Research Interests

Below is a (non-exhaustive) list of topics in which I am interested together with some recent papers I produced in the subject.

Hypertopes and C-groups

  • with T.Connor and S.Jambor, C-groups of PSL(2,q) and PGL(2,q), J. Algebra 427 (2015), 455-466.

    Abstract regular and chiral polytopes

  • with T.Connor and J.De Saedeleer, Almost simple groups with socle PSL(2,q) acting on abstract regular polytopes, J. Algebra 423 (2015), 550-558.
  • with T.Connor and M.Mixer, Abstract regular polytopes for the O'Nan group. International Journal of Algebra and Computation 24 (2014), nr. 1, 59-68.
  • with I.Hubard, Chiral polytopes and Suzuki simple groups, In Eds. R. Connelly, W. Whitely, A. Weiss, Rigidity and Symmetry, Fields Institute Communications 70 (2014), 155-175.
  • with M.-E.Fernandes and M.Mixer, Corrigendum to "Polytopes of high rank for the symmetric groups", Adv. Math. 238 (2013), 506-508.
  • with A.Kiefer, On pairs of commuting involutions in Sym(n) and Alt(n), Comm. Algebra 41 (2013), nr. 12, 4408-4418.
  • with M.-E.Fernandes and M.Mixer, Polytopes of high rank for the alternating groups. J. Combin. Theory Ser. A 119 (2012), 42-56.
  • with M. I. Hartley and I. Hubard, Regular 4-polytopes from the Livingstone graph of Janko's first group. J. Algebraic Combin. 35 (2012), 193-214.
  • with M.-E.Fernandes and M.Mixer, All alternating groups An with n ≥ 12 have polytopes of rank (n-1)/2 . SIAM Journal on Discrete Math. 26 (2012), nr. 2, 482-498.
  • with M. I. Hartley and I. Hubard, Two atlases of abstract chiral polytopes for small groups. Ars Math. Contemp.5 (2012), 371-382.
  • with M.Mixer, Algorithms for classifying regular polytopes with a fixed automorphism group, Contr. Discrete Math. 7 (2012), 105-118.
  • with M.-E. Fernandez, Polytopes of high rank for the symmetric groups. Adv. Math. 228 (2011), 3207-3222.

    Computational Algebra and Computational Incidence Geometry

  • with T.Connor, An Atlas of subgroup lattices of finite almost simple groups. Ars Math. Contemp.8 (2015), 259-266.
  • with T.Connor, A new algorithm to find apartments in coset geometries. Groups, Complexity, Cryptology 5 (2013), nr. 1, 75-89.

    Locally s-arc-transitive graphs

  • with W. Fan, C.H.Li and J.Pan, Locally 2-arc-transitive complete bipartite graphs. J. Combin. Theory Ser. A 120 (2013), 683-699.

    Incidence Geometry

  • with J.De Saedeleer, M.Mixer and T.Pisanski, Core-free, rank two coset geometries from edge-transitive bipartite graphs, Math. Slovaca 64 (2014), 1-16.
  • with F.Buekenhout and J.De Saedeleer, The rank two geometries of the PSL(2,q) groups : part II. Ars Math. Contemp. 6 (2013), 365-388.

    Coding Theory

  • with B.G.Rodrigues, Binary codes of some strongly regular graphs of the McLaughlin graph. Designs, Codes, Crypto. 67 (2013), nr. 1, 93-109.