Professor Sergey Shpectorov PhD

School of Mathematics
Professor of Pure Mathematics

Contact details

Telephone: +44 (0) 121 414 6604
Email: s.shpectorov@bham.ac.uk

View my research portal

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

School web page.

Qualifications

PhD in Mathematics, Moscow State University, 1990

Teaching

Semester 1

LH/LM Number Theory

Semester 2

LH/LM Number Theory

Research

Research activity

Sergey's research interests are in algebra, geometry, and combinatorics. The unifying theme is actions of groups: on geometries, graphs, Riemann surfaces, and, recently, axial algebras, which form a new interesting class of non-associative structures having applications in physics.

In core group theory, Sergey is interested in finite simple groups, their classification, origin and properties of sporadic simple groups, and fusion systems.

He is also interested in purely geometric and purely combinatorial questions, in particular, in the theory of diagram geometries and buildings, algebraic graph theory, and metric graph theory, including partial cubes and similar graphs with good metric properties.

Publications

Recent publications

Article

Franchi, C, Mainardis, M & Shpectorov, S 2025, '2-generated axial algebras of Monster type', Journal of Algebra, vol. 683, pp. 60-115. https://doi.org/10.1016/j.jalgebra.2025.06.023

Gorshkov, IB, McInroy, J, Mudziiri Shumba, TM & Shpectorov, S 2025, 'Automorphism groups of axial algebras', Journal of Algebra, vol. 661, pp. 657-712. https://doi.org/10.1016/j.jalgebra.2024.08.007

Rodrigues, BG & Shpectorov, S 2025, 'Radicals in flip subalgebras of Matsuo algebras', Arabian Journal of Mathematics. https://doi.org/10.1007/s40065-025-00511-5

Franchi, C, Mainardis, M & Shpectorov, S 2023, '2-generated axial algebras of Monster type (2β,β)', Journal of Algebra, vol. 636, pp. 123-170. https://doi.org/10.1016/j.jalgebra.2023.08.020

Mcinroy, J & Shpectorov, S 2023, 'From forbidden configurations to a classification of some axial algebras of Monster type', Journal of Algebra, vol. 627, pp. 58-105. https://doi.org/10.1016/j.jalgebra.2023.03.003

Franchi, C, Mainardis, M & Shpectorov, S 2022, 'An infinite-dimensional 2-generated primitive axial algebra of Monster type', Annali di Matematica Pura ed Applicata, vol. 201, pp. 1279-1293. https://doi.org/10.1007/s10231-021-01157-8

Chapter

Meierfrankenfeld, U & Shpectorov, S 2023, Maximal 2-Local Subgroups of the Monster and Baby Monster. in AA Ivanov (ed.), Algebraic Combinatorics and the Monster Group. London Mathematical Society Lecture Note Series, vol. 487, Cambridge University Press, pp. 200-245. https://doi.org/10.1017/9781009338073.005

Preprint

Gorshkov, I & Shpectorov, S 2026 'Axial Algebras: Questions and Conjectures' arXiv. https://doi.org/10.48550/arXiv.2606.30048

Shah, M & Shpectorov, S 2026 'Enumerating AG-monoids algebraically' arXiv. https://doi.org/10.48550/arXiv.2601.03312

Mudziiri Shumba, TM & Shpectorov, S 2026 'Full automorphism groups of the axial algebra for M₁₁ and related algebras' arXiv. https://doi.org/10.48550/arXiv.2602.07556

Mamontov, A, Shpectorov, S & Zhelyabin, V 2026 'Radicals in primitive axial algebras' arXiv. https://doi.org/10.48550/arXiv.2602.11984

Shpectorov, S & Zhao, T 2025 'Strongly regular graphs with parameters (85,14,3,2) do not exist' arXiv. https://doi.org/10.48550/arXiv.2504.02449

Rodrigues, BG & Shpectorov, S 2024 'Radicals in flip subalgebras' arXiv. https://doi.org/10.48550/arXiv.2409.05236

Gorshkov, I, Shpectorov, S & Staroletov, A 2024 'Solid subalgebras in algebras of Jordan type half' arXiv, pp. 1-38. https://doi.org/10.48550/arXiv.2401.16218

McInroy, J & Shpectorov, S 2022 'Axial algebras of Jordan and Monster type' arXiv, pp. 1-40. https://doi.org/10.48550/arXiv.2209.08043

View all publications in research portal