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 M. E. Fernandes, C. A. Piedade and A. Ivic Weiss, Two families of locally toroidal regular 4-hypertopes arising from toroids. In G. Cunningham, M. Mixer and E. Schulte (eds), Polytopes and Discrete Geometry, Contemp. Math. 764 (2021), 89-100.
with M. E. Fernandes and A. Ivic Weiss, An exploration of locally spherical regular hypertopes. Discrete Comput. Geom. 64, nr. 2 (2020), 519-534.
with D. Hou and Y. Feng, Existence of regular 3-hypertopes with 2n chambers. Discrete Math. 342 (2019), 1857-1863.
with M.-E.Fernandes, C-groups of high rank for the symmetric groups, J. Algebra 508 (2018), 196-218.
with D. Catalano, M.-E.Fernandes and I. Hubard, Hypertopes with tetrahedral diagram. Elec. J. Combin. 25 no. 3 (2018), P3.22.
with M.-E. Fernandes and A. Weiss, Hexagonal extensions of toroidal maps and hypermaps,
M.D.E.Conder et al. (editors), Discrete Geometry and Symmetry, Dedicated to Karoly Bezdek and Egon Schulte on the Occasion of Their 60th Birthdays,
Springer Proceedings in Mathematics and Statistics 234 (2018), 147-170.
with M.-E.Fernandes and A.Ivic-Weiss, Highly symmetric hypertopes, Aequationes Math. 90 (2016), 1045-1067.
with T.Connor and S.Jambor, C-groups of PSL(2,q) and PGL(2,q), J. Algebra 427 (2015), 455-466.
with T.Connor, C-groups of Suzuki type. J. Algebraic Combin. 42 (2015), 849-860.
Abstract regular and chiral polytopes
with A. Vandenschrick, On chiral polytopes having a group PSL(3,q) as automorphism group. J. London Math. Soc., to appear, 25 pages.
String C-group representations of almost simple groups: a survey. In G. Cunningham, M. Mixer and E. Schulte (eds), Polytopes and Discrete Geometry, Contemp. Math. 764 (2021), 157-178.
with P. A. Brooksbank and J. T. Ferrara, Orthogonal groups in characteristic 2 acting on polytopes of high rank. Discrete Comput. Geom. 63 (2020), 656-669.
with D. Hou and Y. Feng, On regular polytopes of 2-power order. Discrete Comput. Geom. 64, nr. 2 (2020), 339-346.
with D. Hou and Y. Feng, 2-groups behaving as automorphism groups of regular 3-polytopes. J. Group Theory 22 (2019), 579-616.
with P. A. Brooksbank, Rank reduction of string C-group representations. Proc. Amer. Math. Soc. 147 (2019), 5421-5426.
with M.-E. Fernandes, String C-group representations of alternating groups. Ars Math. Contemp. 17 (2019), 291-310.
with E.Schulte and H.Van Maldeghem, Groups of Ree type in characteristic 3 acting on polytopes, Ars Math. Contemp. 14 (2018), 209-226.
with M.-E.Fernandes and M.Mixer, An extension of the classification of high rank regular polytopes, Trans. Amer. Math. Soc. 370 (2018), 8833-8857.
with J. Moerenhout and E. O'Reilly-Regueiro, Projective linear groups as automorphism groups of chiral polytopes, J. Geom. 108 (2017), 672-702.
with P.J.Cameron, M.-E.Fernandes and M.Mixer, Highest rank of a polytope for An, Proc. London Math. Soc. 115 (2017), 135-176.
with M. W. Liebeck, Chiral polyhedra and finite simple groups, Bull. London Math. Soc. 49 (2017), 581-592.
with P.J.Cameron, M.-E.Fernandes and M.Mixer, String C-groups as transitive subgroups of Sym(n), J. Algebra 447 (2016), 468-478.
with P.A.Brooksbank, Polytopes of large rank for PSL(4,q), J. Algebra 452 (2016), 390-400.
with J. Moerenhout, Chiral polyhedra arising from almost simple groups with socle PSL(2,q), J. Algebraic Combin. 44, 293-323.
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 J. Mulpas, The String C-group representations of the Suzuki, Rudvalis and O'Nan sporadic groups. Art Discrete Appl. Math., to appear. 13 pages.
with F. Buekenhout and P. Tranchida, A new algorithm to classify chiral polytopes with a given automorphism group. Beitrage Algebra Geom. 62 (2021), 21-36.
with B.G.Rodrigues, On primitive geometries of rank two, Art Discrete Appl. Math. 2 (2019), #P1.08.
with T.Connor, Algorithmic enumeration of regular maps. Ars Math. Contemp. 10 (2016), 211-222.
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.
with N. Garcia-Colin, An infinite family of locally X graphs based on incidence geometries. Art Discrete Appl. Math. 4 (2021), #P3.01.
with P. Tranchida, On residual connectedness in chiral geometries. Algebr. Comb. 4, no. 3 (2021), 491-499.
with K. Stokes, Coset geometries with trialities and their reduced incidence graphs.
Acta Math. Univ. Comenianae 89 (2019), 911-916.
with F.Buekenhout and J.De Saedeleer, Two-transitive pairs in PSL(2,q). Bull. Belg. Math. Soc. - Simon Stevin 23 (2016), 33-55.
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.
Linear codes with complementary duals from some strongly regular subgraphs of the McLaughlin graph, Math. Comm. 21 (2016), 239-249.
with B.G.Rodrigues, Binary codes of some strongly regular graphs of the McLaughlin graph. Designs, Codes, Crypto. 67 (2013), nr. 1, 93-109.