Professor Sergey Shpectorov

Professor Sergey Shpectorov

School of Mathematics
Professor of Pure Mathematics

Contact details

School of Mathematics
Watson Building
University of Birmingham
B15 2TT


  • PhD (Mathematics, Moscow State University 1990)



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


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

Franchi, C, Mainardis, M & Shpectorov, S 2020, 'An infinite-dimensional 2-generated primitive axial algebra of Monster type', Proceedings of the American Mathematical Society.

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

Galt, A, Joshi, V, Mamontov, A, Shpectorov, S & Staroletov, A 2020, 'Double axes and subalgebras of Monster type in Matsuo algebras', Communications in Algebra.

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.

Wang, G & Shpectorov, S 2018, 'l1-embeddability of generic quadrilateral Möbius maps', European Journal of Combinatorics.

McInroy, J & Shpectorov, S 2015, 'On Sidki's presentation for orthogonal groups', Journal of Algebra, vol. 434, pp. 227-248.

Cohen, AM, O'Brien, EA & Shpectorov, S 2015, 'On the uniqueness of the generalized octagon of order (2, 4)', Journal of Algebra, vol. 421, pp. 369-393.

Hall, JI, Rehren, F & Shpectorov, S 2015, 'Primitive axial algebras of Jordan type', Journal of Algebra, vol. 437, pp. 79-115.

Cuypers, H, Roberts, K & Shpectorov, S 2015, 'Recovering the Lie algebra from its extremal geometry', Journal of Algebra, vol. 441, pp. 196-215.

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