Potrait photo of Alastair Litterick

Hi. I'm Alastair Litterick.

I'm a Lecturer in Mathematics at the University of Essex.

I am an algebraist, interested in linear algebraic groups, finite groups of Lie type and everything related to these, including algebraic geometry, group representation theory, Lie algebras, computational algebra, geometric invariant theory, Lie theory, combinatorics and more.

My research interests

Research interests

  • G-complete reducibility

    This area of research investigates the relationship between subgroups of linear algebraic groups, representation theory and geometric invariant theory. To learn more, one possible starting point is this survey article.

  • Subgroup structure of reductive algebraic groups

    This area forms part of an effort dating back to work of E.B. Dynkin in the 1950s, classifying various subgroups of reductive groups. Some of my contributions to this area are here (arXiv) and here (arXiv).

  • Finitely-generated groups and their images in algebraic groups

    This area studies finitely-generated subgroups of linear algebraic groups. These can be studied directly via abstract group theory, algebraic geometry and geometric invariant theory. On the other hand, finitely-generated subgroups are images of finitely generated groups, and so this can also be viewed as a problem in geometric group theory. My introduction to this area was in my Masters thesis at Imperial College, which spawned this note.

  • Computational algebra

    This area produces and uses algorithms to solve problems in algebra, particularly group theory. My modest contributions include methods for enumerating feasible characters of finite subgroups on modules for exceptional algebraic groups (here), and methods for enumerating elementary abelian subgroups in simple algebraic groups (here).


  • Feodor Lynen Research Fellowships

    As an alumnus of the Humboldt Foundation, I am eligible to host researchers from Germany as Feodor Lynen Research Fellows. More information can be found here.

  • Study with me

    I am open to supervising doctoral students in the areas mentioned above and on related topics. Our department advertises PhD scholarships from time to time, which cover home student fees (or an equivalent discount for international students) and a stipend for living costs.

  • Become a colleague at Essex

    Our department is a growing one, and job opportunities crop up regularly. These are usually posted to jobs.ac.uk.

  • Collaborate

    I'm always looking to get involved in new projects, especially if they involve learning something new! To get in contact, please email me.


  1. Complete reducibility of subgroups of reductive algebraic groups over nonperfect fields IV: An F4 example, with F. Bannuscher and T. Uchiyama. Journal of Group Theory 25, no. 3 (2022), pp. 527–541. (Publisher) (ArXiv)
  2. Complete reducibility: Variations on a theme of Serre, with M. Gruchot and G. Röhrle. Manuscripta Mathematica 168 (2021), 439–451. (Publisher) (ArXiv)
  3. Relative complete reducibility and normalised subgroups, with M. Gruchot and G. Röhrle. Forum of Mathematics, Sigma 8 (2020), e30, 32 pp. (Publisher) (ArXiv)
  4. On relative complete reducibility, with C. Attenborough, M. Bate, M. Gruchot and G. Röhrle. Quarterly Journal of Mathematics 71, issue 1 (2020), pp. 324–334. (Publisher) (ArXiv)
  5. Reducible subgroups of exceptional algebraic groups, with A. Thomas. Journal of Pure and Applied Algebra 223, no. 6 (2019) pp. 2489–2529. (Publisher) (ArXiv)
  6. Further rigid triples of classes in G2, with M. Conder. International Journal of Group Theory 8, no. 1 (2019), pp. 5–9. (Publisher) (ArXiv)
  7. On finite simple images of triangle groups, with S. Jambor and C. Marion. Israel Journal of Mathematics 227, issue 1 (2018), pp. 131–162. (Publisher) (ArXiv)
  8. Complete reducibility in good characteristic, with A. Thomas. Transactions of the American Mathematical Society 370, no. 8 (2018) pp. 5279–5340. (Publisher) (ArXiv)
  9. On non-generic finite simple subgroups of exceptional algebraic groups. Memoirs of the American Mathematical Society 253, no 1207 (2018), vi+156 pp. (Publisher) (ArXiv)
  10. A rigid triple of conjugacy classes in G2, with M. Liebeck and C. Marion. Journal of Group Theory 14 (2011), pp. 31–35. (PDF) (Publisher)


  • Complete reducibility and subgroups of exceptional algebraic groups, with D. Stewart and A. Thomas. 42 pages, submitted. (ArXiv)
  • Complete reducibility in bad characteristic, with A. Thomas. 41 pages, submitted. (ArXiv)
  • Elementary abelian subgroups: from algebraic groups to finite groups, with J. An and H. Dietrich. 37 pages, submitted. (ArXiv)
  • Rigid representations of triangle groups, with B. Martin. Preprint, 6 pages. (ArXiv)


2019 – present

Lecturer in Mathematics

University of Essex, Department of Mathematical Sciences

Apr – Oct 2017

Postdoctoral Researcher

Wissenschaftlicher Mitarbeiter at the Ruhr-University, Bochum

2016 – 2017

Postdoctoral Researcher

Wissenschaftlicher Mitarbeiter at Bielefeld University

2013 – 2015

Postdoctoral Research Fellow

University of Auckland

2009 – 2013

Graduate Teaching Assistant

Imperial College London (casual)


Shield of Imperial College London

MSci Mathematics (1st)

Imperial College London, 2009.
Supervised by Martin Liebeck

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