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.

Abstract regular polytopes and C-groups

(Almost) Simple groups acting on polytopes.
  • with E. Schulte, Polytopes with groups of type PGL(2,q). Ars Math. Comtemp., accepted pending revision, 13 pages.
  • with E. Schulte, Groups of type L(2,q) acting on polytopes. Adv. Geom. 7(2007), nr. 4, 529-539.
  • Almost simple groups of Suzuki type acting on polytopes. Proc. Amer. Math. Soc. 134(2006), 3649-3651.
  • with L. Vauthier, An atlas of abstract regular polytopes for small groups. Aequationes Math. 72(2006), nr. 3, 313-320. Abstract polytopes, Petrials, and their connection with thin regular geometries.
  • with M. I. Hartley, On locally spherical polytopes of type {5,3,5}. Discrete Math. 309(2009), 247-254.
  • with M. I. Hartley, A new Petrie-like construction for abstract polytopes. J. Combin. Theory Ser. A 115(2008), 997-1007.
  • with M.I. Hartley On the thin regular geometries of rank four for the Janko group J(1). Innovations in Incidence Geometry 1(2005), 181-190.
  • with M. I. Hartley, Quotients of a universal locally projective polytope of type {5,3,5}. Math. Z. 247(2004), nr. 4, 663-674.

    Computational Incidence Geometry

    Development of the package on incidence geometries and coset geometries, available in the Magma language.
    Algorithmic study of properties in incidence geometry.
  • with P. Jacobs, An algorithmic analysis of the intersection property. LMS J. Comput. Math. 7(2004), 284-299.

    Classification of locally s-arc-transitive graphs.
  • Locally s-arc-transitive graphs related to sporadic simple groups. J. Algebra 322(2009), 882-892.

    Incidence Geometry

    Classifications of geometries arising from a group and satisfying a set of axioms.
  • with F. Buekenhout, On apartments in incidence geometry. Journal of Combinatorics, Information & System Sciences, to appear, 17 pages.
  • Residually weakly primitive and locally two-transitive geometries for sporadic groups. Acad. roy. Belgique, Mem. Cl. Sci., Coll. 4, Ser. 3, Tome XI(2008), 173pp.
  • with F. Buekenhout, A rank six geometry related to the McLaughlin sporadic simple group . Designs, Codes, Crypto. 44(2007), nr. 1/2/3, 151-155.
  • The residually weakly primitive geometries of HS. Australas. J. Combin. 33 (2005), 231-236.
  • A family of geometries related to the Suzuki tower. Comm. Algebra 33 (2005), nr. 7, 2201-2217.
  • Two rank six geometries for the Higman-Sims sporadic group. Discrete Math. 294(2005), nr. 1-2, 123-132.
  • A generalization of a construction due to Van Nypelseer. Beitrage Algebra Geom. 46 (2005), nr. 2, 561-574.
  • with P. Cara, On inductively minimal geometries that satisfy the intersection property. J. Combin. Theory Ser. A. 111 (2005), nr. 2, 327-330.
  • Constructions of rank five geometries for the Mathieu group M_22. J. Geom. 79(2004), nr. 1-2, 146-155.
  • with M. Gailly, The residually weakly primitive geometries of PSL(3,q) with q < 8. Aequationes Math. 67(2004), 195-196.
  • The residually weakly primitive geometries of J_3. Experiment. Math. 13(2004), nr. 4, 429-433.
  • The residually weakly primitive geometries of M_23. Atti Sem. Mat. Fis. Univ. Modena e Reggio Emilia, LII(2004), 313-316.

    Current groups under investigation: the sporadic group O'Nan.
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