Research interests
My main area of research is in group theory. I am interested in simple groups, both finite and algebraic, with a particular focus on subgroup structure, conjugacy classes and representation theory. I am also interested in permutation groups and related combinatorics, and in the application of probabilistic and computational methods.
In March 2021 I gave a series of online lectures on Bases for permutation groups, hosted by the University of Padova.
Publication highlights
I have written 70 research publications, which have attracted more than 750 citations according to MathSciNet. This includes three books and monographs, as well as papers in several leading journals:
 Advances in Mathematics (5 papers)
 Algebra and Number Theory (2)
 Annals of Mathematics
 Journal of the European Mathematical Society (2)
 Mathematische Annalen
 Memoirs of the American Mathematical Society (2)
 Proceedings of the London Mathematical Society (2)
 Transactions of the American Mathematical Society (2)
Books and monographs
 Classical groups, derangements and primes
joint with M. Giudici
Australian Mathematical Society Lecture Series, vol. 25
Cambridge University Press, 2016, xviii+346
ISBN: 9781107629448
 Irreducible geometric subgroups of classical algebraic groups
joint with S. Ghandour and D.M. Testerman
Memoirs of the American Mathematical Society 239 (2016), no. 1130, vi+88
ISBN: 9781470414948
 Irreducible almost simple subgroups of classical algebraic groups
joint with S. Ghandour, C. Marion and D.M. Testerman
Memoirs of the American Mathematical Society 236 (2015), no. 1114,
vi+110
ISBN: 9781470410469
All publications and preprints
 On derangements in simple permutation groups
joint with M. Fusari
58 pages, submitted
 On the regularity number of a finite group and other baserelated invariants
joint with M. AnagnostopoulouMerkouri
Journal of the London Mathematical Society
52 pages, to appear
[Supplementary file]
 Topological generation of simple algebraic groups
joint with S. Gerhardt and R.M. Guralnick
Journal of the European Mathematical Society (JEMS)
87 pages, to appear
 On the topological generation of exceptional groups by unipotent elements
Transformation Groups
30 pages, to appear
 On the generation of simple groups by Sylow subgroups
joint with R.M. Guralnick
Contemporary Mathematics (Amitsur Centennial Symposium), vol. 800 (2024), 81100, Amer. Math. Soc. Providence, RI.
 On the maximal overgroups of Sylow subgroups of finite groups
joint with B. Baumeister, R.M. Guralnick and H.P. TongViet
Advances in Mathematics 444 (2024), 109632, 65 pp.
 Strongly basetwo groups
joint with R.M. Guralnick
Vietnam Journal of Mathematics (Tiep 60th birthday volume) 51 (2023), 657683
 On the classification of extremely primitive affine groups
joint with M. Lee
Israel Journal of Mathematics 255 (2023), 265282
 On the commuting probability of pelements in a finite group
joint with R.M. Guralnick, A. Moretó and G. Navarro
Algebra and Number Theory 17 (2023), 12091229
 On soluble subgroups of sporadic groups
Israel Journal of Mathematics 254 (2023), 313340
 Normalisers of maximal tori and a conjecture of Vdovin
joint with A.R. Thomas
Journal of Algebra 619 (2023), 459504
 On the soluble graph of a finite group
joint with A. Lucchini and D. Nemmi
Journal of Combinatorial Theory, Series A 194 (2023), 105708, 39 pp.
 On base sizes for primitive groups of
product type
joint with H.Y. Huang
Journal of Pure and Applied Algebra 227 (2023), 107228, 43 pp.
 Fixed point ratios for finite primitive groups and applications
joint with R.M. Guralnick
Advances in Mathematics 411 (2022), 108778, 90 pp.
 On the Saxl graphs of primitive groups with soluble stabilisers
joint with H.Y. Huang
Algebraic Combinatorics 5 (2022), 10531087
 The classification of extremely primitive groups
joint with A.R. Thomas
International Mathematics Research Notices IMRN (2022), no. 13, 1014810248
[GAP and Magma code]
 Finite groups, minimal bases and the intersection number
joint with M. Garonzi and A. Lucchini
Transactions of the London Mathematical Society 9 (2022), 2055
 Permutation groups with restricted stabilizers
joint with A. Shalev
Journal of Algebra (special issue in memory of Jan Saxl) 607 (2022), 160185
 Almost elusive permutation groups
joint with E.V. Hall
Journal of Algebra 594 (2022), 519543
 Base sizes for primitive groups with soluble stabilisers
Algebra and Number Theory 15 (2021), 17551807
 On the involution fixity of simple groups
joint with E. Covato
Proceedings of the Edinburgh Mathematical Society 64 (2021), 408426
 The spread of a finite group
joint with R.M. Guralnick and S. Harper
Annals of Mathematics 193 (2021), 619687
 A note on extremely primitive affine groups
joint with A.R. Thomas
Archiv der Mathematik 116 (2021), 141152
 On solvable factors of almost simple groups
joint with C.H. Li
Advances in Mathematics 377 (2021), 107499, 36 pp.
 Finite groups, 2generation and the uniform domination number
joint with S. Harper
Israel Journal of Mathematics 239 (2020), 271367
 Topological generation of exceptional algebraic groups
joint with S. Gerhardt and R.M. Guralnick
Advances in Mathematics 369 (2020), 107177, 50 pp.
 On the minimal dimension of a finite simple group
joint with M. Garonzi and A. Lucchini (with an appendix by T.C. Burness and R.M. Guralnick)
Journal of Combinatorial Theory, Series A 171 (2020), 105175, 32 pp.
 The length and depth of compact Lie groups
joint with M.W. Liebeck and A. Shalev
Mathematische Zeitschrift 294 (2020), 14571476
 On the Saxl graph of a permutation group
joint with M. Giudici
Mathematical Proceedings of the Cambridge Philosophical Society 168 (2020), 219248
 On the length and depth of finite groups
joint with M.W. Liebeck and A. Shalev (with an appendix by D.R. HeathBrown)
Proceedings of the London Mathematical Society 119 (2019), 14641492
 Simple groups, generation and probabilistic methods
Groups St Andrews 2017 in Birmingham, London Mathematical Society Lecture Note Series, 455, Cambridge University Press, pp. 200229, 2019
 Irreducible subgroups of simple algebraic groups  a survey
joint with D.M. Testerman
Groups St Andrews 2017 in Birmingham, London Mathematical Society Lecture Note Series, 455, Cambridge University Press, pp. 230260, 2019
 $A_1$type subgroups containing regular unipotent elements
joint with D.M. Testerman
Forum of Mathematics, Sigma 7 (2019), e12, 61 pp.
 On the uniform domination number of a finite simple group
joint with S. Harper
Transactions of the American Mathematical Society 372 (2019), 545583
[GAP and Magma code]
 The length and depth of algebraic groups
joint with M.W. Liebeck and A. Shalev
Mathematische Zeitschrift 291 (2019), 741760
 On base sizes for almost simple primitive groups
Journal of Algebra 516 (2018), 3874
 On the involution fixity of exceptional groups of Lie type
joint with A.R. Thomas
International Journal of Algebra and Computation 28 (2018), 411466
 Locally elusive classical groups
joint with M. Giudici
Israel Journal of Mathematics 225 (2018), 343402
 Simple groups, fixed point ratios and applications
Local Representation Theory and Simple Groups, EMS Series of Lectures in Mathematics, European Mathematical Society, Zürich, pp. 267322, 2018
 The depth of a finite simple group
joint with M.W. Liebeck and A. Shalev
Proceedings of the American Mathematical Society 146 (2018), 23432358
 Generation of second maximal subgroups and the existence of special primes
joint with M.W. Liebeck and A. Shalev
Forum of Mathematics, Sigma 5 (2017), e25, 41 pp.
 On base sizes for algebraic groups
joint with R.M. Guralnick and J. Saxl
Journal of the European Mathematical Society (JEMS) 19 (2017), 22692341
 Permutation groups and derangements of odd prime order
joint with M. Giudici
Journal of Combinatorial Theory, Series A 151 (2017), 102130
 On irreducible subgroups of simple algebraic groups
joint with C. Marion and D.M. Testerman
Mathematische Annalen 367 (2017), 12591309
 Primitive permutation groups and derangements of prime power order
joint with H.P. TongViet
Manuscripta Mathematica 150 (2016), 255291
 Classical groups, derangements and primes
joint with M. Giudici
Australian Mathematical Society Lecture Series, vol. 25
Cambridge University Press, 2016, xviii+346
 Irreducible geometric subgroups of classical algebraic groups
joint with S. Ghandour and D.M. Testerman
Memoirs of the American Mathematical Society 239 (2016), no. 1130, vi+88
 On Pyber's base size conjecture
joint with Á. Seress
Transactions of the American Mathematical Society 367 (2015), 56335651
 Derangements in primitive permutation groups, with an application to character theory
joint with H.P. TongViet
Quarterly Journal of Mathematics 66 (2015), 6396
 On the prime graph of simple groups
joint with E. Covato
Bulletin of the Australian Mathematical Society 91 (2015), 227240
 Large subgroups of simple groups
joint with S.H. Alavi
Journal of Algebra (special issue in memory of Ákos Seress) 421 (2015), 187233
 Irreducible almost simple subgroups of classical algebraic groups
joint with S. Ghandour, C. Marion and D.M. Testerman
Memoirs of the American Mathematical Society 236 (2015), no. 1114,
vi+110
 Base sizes for $\mathcal{S}$actions of finite classical groups
joint with R.M. Guralnick and J. Saxl
Israel Journal of Mathematics 199 (2014), 711756
 Generation and random generation: from simple groups to maximal subgroups
joint with M.W. Liebeck and A. Shalev
Advances in Mathematics 248 (2013), 5995
 On the generating graph of direct powers of a simple group
joint with E. Crestani
Journal of Algebraic Combinatorics 38 (2013), 329350
 On the uniform spread of almost simple linear groups
joint with S. Guest
Nagoya Mathematical Journal 209 (2013), 35109
 Extremely primitive sporadic and alternating groups
joint with C.E. Praeger and Á. Seress
Bulletin of the London Mathematical Society 44 (2012), 11471154
 Extremely primitive classical groups
joint with C.E. Praeger and Á. Seress
Journal of Pure and Applied Algebra 216 (2012), 15801610
 Prime order derangements in primitive permutation groups
joint with M. Giudici and R.A. Wilson
Journal of Algebra 341 (2011), 158178
 On base sizes for symmetric groups
joint with R.M. Guralnick and J. Saxl
Bulletin of the London Mathematical Society 43 (2011), 386391
 Base sizes for sporadic simple groups
joint with E.A. O'Brien and R.A. Wilson
Israel Journal of Mathematics 177 (2010), 307334
 On the number of prime order subgroups of finite groups
joint with S.D. Scott
Journal of the Australian Mathematical Society 87 (2009), 329357
 Base sizes for simple groups and a conjecture of Cameron
joint with M.W. Liebeck and A. Shalev
Proceedings of the London Mathematical Society 97 (2009), 116162
 On base sizes for actions of finite classical groups
Journal of the London Mathematical Society 75 (2007), 545562
 Fixed point ratios in actions of finite classical groups, IV
Journal of Algebra 314 (2007), 749788
 Fixed point ratios in actions of finite classical groups, III
Journal of Algebra 314 (2007), 693748
 Fixed point ratios in actions of finite classical groups, II
Journal of Algebra 309 (2007), 80138
 Fixed point ratios in actions of finite classical groups, I
Journal of Algebra 309 (2007), 6979
 Fixed point spaces in actions of classical algebraic groups
Journal of Group Theory 7 (2004), 311346
 Fixed point spaces in primitive actions of simple algebraic groups
Journal of Algebra 265 (2003), 744771
Theses
 Fixed point spaces in actions of finite and algebraic simple groups
Ph.D. thesis, Imperial College London (2005)
 Reductive algebraic groups and Tits systems
M.Sc. thesis, University of Warwick (2001)
