Dr Scott Harper MMath PhD

School of Mathematics
Assistant Professor in Algebra
125th Anniversary Fellow

Contact details

Email: s.harper.3@bham.ac.uk

Address: School of Mathematics
Watson Building
University of Birmingham
Edgbaston
Birmingham
B15 2TT
UK

Scott Harper is an Assistant Professor in the School of Mathematics and one of the newly appointed 125th Anniversary Fellows. His general area of research is group theory: the mathematical study of symmetry. This research has recently funded by an EPSRC Postdoctoral Fellowship and a Leverhulme Early Career Fellowship. Scott enjoys communicating his research to a wide audience, and his presentation in the Houses of Parliament at STEM for Britain won the Gold Medal.

For more information, see his personal website.

Qualifications

PhD in Mathematics, University of Bristol, 2019
MMath in Mathematics, University of St Andrews, 2015

Research

Scott's research is in group theory, and his current interests include generating sets and subgroup structure of abstract groups, and derangements and bases of permutation groups. His work connects with representation theory, geometric group theory, Lie theory and combinatorics. He is also interested in proof formalisation, mathematics education and the philosophy of mathematical practice.

Publications

Recent publications

Book

Harper, S 2021, The spread of almost simple classical groups. Lecture Notes in Mathematics, vol. 2286, Springer. https://doi.org/10.1007/978-3-030-74100-6

Article

Fusari, M, Harper, S & Spiga, P 2025, 'Kronecker classes, normal coverings and chief factors of groups', Bulletin of the Australian Mathematical Society. https://doi.org/10.1017/S0004972725000176

Harper, S & Liebeck, MW 2025, 'Representations of extensions of simple groups', Archiv der Mathematik, vol. 124, pp. 365–375. https://doi.org/10.1007/s00013-025-02105-1

Cameron, P, Craven, D, Dorbidi, HR, Harper, S & Sambale, B 2024, 'Minimal cover groups', Journal of Algebra, vol. 660, pp. 345-372. https://doi.org/10.1016/j.jalgebra.2024.06.038

Harper, S 2024, 'Totally deranged elements of almost simple groups and invariable generating sets', Journal of the London Mathematical Society, vol. 109, no. 6, e12935. https://doi.org/10.1112/jlms.12935

Harper, S 2023, 'The maximal size of a minimal generating set', Forum of Mathematics, Sigma, vol. 11, e70. https://doi.org/10.1017/fms.2023.71

Bleak, C, Harper, S & Skipper, R 2023, 'Thompson's group T is 3/2-generated', Israel Journal of Mathematics.

Harper, S 2022, 'Flexibility in generating sets of finite groups', Archiv der Mathematik, vol. 118, pp. 231–237. https://doi.org/10.1007/s00013-021-01691-0

Harper, S 2021, 'Shintani descent, simple groups and spread', Journal of Algebra, vol. 578, pp. 319-355. https://doi.org/10.1016/j.jalgebra.2021.02.021

Burness, T, Guralnick, R & Harper, S 2021, 'The spread of a finite group', Annals of Mathematics, vol. 193, no. 2, pp. 619-687. https://doi.org/10.4007/annals.2021.193.2.5

Harper, S & Lucchini, A 2020, 'Connectivity of generating graphs of nilpotent groups', Algebraic Combinatorics, vol. 3. https://doi.org/10.5802/alco.132

Burness, T & Harper, S 2020, 'Finite groups, 2-generation and the uniform domination number', Israel Journal of Mathematics, vol. 239. https://doi.org/10.1007/s11856-020-2050-8

Donoven, C & Harper, S 2020, 'Infinite 3/2-generated groups', Bulletin of the London Mathematical Society, vol. 52. https://doi.org/10.1112/blms.12356

Bamberg, J, Glasby, S, Harper, S & Praeger, C 2020, 'Permutations with orders coprime to a given integer', Electronic Journal of Combinatorics, vol. 27. https://doi.org/10.37236/8678

Chapter (peer-reviewed)

Harper, S 2024, The spread of finite and infinite groups. in CM Campbell, MR Quick, EF Robertson, CM Roney-Dougal & DI Stewart (eds), Groups St Andrews 2022 in Newcastle. 1 edn, London Mathematical Society Lecture Notes Series, vol. 496, Cambridge University Press, pp. 74-117. https://doi.org/10.1017/9781009563208.004

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