Curtis, in preparation
• "Natural Modules for the Mathieu Groups", in preparation

I am also acknowledged for my contributions to the following

• "Universal measuring coalgebras and R-transformation algebras" M. Batchelor and J. Thomas, preprint Cambridge 2007.
• "A Course On Finite Groups" H.E. Rose, Springer, in preparation.
• Review of the 2007 LMS popular lectures in the November 2007 LMS newsletter (click "Report").

Short CV

Group theory in Birmingham

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I am a referee for the Journal of Algebra and a reviewer for the American Mathematical Society's Mathematical Reviews.

I am a member of the London Mathematical Society and of the Isaac Newton Institute and I occasionally do a bit of mentoring for the UK Mathematics Trust.

On occasion I sometimes try to keep up-to-date(ish) my sporadic group references.

I was a co-organiser of the 9th annual Post-Graduate Group Theory Conference. I was also co-organiser of the Birmingham pure mathematics postgraduate seminars. Perhaps you recently heard me speak in Manchester, Galway, Bath or London?

Here is a shameless plug for my supervisor's recent book "Symmetric Generation of Groups".

What follows is a constructive proof of the existence of wonderful people on this, the best of all possible worlds, (listed alphabeticaly) Tom Barber; Nathan Barker; David Bundy (in German); Clare Burrage; Oliver Cooley; James Cranch; Geoff Curtiss; Callum Durnford; Jan Essert (in German and French); Ali Everett; Matt Fayers; Alexander Frolkin; Andreas Glang; Simon Goodwin (formerly, an honorary Fairbairn); Ralf Gramlich; Joe Grant; Max Horn (in English and German and even alternatively here); Björn Hüpping (in German); Nate Iverson; Darren Kenneally; David Knipe; Vladimir Lazic; Carl Mctague; Chris Parker; Tony Skyner; Chris Spencer; James Sprittles; Jay Taylor; Hung Tong-Viet; Andrew Treglown; Rebecca Waldecker; Clare Watters; Mark Williamson; Josh Wiscons; Julian Wiseman,

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last updated: October 2009