Professor Aidan Sims
Professor
- BMath/BCompSci, University of Newcastle, 1999.
- BMath Hons (Class I, University Medal) University of Newcastle, 2000.
- PhD (Mathematics), University of Newcastle, 2004.
- Graduate Certificate in the Practice of Tertiary Teaching, University of Newcastle, 2005.
Science
School of Mathematics & Statistics
I completed my PhD in Operator Algebras under Iain Raeburn at the University of Newcastle in 2003. After a brief fixed-term lectureship at Newcastle, I moved to a permanent lecureship position at the University of Wollongong funded by an Australian Postdoctoral Fellowship in 2007. I was promoted to a professorship in 2012, served as Head of School (2018-2021) and was made a Distinguished Professor in 2023. In 2025 I moved to UNSW to lead the newly formed Quantum Mathematics Research Cluster.
I have served on the Council of the AustMS (2015-2017), as its Vice President (2022-2023) and as its President (2025-2026). I have also served for over 10 years on the Australian Mathematical Sciences Institute's Research Committee.
I have been an associate editor of the Bulletin of the AustMS and the Journal of the AustMS since 2015, and of the Journal of Mathematical Analysis and Applications since 2019.
E-mail
Location
School of Mathematics and Statistics
UNSW Sydney
Anita B. Lawrence Centre Room 6102
- Publications
- Media
- Grants
- Awards
- Research Activities
- Engagement
- Teaching and Supervision
National competitive grants.
- 2005–2008, A. Sims, Operator algebras associated to product systems, and higher-rank-graph algebras, ARC Discovery–Projects grant (Australian Postdoctoral Fellowship) DP0557243, $221K.
- 2006–2009, D. Pask and A. Sims, Pictures for operator algebras: higher-rank graphs, ARC Discovery–Projects grant DP0665131, $279K .
- 2009–2011 A. Sims, Co-universal operator algebras, ARC Discovery–Projects grant DP0984399, $176K.
- 2009–2011, A. an Huef and A. Sims, Operator algebras associated to groupoids, ARC Discovery–Projects grant DP0984360, $255K. (As of January 2010, this grant is held by Aidan Sims and David Pask; Sims is lead CI.)
- 2010–2014 A. Sims, Operator algebras as models for dynamics and geometry, ARC Future Fellowship FT100100533, $562K.
- 2012–2014 A. Sims and A. Rennie, Invariants for dynamics via operator algebras, ARC Discovery–Projects grant DP120100507, $435K.
- 2012–2014, D. Pask and A. Sims, Cohomology, symbolic dynamics and operator algebras, ARC Discovery–Projects grant DP120100389, $330K.
- 2015–2017 A. Sims, Equilibrium states and fine structure for operator algebras, ARC Discovery–Projects grant DP150101595, $345K.
- 2015–2017, A. Sims, D. Pask and R. Hazrat, Groupoids as bridges between algebra and analysis, ARC Discovery–Projects grant DP150101598, $311K.
- 2018–2020, A. Sims, A. an Huef and S. White, Taming infinite dimensions: quasidiagonality and nuclear dimension, ARC Discovery–Projects grant DP180100595, $347K.
- 2020–2022, A. Sims, J. Ramagge, D. Pask, N. Brownlowe and L.O. Clark, There and back again: operator algebras, algebras and dynamical systems, ARC Discovery–Projects grant DP200100155, $461K.
- 2022–2024, A. Sims, Noncommutative analysis for self-similar structure, ARC Discovery–Projects grant DP220101631, $384K.
- 2025–2027, A. Sims, J. Ramagge, N. Brownlowe, Becky Armstrong, and Anna Duwenig, A new twist on product decompositions: twisted algebras for Zappa–Szép products, ARC Discovery–Projects grant DP250100297, $574K.
Other funding.
- 2012, R. Hazrat and A. Sims, Graph C*-algebras, Leavitt path algebras and symbolic dynamics, AMSI workshop funding and AustMS Special Interest Meetings grant, $13.5K.
- 2016, M. Goffeng, A. Rennie and A. Sims, Refining C*-algebraic invariants for dynamics using KK-theory, MATRIX@melbourne research program, total funding $25K.
- 2017, N. Brown, F. Perera, A. Sims, S. White, and W. Winter, Operator algebras: Dynamics and Interactions, Centre de Recerca Mathemàtica, Universitat Autònoma de Barcelona, total funding €89K.
- 2019, N. Larsen, M.V. Lawson, A. Sims and A. Vdovina, Higher-rank graphs: geometry, symmetry, dynamics, International Centre for Mathematical Sciences, University of Edinburgh and Heriott–Watt University, total funding £41K.
- 2023, N. Larsen, M.V. Lawson, A. Sims, A. Vdovina and M.F. Whittaker Algebra, Geometry and C*-algebras, International Centre for Mathematical Sciences, University of Edinburgh and Heriott–Watt University, total funding £43K.
- 2024, A. Duwenig, A. an Huef, A. Sims and D. Yang, Cartan subalgebras in operator algebras, and topological full groups (24w5175), Banff International Research Station, total funding CAD$50K.
- UOW Vice Chancellor's Researcher of the Year, 2015
- Fellow of the Australian Mathematical Society, 2015
- Australian Mathematical Society Medal, 2016
- Fellow of the Australian Academy of Science, 2025
I am broadly interested in Quantum mathematics by which I mean the general theory of functional analysis, operator algebras and noncommutative geometry and their links to quantum physics and quantum information theory. More specifically, much of my research is concerned with abstract algebras and C*-algebras associated to:
- combinatorial structures such as directed graphs and higher-rank graphs;
- algebraic objects such as groups, semigroups and small categories with suitable cancellative properties;
- generalised C*-dynamical systems as captured by product systems of Hilbert bimodules; and
- topological dynamics encoded by locally compact étale groupoids and Fell bundles over such objects.
One major theme of my research is the extent to which such objects explicitly encode the structural properties of the associated C*-algebras including features like ideal structure, stable finiteness and pure infiniteness, KMS-state structure and invariants such as K-theory and KK-classes. A second major theme involves seeking to go in the other direction, determining and also the amount of algebraic or C*-algebraic data that is required to reconstruct the underlying generating object. This has led to connections with Dixmier–Douady theory and work on deformations of C*-algebras by cohomological data. Since the advent of Renault's theorem about Cartan pairs of C*-algebras and the subsequent introduction of Steinberg algebras associated to étale groupoids, I have been pursuing a research program that investigates groupoids and related data as a unifying coordinatising framework for both abstract algebras and C*-algebras, and as, in the words of Abrams, a Rosetta stone for translating structural theorems about one of these classes of objects into the context of the other.