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Research bio

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.


Articles in preparation

  1. B. Armstrong, K.A. Brix, T.M. Carlsen, S. Eilers, and J. Winkel, An algorithm for deciding conjugacy of graphs, in preparation.
  2. B. Armstrong, A.C.S. Ng, A. Sims, and Y. Zhou, Twists without continuous sections, in preparation.

Preprints

  1. B. Armstrong, L.O. Clark, M. Gandehari, E.J. Kang, and D. Yang, Representing topological full groups in Steinberg algebras and C*-algebras, preprint, 2023, arXiv:2309.04927 [math.OA].

Publications

  1. B. Armstrong, N. Brownlowe, and A. Sims, Simplicity of twisted C*-algebras of Deaconu–Renault groupoids, J. Noncommut. Geom. (2023), 1–48. [arXiv version]
  2. 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 (2023), 1–15. [arXiv version]
  3. 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]
  4. 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]
  5. 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]
  6. B. Armstrong, A uniqueness theorem for twisted groupoid C*-algebras, J. Funct. Anal. 283 (2022), 1–33. [arXiv version]
  7. 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]
  8. 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]
  9. 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, Conjugacy of local homeomorphisms via groupoids and C*-algebras, extended abstract, Oberwolfach Rep. 19 (2022), 2117–2120.
  2. B. Armstrong, Simplicity of twisted C*-algebras of topological higher-rank graphs, PhD thesis abstract, Bull. Aust. Math. Soc. 101 (2020), 512–513.
  3. 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

2023–2024 UOW AEGiS Connect Grant: Lambda-Bundles and Groupoid Twists  (value: 13,101 AUD)
Held as Associate Investigator with Abraham Ng (Lead CI) and Aidan Sims (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