Publications

Here is a list of my publications. Where available, a link to the MathSciNet reference, and a PDF of the paper, is present.

Book

The Theory of Fusion Systems: An algebraic approach. Published with CUP, ISBN 9781107005969. CUP website, Amazon.co.uk. Errata list can be found here (if anyone finds any errors not on this list, please let me know).

In Preparation, Preprints and Submitted Articles

[16] (Joint with Olivier Dudas and Raphaël Rouquier) Brauer trees for unipotent blocks of E7 and E8, in preparation.

[15] Brauer Trees of Non-Crystallographic groups of Lie type, in preparation.

[14] Perverse Equivalences and Broué's Conjecture II: The cyclic case, preprint. PDF with appendix, PDF without appendix.

[13] (Joint with Raphaël Rouquier) Perverse Equivalences and Broué's Conjecture, submitted. PDF

[12] (Joint with Peter Pappas) On the Unit Conjecture for Group Rings, submitted. PDF

In Press

[11] Relating Simple Modules in Weight 2 Blocks of Symmetric Groups, Quart. J. Math. Oxford, to appear. DOI, PDF, Old PDF

[10] On Tensor Products of Simple Modules for Simple Groups, Algebr. Represent. Theory, to appear. DOI, PDF, Old PDF

Published Articles

[9] (Joint with Adam Glesser) Fusion Systems on Small p-Groups, Trans. Amer. Math. Soc., 364 (2012), 5945--5967. DOI, PDF

[8] Normal Subsystems of Fusion Systems, J. Lond. Math. Soc., 84 (2011), 137-158. DOI, PDF, Old PDF

[7] (Joint with Charles Eaton, Radha Kessar, and Markus Linckelmann) Blocks with a Klein Four Defect Group, Math. Z. 268 (2011), 441--476. DOI, PDF, Old PDF

[6] Algebraic Modules and the Auslander–Reiten Quiver, J. Pure Appl. Algebra 215 (2011), 221–231.MathSciNet, DOI, PDF, Old PDF

[5] Lower Bounds for Representation Growth, J. Group Theory 13 (2010), no. 6, 873–890. MathSciNet, DOI, PDF, Old PDF

[4] Control of Fusion and Solubility in Fusion Systems, J. Algebra 323 (2010), no. 9, 2429--2448. MathSciNet, DOI, PDF, Old PDF

[3] Simple Modules for Groups with Abelian Sylow 2-subgroup Are Algebraic, J. Algebra 231 (2009), no. 5, 1473–1479. MathSciNet, DOI, PDF, Errata for PDF (with thanks to the referee of [8]), Old PDF

[2] (Joint with Andrew Holloway, Lei Xiao, Javier del Campo, and Gregory Wildgoose) Developing Random Network Theory for Carbon Nanotube Modified Electrode Voltammetry: Introduction and Application to Estimating the Potential Drop between MWCNT-MWCNT Contacts, J. Phys. Chem. C 112 (2008), no. 35, 13729–13738. DOI, PDF.

[1] Symmetric Group Character Degrees and Hook Numbers, Proc. Lond. Math. Soc. (3) 96 (2008), no. 1, 26–50. MathSciNet, DOI, PDF, Old PDF

Non-Published Articles (generally short notes)

[6] Thompson p-Nilpotence and Fusion Systems, preprint, June 2011. PDF

[5] Alperin's Fusion Theorem and Fusion Systems, preprint, September 2010. PDF

[4] Contrasting the Definitions of Normal Subsystems in Fusion Systems, preprint, July 2009. PDF

[3] Strong Closure and p-Normality for Fusion Systems, preprint, July 2009. PDF

[2] On ZJ-Theorems for Fusion Systems, preprint, March 2009. PDF

[1] The Number of t-Cores of Size n, preprint, August 2006. PDF

Theses

Here is a list of my theses, from my 2004 Masters dissertation under Geoffrey Robinson to my D.Phil. thesis under Michael Collins in 2007/2008.

The modular representation theory of finite groups, M.Sci. dissertation, 2004. PDF

Scott modules and lower defect groups, D.Phil. transfer thesis, 2005. PDF

Algebraic modules for finite groups, D.Phil. thesis, 2007. PDF, PDF (double-sided)

MathSciNet

You can see a list of my publications on MathSciNet here.