Research

Preprints and papers

  1. Complex Lorentzian Leech lattice and the bi-monster, Journal of Algebra 309 (2007), no. 1, 32--56. arXiv:math/0508228, pdf. 
  2. Reflection group of the quaternionic Lorentzian Leech lattice, Journal of Algebra 309 (2007), No. 1, 57--68. arXiv:math/0511650, pdf. 
  3. Comnbinatorial cell complexes and Poincare duality, Geometriae Dedicata Vol. 147 Number 1, (2010) 357--387. arXiv:0807.4165, pdf. 
  4. On Coxeter diagrams of complex reflection groups, Trans. Amer. Math. Soc. 364, No. 9 (2012) 4909--4936. arXiv:0809.2427, pdf. 
  5. Complex Lorentzian Leech lattice and the bimonster (II) Trans. Amer. Math. Soc. 368 (2016) 4171--4195. arXiv:0811.0062, pdf. 
  6. Modular lattices from finite projective planes, Journal de Théorie des Nombres de Bordeaux 26 (2014) 269--279. arXiv:1210.2431, pdf. 
  7. with Daniel Allcock: Geometric generators for braid like groups, Geometry & Topology 20 (2016) 747--778. arXiv:1403:2401, pdf.
  8. with Ryan Johnson: Indicators of Tambara-Yamagami categories and Gauss sums, Algebra & Number theory 9 (2015) No. 8, 1793--1823. arXiv:1405.7950, pdf.
  9. The octonions as a twisted group algebra, Finite Fields and Their Applications 50 (2018) 113--121.arXiv:1702.05705, pdf. 
  10. with Daniel Allcock: Generators for a complex hyperbolic braid group, Geometry & Topology 22 No. 6 (2018) 3435--3500. arXiv: 1702.05707, pdf.
  11. A Poincare series on hyperbolic space, Adv. Appl. Math. 95 (2018) 177--198. arXiv:1707.07790, pdf. 
  12. Root space decomposition of g2g2 from octonions, J. Pure. Appl. Algebr. 222 (2018) 3036--3042. arXiv:1708.02367, pdf. 
  13. A new complex reflection group in PU(9,1) and the Barnes-Wall lattice, to appear in Pacific Journal of Math (2019) arXiv:1804.05778, pdf.