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Research bio

I am a pure mathematician working in Operator Algebra and Rings and Algebras. My research is primarily focused on C*-algebras and abstract rings and 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.


Publications

  1. B. Armstrong, A.C.S. Ng, A. Sims, and Y. Zhou, A twist over a minimal étale groupoid that is topologically nontrivial over the interior of the isotropy, Proc. Amer. Math. Soc. 153 (2025), 1849–1866. [arXiv version]
  2. B. Armstrong, L.O. Clark, M. Ghandehari, E.J. Kang, and D. Yang, Representing topological full groups in Steinberg algebras and C*-algebras, J. Math. Anal. Appl. 534 (2024), 1–13. [arXiv version]
  3. B. Armstrong, N. Brownlowe, and A. Sims, Simplicity of twisted C*-algebras of Deaconu–Renault groupoids, J. Noncommut. Geom. 18 (2024), 265–312. [arXiv version]
  4. B. Armstrong, J.H. Brown, L.O. Clark, K. Courtney, Y.-F. Lin, K. McCormick, and J. Ramagge, The local bisection hypothesis for twisted groupoid C*-algebras, Semigroup Forum 107 (2023), 609–623. [arXiv version]
  5. B. Armstrong, L.O. Clark, and A. an Huef, Inclusions of C*-algebras of graded groupoids, J. Operator Theory 89 (2023), 285–299. [arXiv version]
  6. B. Armstrong, K.A. Brix, T.M. Carlsen, and S. Eilers, Conjugacy of local homeomorphisms via groupoids and C*-algebras, Ergodic Theory Dynam. Systems 43 (2023), 2516–2537. [arXiv version]
  7. 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, Int. Math. Res. Not. IMRN 2023 (2023), 2474–2542. [arXiv version]
  8. B. Armstrong, A uniqueness theorem for twisted groupoid C*-algebras, J. Funct. Anal. 283 (2022), 1–33. [arXiv version]
  9. B. Armstrong, L.O. Clark, A. an Huef, M. Jones, and Y.-F. Lin, Filtering germs: Groupoids associated to inverse semigroups, Expo. Math. 40 (2022), 127–139. [arXiv version]
  10. B. Armstrong, L.O. Clark, K. Courtney, Y.-F. Lin, K. McCormick, and J. Ramagge, Twisted Steinberg algebras, J. Pure Appl. Algebra 226 (2022), 1–33. [arXiv version]
  11. 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. [arXiv version]

Other published articles

  1. B. Armstrong, Representing topological full groups in Steinberg algebras and C*-algebras, extended abstract, Oberwolfach Rep. 21 (2024), 13–16.
  2. B. Armstrong, Conjugacy of local homeomorphisms via groupoids and C*-algebras, extended abstract, Oberwolfach Rep. 19 (2022), 2117–2120.
  3. B. Armstrong, Simplicity of twisted C*-algebras of topological higher-rank graphs, PhD thesis abstract, Bull. Aust. Math. Soc. 101 (2020), 512–513.
  4. B. Armstrong, M. Fielding, S. Kirk, and J. Ramagge, Factors affecting success in CHEM101 at UOW, Austral. Math. Soc. Gaz. 41 (2014), 91–98.

Research funding

2025–2027 Discovery Project Grant DP250100297  (value: 573,990 AUD)
Title: A new twist on product decompositions: twisted algebras for Zappa–Szép products
Held as Partner Investigator with Chief Investigators Aidan Sims (Lead CI),
Jacqui Ramagge, Nathan Brownlowe, and Anna Duwenig
The Australian Research Council (ARC)
2025–2027 Marsden Fund Fast-Start Grant 24-VUW-014  (value: 326,612 AUD)
Title: Coordination: A twisted groupoid approach to algebra and functional analysis
Held as Principal Investigator with Benjamin Steinberg as Associate Investigator
The Royal Society of New Zealand (RSNZ)
2025 BIRS “Research in Teams” Funding  (funded invited research visit)
Banff International Research Station (BIRS), Alberta, Canada
2024 Research Travel Grant  (value: 2,510 AUD)
The New Zealand Mathematical Society
2024 Simons Visiting Professorship  (value: 5,296 AUD)
The Simons Foundation & the Cluster of Excellence “Mathematics Münster”, Germany
2023 UOW AEGiS Connect Grant  (value: 13,101 AUD)
Title: Lambda-Bundles and Groupoid Twists
Held as Associate Investigator with Abraham Ng as Lead CI and Aidan Sims as Second CI
University of Wollongong, Australia
2023 Women in Operator Algebras (WOA) III Workshop Travel Funding  (value: 2,270 AUD)
The Clay Mathematics Institute
2022 ICMS “Research in Groups” Funding  (funded invited research visit)
International Centre for Mathematical Sciences (ICMS), Edinburgh, United Kingdom
2019 Lift-Off Fellowship  (value: 4,000 AUD)
The Australian Mathematical Society
2018 Cheryl E. Praeger Travel Award  (value: 1,963 AUD)
The Women in Mathematics Special Interest Group of the Australian Mathematical Society
2018 Heidelberg Laureate Forum Travel Funding  (value: 3,000 AUD)
The Australian Mathematical Society and the Australian Mathematical Sciences Institute
2018 Early Career Mobility Scheme Travel Grant  (value: 4,800 AUD)
The University of Sydney, Australia and the University of Glasgow, United Kingdom
2017–2018 Postgraduate Research Support Scheme Funding  (value: 6,000 AUD)
The University of Sydney, Australia