Personal profile
Research overview
Peter Cameron is currently an Emeritus Professor of Mathematics in the School of Mathematics and Statistics, having been a (part-time) professor since 2013. He previously spent 11 years at the University of Oxford and 26 years at Queen Mary University of London. His research is in the areas of algebra (groups, permutation groups, semigroups), combinatorics (enumeration, design theory and finite geometry, graph theory), and model theory (countably categorical structures). He is known for his work exploring consequences of the Classification of Finite Simple Groups for permutation group theory, for automorphism groups of countably categorical structures (he invented the term "oligomorphic" to describe these groups), and more recently applications of permutation groups in semigroup theory and in design of experiments in statistics. He has published nearly 400 papers and has 250 coauthors. A highly cited paper uses the classification of the ADE Coxeter--Dynkin diagrams and associated root systems in the proof of a conjecture of Hoffman on graphs with least eigenvalue -2.
Teaching activity
After arriving in St Andrews, Peter Cameron taught MT5821, Advanced Combinatorics (now MT5861) for 10 years. and a new module MT5867 on Set Theory and Mathematical Logic for 2 years (with Nik Ruskuc). He has also supervised independent learning modules on various topics including logic, combinatorics, and representation theory. Previous teaching activity includes devising a first-semester introductory module to University mathematics at Queen Mary University of London, and courses in number theory, linear algebra, algebraic structures, group theory, logic, and topology, as well as short courses at Masters/PhD level on Synchronization, Laplacian Eigenvalues, Group Theory, and the Random Graph.
He was awarded Students Association Teaching Innovation Prize 2015
Academic/Professional Qualification
BSc (Hons), University of Queensland
DPhil, MA, University of Oxford
Other expertise
Chair, British Combinatorial Committee, 1994-2022
Profile Keywords
Groups and their operands
Education/Academic qualification
Doctor of Philosophy, Structure of suborbits in some primitive permutation groups, University of Oxford
Award Date: 1 Dec 1971
Bachelor of Science, University of Queensland
Award Date: 1 May 1968
External positions
Professor Emeritus, Queen Mary University of London
1 Sept 2012 → …
Fingerprint
- 1 Similar Profiles
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The geometry of diagonal groups
Bailey, R. A., Cameron, P. J., Praeger, C. E. & Schneider, C., Aug 2022, In: Transactions of the American Mathematical Society. 375, 8, p. 5259-5311Research output: Contribution to journal › Article › peer-review
Open AccessFile -
Graphs defined on groups
Cameron, P. J., Jun 2022, In: International Journal of Group Theory. 11, 2, p. 53-107Research output: Contribution to journal › Article › peer-review
Open AccessFile -
The Hall–Paige conjecture, and synchronization for affine and diagonal groups
Bray, J., Cai, Q., Cameron, P. J., Spiga, P. & Zhang, H., Mar 2020, In: Journal of Algebra. 545, p. 27-42Research output: Contribution to journal › Article › peer-review
Open AccessFile -
Highest rank of a polytope for An
Cameron, P. J., Fernandes, M. E., Leemans, D. & Mixer, M., 4 Jul 2017, In: Proceedings of the London Mathematical Society. 115, 1, p. 135-176 42 p.Research output: Contribution to journal › Article › peer-review
Open AccessFile -
Between primitive and 2-transitive: synchronization and its friends
Araújo, J., Cameron, P. J. & Steinberg, B., 2017, In: EMS Surveys in Mathematical Sciences. 4, 2, p. 101-184Research output: Contribution to journal › Article › peer-review
Open AccessFile
Datasets
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Diameters of graphs related to groups and base sizes of primitive groups - GAP and Magma code (thesis data)
Freedman, S. D. (Creator), Roney-Dougal, C. M. (Supervisor) & Cameron, P. J. (Supervisor), University of St Andrews, 16 Aug 2022
DOI: 10.17630/56ceed97-0a86-4684-b0a9-e454c1a7440b, http://hdl.handle.net/10023/26895
Dataset: Thesis dataset
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Solving decision problems in finitely presented groups via generalized small cancellation theory (thesis data)
Jurina, S. (Creator), Cameron, P. J. (Supervisor) & Roney-Dougal, C. M. (Supervisor), University of St Andrews, 21 Mar 2023
DOI: 10.17630/0f7a7c71-26f5-4346-9bf1-3da33e354721, https://doi.org/10.17630/sta/429
Dataset: Thesis dataset
File
Projects
- 2 Finished
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Bi-synchronizing automata: Bi-synchronizing automata, outer automorphism groups of Higman-Thompson groups, and automorphisms of the shift
Bleak, C. (PI) & Cameron, P. (CoI)
1/05/18 → 30/04/21
Project: Standard
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Durham Symposia: Permutation Groups and Transformation Semigroups
Mitchell, J. (PI) & Cameron, P. (CoI)
1/01/15 → 30/07/15
Project: Standard
Activities
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The road closure problem
Cameron, P. (Speaker)
9 Dec 2025Activity: Talk or presentation types › Invited talk
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PhD examination
Cameron, P. (External examiner)
9 Dec 2025Activity: Examination types › External examination
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Permutation groups, lattices and orthogonal block structures
Bailey, R. A. (Speaker) & Cameron, P. (Speaker)
15 Oct 2025Activity: Talk or presentation types › Invited talk
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Graphs (and simplicial complexes) defined on groups
Cameron, P. (Speaker)
7 Oct 2025Activity: Talk or presentation types › Invited talk
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Inverse group theory
Cameron, P. (Speaker)
29 Sept 2025Activity: Talk or presentation types › Invited talk
Prizes
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Senior Whitehead Prize
Cameron, P. J. (Recipient), 10 Nov 2017
Prize: Prize (including medals and awards)