Professor Sergey Shpectorov PhD

Professor Sergey Shpectorov

School of Mathematics
Professor of Pure Mathematics

Contact details

School of Mathematics
Watson Building
University of Birmingham
B15 2TT


  • PhD in Mathematics, Moscow State University, 1990


Semester 1

LH/LM Integer Programming and Combinatorial Optimisation

LI/LH Linear Algebra and Linear Programming

Semester 2

LH/LM Group Theory


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.


Recent publications


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.

Khasraw, SMS, McInroy, J & Shpectorov, S 2022, 'Enumerating 3-generated axial algebras of Monster type', Journal of Pure and Applied Algebra, vol. 226, no. 2, 106816.

McInroy, J & Shpectorov, S 2022, 'Split spin factor algebras', Journal of Algebra, vol. 595, pp. 380-397.

Galt, A, Joshi, V, Mamontov, A, Shpectorov, S & Staroletov, A 2021, 'Double axes and subalgebras of Monster type in Matsuo algebras', Communications in Algebra, vol. 49, no. 10, pp. 4208-4248.

Hall, JI & Shpectorov, S 2021, 'The spectra of finite 3-transposition groups', Arabian Journal of Mathematics, vol. 10, no. 3, pp. 611-638.

McInroy, J & Shpectorov, S 2020, 'An expansion algorithm for constructing axial algebras', Journal of Algebra, vol. 550, pp. 379-409.,

Medts, TD, Peacock, SF, Shpectorov, S & Couwenberghe, MV 2020, 'Decomposition algebras and axial algebras', Journal of Algebra, vol. 556, pp. 287-314.

Blok, R, Hoffman, C & Shpectorov, S 2019, 'Classification of Curtis-Tits and Phan amalgams with 3-spherical diagram', Israel Journal of Mathematics, vol. 230, no. 1, pp. 97–140.

Alfuraidan, MR, Sarumi, IO & Shpectorov, S 2019, 'On the Non-Existence of srg(76,21,2,7)', Graphs and Combinatorics, vol. 35, no. 4, pp. 847-854.

Khasraw, S, McInroy, J & Shpectorov, S 2019, 'On the structure of axial algebras', Transactions of the American Mathematical Society, vol. 373, no. 3, pp. 2135-2156.

Hall, JI, Segev, Y & Shpectorov, S 2018, 'Miyamoto involutions in axial algebras of Jordan type half', Israel Journal of Mathematics, vol. 223, no. 1, pp. 261-308.

Hall, JI, Segev, Y & Shpectorov, S 2018, 'On primitive axial algebras of Jordan type', Bulletin of the Institute of Mathematics Academia Sinica New Series, vol. 13, no. 4, pp. 397-409.

De Bruyn, B & Shpectorov, S 2018, 'The hyperplanes of the near hexagon related to the extended ternary Golay code', Geometriae Dedicata.


McInroy, J & Shpectorov, S 2022 'Axial algebras of Jordan and Monster type' arXiv, pp. 1-40.

McInroy, J & Shpectorov, S 2022 'From forbidden configurations to a classification of some axial algebras of Monster type' arXiv, pp. 1-48.

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