Publications

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

Books

Representation Theory of Finite Groups: a Guidebook. Published with Springer, ISBN 9783030217914. Springer website, Amazon.co.uk. Errata list can be found here (HTML version) (if anyone finds any errors not on this list, please let me know).

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

In Preparation, Preprints and Submitted Articles

On the maximal subgroups of E₈(q), in preparation.

(Joint with Radha Kessar) The Brauer trees of finite groups, in preparation.

The maximal subgroups of E₇(q) and related almost simple groups, preprint.

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

Published Articles

[24] Medium-rank Lie primitive and maximal subgroups of exceptional groups of Lie type, Mem. Amer. Math. Soc. 288 no. 1434 (2023). DOI, arXiv. Auxiliary files 1, Auxiliary files 2, Auxiliary files 3 (this is 126MB).

[23] The maximal subgroups of F₄(q), E₆(q) and ²E₆(q) and related almost simple groups, Invent. Math. 234 (2023), 637-719. arXiv. Auxiliary files. Errata list (PDF, 129kb), Errata list (HTML version).

[22] An Ennola duality for subgroups of groups of Lie type, Monats. Math. 199 (2022), 785-799. DOI. Errata list (PDF, 123kb), Errata list (HTML version)

[21] (Joint with David Stewart and Adam Thomas) A new maximal subgroup of E₈ in characteristic 3, Proc. Amer. Math. Soc. 150 (2022), 1435-1448. DOI, PDF (HTML version), arXiv

[20] Maximal PSL₂ subgroups of exceptional groups of Lie type, Mem. Amer. Math. Soc. 276 no. 1355 (2022). DOI, PDF, Magma code

[19] Trivial-source endotrivial modules for sporadic groups, Beitr. Algebra Geom. 62 (2020), 317-343. DOI, arXiv.

[18] (Joint with Olivier Dudas and Raphaël Rouquier) The Brauer trees of unipotent blocks, J. Eur. Math. Soc. 22 (2020), 2821-2877. DOI, arXiv.

[17] Groups with a p-element acting with a single non-trivial Jordan block on a simple module in characteristic p, J. Group Theory 21 (2018), 719-787. DOI, PDF, Errata (HTML version)

[16] (Joint with Bob Oliver and Jason Semeraro) Reduced fusion systems over p-groups with an abelian subgroup of index p: II, Adv. Math. 322 (2017), 201-268. PDF, Errata (HTML version)

[15] Alternating subgroups of exceptional groups of Lie type, Proc. Lond. Math. Soc. 115 (2017), 449-501. DOI, PDF, Errata to published version, Version incorporating known corrections and updates.

[14] Brauer Trees of Non-Crystallographic groups of Lie type, J. Algebra 398 (2014), 481-495. DOI, PDF

[13] (Joint with Peter Pappas) On the Unit Conjecture for Supersoluble Group Algebras, J. Algebra 394 (2013), 310-356. DOI, PDF, Old PDF

[12] (Joint with Raphaël Rouquier) Perverse Equivalences and Broué's Conjecture, Adv. Math. 248 (2013), 1-53. DOI, PDF, Old PDF

[11] On Tensor Products of Simple Modules for Simple Groups, Algebr. Represent. Theory 126 (2013), 377-404. DOI, PDF, Old PDF, Errata (HTML version)

[10] Relating Simple Modules in Weight 2 Blocks of Symmetric Groups, Quart. J. Math. Oxford 63 (2013), 377-404. DOI, PDF, Old PDF

[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-subgroups Are Algebraic, J. Algebra 231 (2009), no. 5, 1473–1479. MathSciNet, DOI, PDF, Errata for PDF (with thanks to the referee of [11]), 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

An Atlas of Modular Representation Theory

Version 1 may be found here on the arXiv. New version coming Summer 2021 (hopefully!)

Non-Published Articles (generally short notes)

[7] The structure of projective indecomposable modules for A_n, n ≥ 12, preprint, May 2016. arXiv

[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.