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.,

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.

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.

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.

Blok, R, Hoffman, C & Shpectorov, S 2018, 'Classification of Curtis-Tits and Phan amalgams with 3-spherical diagram', Israel Journal of Mathematics.

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.

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.

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

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

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, 'Universal axial algebras and a theorem of Sakuma', Journal of Algebra, vol. 421, pp. 394-424.

Magaard, K, Shpectorov, S & James, A 2015, 'The lift invariant distinguishes components of Hurwitz spaces for A5', Proceedings of the American Mathematical Society, vol. 143, pp. 1377-1390.

McInroy, JF, Pralle, H & Shpectorov, S 2014, 'New flag-transitive geometries for the groups {Mathematical expression} and {Mathematical expression}', Geometriae Dedicata, vol. 173, no. 1, pp. 65–82.

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