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I am a pure mathematician working in operator algebra and related fields. My research is primarily focused on C*-algebras and abstract algebras associated to mathematical objects such as groupoids, and directed graphs and their topological and higher-rank analogues. A significant portion of my research involves "twisting" these algebras by cohomological data and studying the effect on important properties of the algebras, such as simplicity. My work on the C*-algebras of graphs and groupoids forms part of a larger quest by operator algebraists to completely classify C*-algebras.

Publications & Preprints

  1. B. Armstrong, K.A. Brix, T.M. Carlsen, and S. Eilers, Conjugacy of local homeomorphisms via groupoids and C*-algebras, preprint, 2021, arXiv:2105.00479v1 [math.OA].
  2. B. Armstrong, A uniqueness theorem for twisted groupoid C*-algebras, preprint, 2021, arXiv:2103.03063v1 [math.OA].
  3. B. Armstrong, G.G. de Castro, L.O. Clark, K. Courtney, Y.-F. Lin, K. McCormick, J. Ramagge, A. Sims, and B. Steinberg, Reconstruction of twisted Steinberg algebras, preprint, 2021, arXiv:2101.08556v1 [math.RA].
  4. B. Armstrong, L.O. Clark, A. an Huef, M. Jones, and Y.-F. Lin, Filtering germs: groupooids associated to inverse semigroups, preprint, 2020, arXiv:2010.16113v2 [math.RA].
  5. B. Armstrong, Simplicity of twisted C*-algebras of topological higher-rank graphs, PhD thesis abstract, Bull. Aust. Math. Soc. 101 (2020), 512–513.
  6. B. Armstrong, L.O. Clark, K. Courtney, Y.-F. Lin, K. McCormick, and J. Ramagge, Twisted Steinberg algebras, preprint, 2020, arXiv:1910.13005v2 [math.RA].
  7. B. Armstrong and N. Brownlowe, Product-system models for twisted C*-algebras of topological higher-rank graphs, J. Math. Anal. Appl. 466 (2018), 1443–1475.
  8. B. Armstrong, M. Fielding, S. Kirk, and J. Ramagge, Factors affecting success in CHEM101 at UOW, Austral. Math. Soc. Gaz. 41 (2014), 91–98.