## Publications and preprints

### Books and monographs

1. Probabilistic group theory
joint with M.W. Liebeck and A. Shalev
in preparation

2. Classical groups, derangements and primes
joint with M. Giudici
Australian Mathematical Society Lecture Series, vol. 25
Cambridge University Press, 2016, xviii+346
ISBN: 978-1-1076-2944-8

3. 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: 978-1-4704-1494-8

4. 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: 978-1-4704-1046-9

### Articles and preprints

1. On solvable factors of almost simple groups
joint with C.H. Li
submitted

2. Topological generation of exceptional algebraic groups
joint with S. Gerhardt and R.M. Guralnick
submitted

3. 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, to appear

4. Finite groups, 2-generation and the uniform domination number
joint with S. Harper
Israel Journal of Mathematics, to appear

5. The length and depth of compact Lie groups
joint with M.W. Liebeck and A. Shalev
Mathematische Zeitschrift 294 (2020), 1457-1476

6. On the Saxl graph of a permutation group
joint with M. Giudici
Mathematical Proceedings of the Cambridge Philosophical Society 168 (2020), 219-248

7. On the length and depth of finite groups
joint with M.W. Liebeck and A. Shalev (with an appendix by D.R. Heath-Brown)
Proceedings of the London Mathematical Society 119 (2019), 1464-1492

8. Simple groups, generation and probabilistic methods
Groups St Andrews 2017 in Birmingham, London Mathematical Society Lecture Note Series, 455, Cambridge University Press, pp. 200-229, 2019

9. 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. 230-260, 2019

10. $A_1$-type subgroups containing regular unipotent elements
joint with D.M. Testerman
Forum of Mathematics, Sigma 7 (2019), e12, 61 pp.

11. On the uniform domination number of a finite simple group
joint with S. Harper
Transactions of the American Mathematical Society 372 (2019), 545-583
[GAP and Magma code]

12. The length and depth of algebraic groups
joint with M.W. Liebeck and A. Shalev
Mathematische Zeitschrift 291 (2019), 741-760

13. On base sizes for almost simple primitive groups
Journal of Algebra 516 (2018), 38-74

14. On the involution fixity of exceptional groups of Lie type
joint with A.R. Thomas
International Journal of Algebra and Computation 28 (2018), 411-466

15. Locally elusive classical groups
joint with M. Giudici
Israel Journal of Mathematics 225 (2018), 343-402

16. Simple groups, fixed point ratios and applications
Local Representation Theory and Simple Groups (eds. R. Kessar, G. Malle, D. Testerman)
EMS Series of Lectures in Mathematics, European Mathematical Society, Zürich
pp. 267-322, 2018

17. The depth of a finite simple group
joint with M.W. Liebeck and A. Shalev
Proceedings of the American Mathematical Society 146 (2018), 2343-2358

18. 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.

19. On base sizes for algebraic groups
joint with R.M. Guralnick and J. Saxl
Journal of the European Mathematical Society (JEMS) 19 (2017), 2269-2341

20. Permutation groups and derangements of odd prime order
joint with M. Giudici
Journal of Combinatorial Theory, Series A 151 (2017), 102-130

21. On irreducible subgroups of simple algebraic groups
joint with C. Marion and D.M. Testerman
Mathematische Annalen 367 (2017), 1259-1309

22. Primitive permutation groups and derangements of prime power order
joint with H.P. Tong-Viet
Manuscripta Mathematica 150 (2016), 255-291

23. On Pyber's base size conjecture
joint with Á. Seress
Transactions of the American Mathematical Society 367 (2015), 5633-5651

24. Derangements in primitive permutation groups, with an application to character theory
joint with H.P. Tong-Viet
Quarterly Journal of Mathematics 66 (2015), 63-96

25. On the prime graph of simple groups
joint with E. Covato
Bulletin of the Australian Mathematical Society 91 (2015), 227-240

26. Large subgroups of simple groups
joint with S.H. Alavi
Journal of Algebra (special issue in memory of Ákos Seress) 421 (2015), 187-233

27. Base sizes for $\mathcal{S}$-actions of finite classical groups
joint with R.M. Guralnick and J. Saxl
Israel Journal of Mathematics 199 (2014), 711-756

28. Generation and random generation: from simple groups to maximal subgroups
joint with M.W. Liebeck and A. Shalev
Advances in Mathematics 248 (2013), 59-95

29. On the generating graph of direct powers of a simple group
joint with E. Crestani
Journal of Algebraic Combinatorics 38 (2013), 329-350

30. On the uniform spread of almost simple linear groups
joint with S. Guest
Nagoya Mathematical Journal 209 (2013), 35-109

31. Extremely primitive sporadic and alternating groups
joint with C.E. Praeger and Á. Seress
Bulletin of the London Mathematical Society 44 (2012), 1147-1154

32. Extremely primitive classical groups
joint with C.E. Praeger and Á. Seress
Journal of Pure and Applied Algebra 216 (2012), 1580-1610

33. Prime order derangements in primitive permutation groups
joint with M. Giudici and R.A. Wilson
Journal of Algebra 341 (2011), 158-178

34. On base sizes for symmetric groups
joint with R.M. Guralnick and J. Saxl
Bulletin of the London Mathematical Society 43 (2011), 386-391

35. Base sizes for sporadic simple groups
joint with E.A. O'Brien and R.A. Wilson
Israel Journal of Mathematics 177 (2010), 307-334

36. On the number of prime order subgroups of finite groups
joint with S.D. Scott
Journal of the Australian Mathematical Society 87 (2009), 329-357

37. 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), 116-162

38. On base sizes for actions of finite classical groups
Journal of the London Mathematical Society 75 (2007), 545-562

39. Fixed point ratios in actions of finite classical groups, IV
Journal of Algebra 314 (2007), 749-788

40. Fixed point ratios in actions of finite classical groups, III
Journal of Algebra 314 (2007), 693-748

41. Fixed point ratios in actions of finite classical groups, II
Journal of Algebra 309 (2007), 80-138

42. Fixed point ratios in actions of finite classical groups, I
Journal of Algebra 309 (2007), 69-79

43. Fixed point spaces in actions of classical algebraic groups
Journal of Group Theory 7 (2004), 311-346

44. Fixed point spaces in primitive actions of simple algebraic groups
Journal of Algebra 265 (2003), 744-771

### Theses

1. Fixed point spaces in actions of finite and algebraic simple groups
Ph.D. thesis, Imperial College London (2005)

2. Reductive algebraic groups and Tits systems
M.Sc. thesis, University of Warwick (2001)