Dr Scott Harper MMath PhD

Dr Scott Harper

School of Mathematics
Assistant Professor in Algebra
125th Anniversary Fellow

Contact details

Email
s.harper.3@bham.ac.uk
View my research portal
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

Biography

Scott Harper attended Kirkcaldy High School, a comprehensive state school in Fife, and he was awarded the school's Dux Medal. He then studied Mathematics at the University of St Andrews, graduating with an MMath and receiving the Sanderson Prize as the top mathematics undergraduate.

Following a PhD in Mathematics with Prof Tim Burness at the University of Bristol, he held research fellow positions at the University of Padua, the Heilbronn Institute for Mathematical Research in Bristol and at the University of St Andrews, the last of these being supported by an Leverhulme Early Career Fellowship and then an EPSRC Postdoctoral Fellowship. In April 2025, Scott was appointed as an Assistant Professor at the University of Birmingham, and he is one the 125th Anniversary Fellows.

Scott's general area of research is group theory: the mathematical study of symmetry. He is interested in properties of abstract groups, such as generating sets and subgroup structure, and he is also interested in properties of group actions, such as derangements and bases of permutation groups. While group theoretic questions are usually the motivation for his work, some of his projects would be better described as representation theory, geometric group theory, Lie theory or combinatorics. Lately, he has become involved in formalising proofs in Lean. He is also interested in mathematics education and the philosophy of mathematical practice.

In 2024, Scott was awarded the Reinhold Baer Prize, and his presentation in the Houses of Parliament at STEM for Britain 2021 won the Gold Medal.

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

View all publications in research portal