Publications and Preprints

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Publications

Research

Teaching
My arXiv page can be found here
My MathSciNet page can be found here

In preparation

  1. A new family of baric axial algebras

  2. Varieties of axial algebras
    with Simon Peacock
    in preparation

  3. Expansions of axial decomposition algebras
    with Simon Peacock and Michiel Van Couwenberghe
    in preparation

  4. Axial decomposition algebras for the pariah groups $J_3$ and $Ly$
    with Simon Peacock and Michiel Van Couwenberghe
    in preparation

  5. Computations with algebras of Jordan type
    with Sergey Shpectorov
    in preparation

Publications and Preprints

  1. Quotients of the Highwater algebra and its cover
    with Clara Franchi and Mario Mainardis
    submitted, 46 pages, May 2022
    arXiv

  2. Axial algebras of Jordan and Monster type
    with Sergey Shpectorov
    Proceedings of Groups St Andrews 2022, to appear, 40 pages
    arXiv

  3. Forbidden configurations for axial algebras of Monster type
    with Sergey Shpectorov
    Journal of Algebra, to appear, 49 pages
    arXiv

  4. $3$-generated axial algebras with a minimal Miyamoto group
    11 pages, Apr 2020
    arXiv

  5. Split spin factor algebras
    with Sergey Shpectorov
    Journal of Algebra 595 (2022), 380-397
    arXiv | doi:10.1016/j.jalgebra.2021.12.022

  6. Enumerating $3$-generated axial algebras of Monster type
    with Sanhan Khasraw and Sergey Shpectorov
    Journal of Pure and Applied Algebra 226 (2022), no. 2, 21 pages
    arXiv | doi:10.1016/j.jpaa.2021.106816

  7. Miyamoto groups of code algebras generated by small idempotents
    with Alonso Castillo-Ramirez
    Journal of Pure and Applied Algebra 225 (2021), no. 6, 19 pages
    arXiv | doi:10.1016/j.jpaa.2020.106619

  8. An expansion algorithm for constructing axial algebras
    with Sergey Shpectorov
    Journal of Algebra 550 (2020), 379-409
    arXiv | doi:10.1016/j.jalgebra.2019.12.018

  9. On the structure of axial algebras
    with Sanhan Khasraw and Sergey Shpectorov
    Transactions of the American Mathematical Society 373 (2020), 2135-2156
    arXiv | doi:10.1090/tran/7979

  10. Code algebras which are axial algebras and their $\mathbb{Z}_2$-gradings
    with Alonso Castillo-Ramirez
    Israel Journal of Mathematics 233 (2019), 401-438
    arXiv | doi:10.1007/s11856-019-1911-5

  11. Code algebras, axial algebras and VOAs
    with Alonso Castillo-Ramirez and Felix Rehren
    Journal of Algebra 518 (2019), 146-176
    arXiv | doi:10.1016/j.jalgebra.2018.09.038

  12. Vahlen groups defined over commutative rings
    Mathematische Zeitschrift 284 (2016), no. 3, 901-917
    arXiv | doi:10.1007/s00209-016-1678-x

  13. On Sidki's presentation for orthogonal groups
    with Sergey Shpectorov
    Journal of Algebra 434 (2015), 227-248
    arXiv | doi:10.1016/j.jalgebra.2015.02.031

  14. An amalgam uniqueness result for recognising $q^6:SU_3(q)$, $G_2(q)$, or $3^\cdot M_{10}$ using biaffine polar spaces
    Journal of Algebra 400 (2014), 105-122
    doi:10.1016/j.jalgebra.2013.10.028

  15. New flag-transitive geometries for the groups $Sp_4(K)$ and $SU_5(K)$
    with Harm Pralle and Sergey Shpectorov
    Geometriae Dedicata 173 (2014), 65-82
    doi:10.1007/s10711-013-9928-0

  16. Biaffine polar spaces
    Advances in Geometry 13 (2013), no. 3, 449-469
    doi:10.1515/advgeom-2012-0034

  17. On the simple connectedness of hyperplane complements in dual polar spaces, II
    with Sergey Shpectorov
    Discrete Mathematics 310 (2010), no. 8, 1381-1388.
    doi:10.1016/j.disc.2010.01.007

  18. A family of biaffine geometries and their resulting amalgams
    PhD thesis, University of Birmingham (2010)
    thesis

  19. On the simple connectivity of hyperplane complements in dual polar spaces
    MPhil(Qual) thesis, University of Birmingham (2008)
    thesis

Computer programs

  1. A magma package to construct axial algebras with a given Miyamoto group

  2. A magma package for working with large-dimensional decomposed $G$-modules
    with Sergey Shpectorov

  3. A magma package for fusion laws
    with Simon Peacock and Michiel Van Couwenberghe

  4. A magma package for decomposition algebras
    with Simon Peacock and Michiel Van Couwenberghe

  5. A program for calculating the fundamental group of a geometry written in GAP