SCHOOL OF MATHEMATICS AND APPLIED STATISTICS 
Aidan Sims
0000000219656451



 Office: 39C.195
 Phone: +61 2 4221 5003
 Fax: +61 2 4221 4845
 Email: asims@uow.edu.au
 Address:
 School of Mathematics and Applied Statistics
 University of Wollongong
 NSW 2522 AUSTRALIA
Research Funding
 National competitive grants.

2005–2008, A. Sims, Operator algebras associated to product systems, and higherrankgraph algebras, ARC Discovery–Projects grant (Australian Postdoctoral Fellowship), $221K.

2006–2009, D. Pask and A. Sims, Pictures for operator algebras: higherrank graphs, ARC Discovery–Projects grant, $279K.

2009–2011 A. Sims, Couniversal operator algebras, ARC Discovery–Projects grant, $176K.

2009–2011, A. an Huef and A. Sims, Operator algebras associated to groupoids, ARC Discovery–Projects grant, $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, $562K.

2012–2014 A. Sims and A. Rennie, Invariants for dynamics via operator algebras, ARC Discovery–Projects grant, $435K.

2012–2014, D. Pask and A. Sims, Cohomology, symbolic dynamics and operator algebras, ARC Discovery–Projects grant, $330K.

2015–2017 A. Sims, Equilibrium states and fine structure for operator algebras, ARC Discovery–Projects grant, $345K.

2015–2017, A. Sims, D. Pask and R. Hazrat, Groupoids as bridges between algebra and analysis, ARC Discovery–Projects grant, $311K.

2018–2020, A. Sims, A. an Huef
and S. White, Taming infinite dimensions: quasidiagonality and nuclear dimension, ARC Discovery–Projects grant, $347K.
 Other funding.

2004–2005, A. Sims, Investigating the structure of C*algebras associated to higherrank graphs, University of Newcastle Early Career Researcher Grant, $7K.

2009, A. Sims, Stably finite operator algebras associated to graphs, University of Wollongong URC Grant, $9.6K (relinquished on award of ARC DP).

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.

2013, N. Brownlowe,
A. Sims and
M.F. Whittaker,
Operator algebras associated to tilings, UOW University International Collaborations grant, $15K.

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.
Publications
 2001–2005

N. J. Fowler
and A. Sims,
Product systems over rightangled Artin semigroups,
Trans. Amer. Math. Soc.
354
(2001),
1487–1509.
[PDF]

I. Raeburn,
A. Sims
and T. Yeend,
Higherrank graphs and their C*algebras,
Proc. Edinburgh Math. Soc.
46
(2003),
99–115.
[http://arxiv.org/abs/math/0107222].
[PDF]

I. Raeburn,
A. Sims
and T. Yeend,
The C*algebras of finitely aligned higherrank graphs,
J. Funct. Anal.
213
(2004),
206–240.
[http://arxiv.org/abs/math/0305370].
[PDF].

I. Raeburn
and A. Sims,
Product systems of graphs and the C*algebras of higherrank graphs,
J. Operator Th.
53
(2005),
399–429.
[http://arxiv.org/abs/math/0305371].
[PDF].
 2006–2008

A. Sims,
Relative Cuntz–Krieger algebras of finitely aligned higherrank graphs,
Indiana Univ. Math. J.
55
(2006),
849–868.
[http://arxiv.org/abs/math/0312152].
[PDF].

A. Sims,
Gaugeinvariant ideals in the C*algebras of finitely aligned higherrank graphs,
Canad. J. Math.
58
(2006),
1268–1290.
[http://arxiv.org/abs/math/0406592]
[PDF]

D. Pask,
I. Raeburn,
M. Rørdam
and A. Sims,
Rank2 graphs whose C*algebras are direct limits of circle algebras,
J. Funct. Anal.
239
(2006),
137–178.
[http://arxiv.org/abs/math/0512254]
[PDF]

S. Allen,
D. Pask
and A. Sims,
A dual graph construction for higherrank graphs, and Ktheory for finite 2graphs,
Proc. Amer. Math. Soc.
134
(2006),
455–464.
[http://arxiv.org/abs/math/0402126]
[PDF]

D. Robertson
and A. Sims,
Simplicity of C*algebras associated to higherrank graphs,
Bull. London Math. Soc.
39
(2007)
337–344.
[http://arxiv.org/abs/math/0602120]
[PDF]

D. Pask
A. Rennie
and A. Sims,
The noncommutative geometry of kgraph C*algebras,
J. Ktheory
1
(2008),
259–304.
[http://arxiv.org/abs/math/0512438]
[PDF]

A. Kumjian,
D. Pask
and A. Sims,
C*algebras associated to coverings of kgraphs,
Documenta Math.
13
(2008)
161–205.
[http://arxiv.org/abs/math/0612204]
[PDF]

T. Katsura,
P. Muhly,
A. Sims
and M. Tomforde,
Ultragraph C*algebras via topological quivers,
Studia Math.
187
(2008),
137–155.
[http://arxiv.org/abs/math/0611318]
[PDF]
 2009–2010

T. Katsura,
A. Sims,
and M. Tomforde,
Realizations of AFalgebras as graph algebras, Exel–Laca algebras and ultragraph algebras,
J. Funct. Anal.
257
(2009)
1589–1620.
[http://arxiv.org/abs/0810.4091]
[PDF]

D. Pask,
J. Quigg
and A. Sims,
Coverings of skewproducts and crossed products by coactions,
J. Austral. Math. Soc.
86
(2009),
379–398.
[http://arxiv.org/abs/0706.0362]
[PDF]

C. Farthing,
D. Pask
and A. Sims,
Crossed products of kgraph C*algebras by Z^{l},
Houston J. Math.
35
(2009),
903–933.
[http://arXiv.org/abs/0706.3547]
[PDF]

D. Robertson
and A. Sims,
Simplicity of C*algebras associated to rowfinite locally convex higherrank graphs,
Israel J. Math.
172
(2009),
171–192.
[http://arxiv.org/abs/0708.0245]
[PDF]

D. Pask
A. Rennie
and A. Sims,
Noncommutative manifolds from graph and kgraph C*algebras,
Comm. Math. Phys.
292
(2009),
607–636.
[http://arXiv.org/math.OA/0701527]
[PDF]

A. Sims and
T. Yeend,
C*algebras associated to product systems of Hilbert bimodules,
J. Operator Theory
64
(2010),
349–376.
[http://arxiv.org/abs/0712.3073]
[PDF]

A. Sims and
S.B.G. Webster,
A direct approach to couniversal algebras associated to directed graphs,
Bull. Malays. Math. Sci. Soc. (2)
33
(2010),
211–220.
[http://arxiv.org/abs/0912.3303]
[PDF]

A. Sims,
The couniversal C*algebra of a rowfinite graph,
New York J. Math.
16
(2010),
507–524.
[http://arxiv.org/abs/0809.2333]
[PDF]

P. Lewin
and A. Sims,
Aperiodicity and cofinality for finitely aligned higherrank graphs,
Math. Proc. Cambridge Philos. Soc.
149
(2010),
333–350.
[http://arxiv.org/abs/0905.0735]
[PDF]

T. Katsura,
P. Muhly,
A. Sims
and M. Tomforde,
Graph algebras, Exel–Laca algebras, and ultragraph algebras coincide up to Morita equivalence,
J. reine angew. Math.
640
(2010),
135–165.
[http://arxiv.org/abs/0809.0164]
[PDF]

V. Deaconu,
A. Kumjian,
D. Pask
and A. Sims,
Graphs of C*correspondences and Fell bundles,
Indiana Univ. Math. J.
59
(2010),
1687–1736.
[http://arxiv.org/abs/0901.0032]
[PDF]
 2011–2012

A. Kumjian,
D. Pask
and A. Sims,
Generalised morphisms of kgraphs: kmorphs,
Trans. Amer. Math. Soc.
363
(2011),
2599–2626.
[http://arXiv.org/abs/0712.1072]
[PDF]

A. an Huef,
A. Kumjian
and A. Sims,
A Dixmier–Douady classification for Fell algebras,
J. Funct. Anal.
260
(2011),
1543–1581.
[http://arxiv.org/abs/1004.1787]
[PDF]

T. Carlsen,
N. Larsen,
A. Sims
and S.T. Vittadello,
Couniversal algebras associated to product systems, and gaugeinvariant uniqueness theorems,
Proc. London Math. Soc.
103
(2011),
563–600.
[http://arxiv.org/abs/0906.4825]
[PDF]

D.G. Evans
and A. Sims,
When is the Cuntz–Krieger algebra of a higherrank graph approximately finitedimensional?,
J. Funct. Anal.
263
(2012),
183–215.
[http://arxiv.org/abs/1112.4549]
[PDF]

A. Kumjian,
D. Pask
and A. Sims,
Homology for higherrank graphs and twisted C*algebras,
J. Funct. Anal.
263
(2012),
1539–1574.
[http://arxiv.org/abs/1110.1433]
[PDF]

A. Sims and
D.P. Williams,
Renault’s equivalence theorem for reduced groupoid C*algebras,
J. Operator Th.
68
(2012),
223–239.
[http://arxiv.org/abs/1002.3093]
[PDF]
 2013–2014

A. Kumjian,
D. Pask
and A. Sims,
On the Ktheory of twisted higherrankgraph C*algebras,
J. Math. Anal. Appl.
401
(2013),
104–113.
[http://arxiv.org/abs/1211.1445]
[PDF]

A. an Huef,
M. Laca,
I. Raeburn
and A. Sims,
KMS states on the C*algebras of finite graphs,
J. Math. Anal. Appl.
405
(2013),
388–399.
doi:10.1016/j.jmaa.2013.03.055
[http://arxiv.org/abs/1205.2194]
[PDF]

R. Hazlewood,
I. Raeburn,
A. Sims and
S.B.G. Webster,
On some fundamental results about higherrank graphs and their C*algebras,
Proc. Edinburgh Math. Soc.
56
(2013),
575–597.
[http://arxiv.org/abs/1110.2269]
[PDF]

N. Brownlowe,
A. Sims
and S.T. Vittadello,
Couniversal C*algebras associated to generalised graphs,
Israel J. Math
193
(2013),
399–440.
[http://arxiv.org/abs/1009.1184]
[PDF]

A. Sims and
D.P. Williams,
An equivalence theorem for reduced Fell bundle C*algebras,
New York J. Math.
19
(2013)
159–178.
[http://nyjm.albany.edu/j/2013/1911v.pdf]
[PDF]

A. Sims and
D.P. Williams,
Amenability for Fell bundles over groupoids,
Illinois J. Math.
67
(2013),
429–444.
[http://arxiv.org/abs/1201.0792]
[PDF]

A. an Huef,
M. Laca,
I. Raeburn
and A. Sims,
KMS states on C*algebras associated to higherrank graphs,
J. Funct. Anal.
266
(2014),
265–283.
[http://arxiv.org/abs/1212.6811]
[PDF]

T. Carlsen,
S. Kang
J. Shotwell
and A. Sims,
The primitive ideals of the Cuntz–Krieger algebra of a rowfinite higherrank graph with no sources,
J. Funct. Anal
266
(2014),
2570–2589.
[http://arxiv.org/abs/1305.6388]
[PDF]

J.H. Brown,
L.O. Clark,
C. Farthing
and A. Sims,
Simplicity of algebras associated to étale groupoids,
Semigroup Forum
88
(2014),
433–452.
[http://arxiv.org/abs/1204.3127]
[PDF]

H. Li,
D. Pask,
and A. Sims,
An elementary approach to C*algebras associated to topological graphs,
New York J. Math.
20
(2014),
447–469.
[http://nyjm.albany.edu/j/2014/2026v.pdf]
[PDF]

A. Sims, B. Whitehead and
M.F. Whittaker,
Twisted C*algebras associated to finitely aligned higherrank graphs,
Documenta Math.
19
(2014),
831–866.
[http://arxiv.org/abs/1310.7656]
[PDF]

S. Kang
and A. Sims,
Couniversal C*algebras associated to aperiodic kgraphs,
Glasgow J. Math.
56
(2014),
537–550.
[http://arxiv.org/abs/1108.3674]
[PDF]

L.O. Clark,
C. Farthing,
A. Sims and
M. Tomforde,
A groupoid generalization of Leavitt path algebras,
Semigroup Forum
89
(2014),
501–517.
doi:10.1007/s002330149594z
[http://arxiv.org/abs/1110.6198]
[PDF]
 2015–2016

E. Ruiz,
A. Sims and
M. Tomforde,
The nuclear dimension of graph C*algebras,
Adv. Math.
272
(2015),
96–123.
[http://arxiv.org/abs/1312.0507]
[PDF]

L.O. Clark and
A. Sims,
Equivalent groupoids have Morita equivalent Steinberg algebras,
J. Pure Appl. Algebra
219
(2015),
2062–2075.
[http://arxiv.org/abs/1311.3701]
[PDF]

D. Pask,
A. Sierakowski
and A. Sims,
Twisted kgraph algebras associated to Bratteli diagrams,
Integral Equations Operator Theory
81
(2015),
375–408.
[http://arxiv.org/abs/1403.4324]
[PDF]

A. Kumjian,
D. Pask
and A. Sims,
On twisted higherrank graph C*algebras,
Trans. Amer. Math. Soc.
367
(2015),
5177–5216.
[http://arxiv.org/abs/1112.6233]
[PDF]

A. an Huef,
M. Laca,
I. Raeburn
and A. Sims,
KMS states on the C*algebra of a higherrank graph and periodicity in the path space,
J. Funct. Anal.
268
(2015),
1840–1875.
[http://arxiv.org/abs/1404.6819]
[PDF]

E. Ruiz,
A. Sims and
A.P.W. Sørensen,
UCTKirchberg algebras have nuclear dimension 1,
Adv. Math.
279
(2015),
1–28.
[http://arxiv.org/abs/1406.2045]
[PDF]

M. Laca,
N.S. Larsen,
S. Neshveyev,
A. Sims and
S.B.G. Webster,
von Neumann algebras of strongly connected higherrank graphs,
Math. Ann. 363 (2015), Page 657–678.
[http://arxiv.org/abs/1409.6481]
[PDF]

A. an Huef,
M. Laca,
I. Raeburn
and A. Sims,
KMS states on the C*algebras of reducible graphs,
Ergodic Theory Dynam. Systems 35 (2015), 2535–2558.
doi:10.1017/etds.2014.52
[http://arxiv.org/abs/1402.0276]
[PDF]

D. Robertson,
J. Rout
and A. Sims,
KMS states on generalised Bunce–Deddens algebras and their Toeplitz extensions,
Bull. Malaysian Math. Sci. Soc., 2015, 10.1007/s4084001502448.
[http://arxiv.org/abs/1501.01712]
[PDF]

A. Sims and
D.P. Williams,
The primitive ideals of some étale groupoid C*algebras,
Algebr. Represent. Theory, 19 (2016), 255–276 10.1007/s1046801595734.
[http://arxiv.org/abs/1501.02302]
[PDF]

J.H. Brown,
G. Nagy
S. Reznikoff,
A. Sims,
and D.P. Williams,
Cartan subalgebras in C*algebras of étale Hausdorff groupoids,
Integral Equations Operator Theory 85 (2016), 109–126.
doi:10.1007/s0002001622852
[http://arxiv.org/abs/1503.03521]
[PDF]

S. Kaliszewski,
A. Kumjian,
J. Quigg
and A. Sims,
Topological realizations and fundamental groups of higherrank graphs,
Proc. Edinburgh Math. Soc. (2) 59 (2016), 143–168.
[http://arxiv.org/abs/1205.2858]
[PDF]

J.H. Brown,
L.O. Clark,
A. Sierakowski
and A. Sims,
Purely infinite simple C*algebras that are principal groupoid C*algebras,
J. Math. Anal. Appl. 439 (2016), 213–234.
[http://arxiv.org/abs/1504.04794]
[PDF]

A. Kumjian,
D. Pask,
A. Sims and
M.F. Whittaker,
Topological spaces associated to higherrank graphs,
J. Combinatorial Th. A. 143 (2016), 19–41.
doi:10.1016/j.jcta.2016.04.005
[http://arxiv.org/abs/1310.6100]
[PDF]

L.O. Clark,
A. an Huef,
and A. Sims,
AFembeddability of 2graph algebras and quasidiagonality of kgraph algebras,
J. Funct. Anal., 271 (2016), 958–991.
[http://arxiv.org/abs/1508.02746]
[PDF]

A. Kumjian,
D. Pask
and A. Sims,
Simplicity of twisted C*algebras of higherrank graphs and crossed products by quasifree actions,
J. Noncommut. Geom., 10 (2016), 515–549.
[http://arxiv.org/abs/1411.3860]
[PDF]

T.M. Carlsen,
and A. Sims,
On Hong and Szymanski's description of the primitiveideal space of a graph algebra,
in Operator algebras and Applications, Carlsen, Larsen, Neshveyev and Skau (eds),
The Abel Symposium 2015, Springer 2016, pp 109–126.
[http://arxiv.org/abs/1512.02850]
[PDF]
 2017–

A. Rennie,
D. Robertson
and A. Sims,
The extension class and KMS states for Cuntz–Pimsner algebras of some biHilbertian bimodules,
J. Topol. Anal., 9 (2017), 297–327.
[http://arxiv.org/abs/1501.05363]
[PDF]

P. Ara,
J. Bosa,
R. Hazrat,
and A. Sims,
Reconstruction of graded groupoids from graded Steinberg algebras,
Forum Math. 28 (2017), 10231037.
doi:110.1515/forum20160072
[http://arxiv.org/abs/1601.02872]
[PDF]

T.M. Carlsen,
E. Ruiz,
and A. Sims,
Equivalence and stable isomorphism of groupoids, and diagonalpreserving stable isomorphisms of graph C*algebras and Leavitt path algebras,
Proc. Amer. Math. Soc., 145 (2017), 1581–1592.
[http://arxiv.org/abs/1602.02602]
[PDF]

N. Brownlowe,
M. Hawkins,
and A. Sims,
The Toeplitz noncommutative solenoid and its KMS states,
Ergodic Theory Dynam. Sysems, published online 2017.
doi:10.1017/etds.2017.7
[http://arxiv.org/abs/1608.01782]
[PDF]

A. Rennie,
and A. Sims,
Noncommutative vector bundles for nonunital algebras,
SIGMA 13 (2017), 041, 12 pages,
doi:10.3842/SIGMA.2017.041
[http://arxiv.org/abs/1612.03559]
[PDF]

A. Rennie,
D. Robertson
and A. Sims,
Groupoid algebras as Cuntz–Pimsner algebras,
Math. Scand. 120 (2017), 115–123.
[http://arxiv.org/abs/1402.7126]
[PDF]

D. Pask,
A. Sierakowski
and A. Sims,
Real rank and topological dimension of higher rank graph algebras,
Indiana Univ. Math. J. 66 (2017) 2137–2168.
[http://arxiv.org/abs/1503.08517]
[PDF]

J.N. Renault,
A. Sims,
D.P. Williams,
and T. Yeend,
Uniqueness theorems for topological higherrank graph C*algebras,
Proc. Amer. Math. Soc., 146 (2018), 669–684.
[http://arxiv.org/abs/0906.0829]
[PDF]

A. Kumjian,
M. Ionescu,
A. Sims,
and D.P. Williams,
A stabilization theorem for Fell bundles over groupoids,
Proc. Roy. Soc. Edinburgh Sect. A, 148 (2018), 79–100.
[http://arxiv.org/abs/1512.06046]
[PDF]

P. Ara,
H. Li,
R. Hazrat,
and A. Sims,
Graded Steinberg algebras and their representations,
Algebra Number Theory, 12 (2018), 131–172.
[http://arxiv.org/abs/1704.01214]
[PDF]

J. Claramunt and
A. Sims,
Preferred traces on C*algebras of selfsimilar groupoids arising as fixed points,
J. Math. Anal. Appl. 466 (2018), 806–818.
[http://arxiv.org/abs/1712.00302]
[PDF]
 In press

A. Rennie,
D. Robertson
and A. Sims,
Groupoid Fell bundles for product systems over quasilattice ordered groups,
Math. Proc. Cambridge Philos. Soc., to appear.
[http://arxiv.org/abs/1501.05476]
[PDF]

L.O. Clark,
C. EdieMichell
A. an Huef,
and A. Sims,
Ideals in Steinberg algebras of strongly effective groupoids, with applications to Leavitt path algebras,
Trans. Amer. Math. Soc., to appear.
[http://arxiv.org/abs/1601.07238]
[PDF]

P. Hajac,
R. Nest,
D. Pask,
A. Sims,
and B. Zielinski,
Noncommutative line bundles associated to twisted multipullback quantum odd spheres,
J. Noncommutative Geometry, to appear.
[http://arxiv.org/abs/1512.08816]
[PDF]

T. Rainone
and A. Sims,
A dichotomy for groupoid C*algebras,
Ergodic Theory Dynam. Systems, to appear.
[http://arxiv.org/abs/1707.04516]
[PDF]

A. Kumjian,
D. Pask
and A. Sims,
Graded C*algebras, graded Ktheory and twisted Pgraph algebras,
J. Operator Th., to appear.
[http://arxiv.org/abs/1706.00563]
[PDF]

A. Buss
and A. Sims,
Opposite algebras of groupoid C*algebras,
Israel J. Math, to appear.
[http://arxiv.org/abs/1708.04105]
[PDF]
 Preprints

D. Pask,
A. Sierakowski
and A. Sims,
Unbounded quasitraces, stable finiteness and pure infiniteness,
preprint 2017.
[http://arxiv.org/abs/1705.01268]
[PDF]

Z. Afsar
and A. Sims,
KMS states on the C*algebras of Fell bundles over groupoids,
preprint 2017.
[http://arxiv.org/abs/1708.00629]
[PDF]

C. Bruce,
M. Laca,
J. Ramagge
and A. Sims,
Equilibrium states and growth rates of quasilattice ordered groups,
preprint 2017.
[http://arxiv.org/abs/1709.07606]
[PDF]

T.M. Carlsen,
E. Ruiz,
A. Sims,
and M. Tomforde
Reconstruction of groupoids and C*rigidity of dynamical systems,
preprint 2017.
[http://arxiv.org/abs/1711.01052]
[PDF]

A. Kumjian,
M. Ionescu,
A. Sims,
and D.P. Williams,
The Dixmier–Douady classes of certain groupoid C*algebras with continuous trace,
preprint 2017.
[http://arxiv.org/abs/1801.00832]
[PDF]

A. Rennie,
D. Robertson
and A. Sims,
Poincaré duality for Cuntz–Pimsner algebras of bimodules,
preprint 2018.
[http://arxiv.org/abs/1804.08114]
[PDF]

L.O. Clark,
R. Exel,
E. Pardo,
A. Sims, and
C. Starling,
Simplicity of algebras associated to nonHausdorff groupoids,
preprint 2018.
[http://arxiv.org/abs/1806.04362]
[PDF]

A. Sims,
The suspension of a graph, and associated C*algebras,
preprint 2018.
[http://arxiv.org/abs/1807.08067]
[PDF]
 Other

A. Sims and
B. Sims,
Assessing the minimality of change in belief revision: capacities,
in Frontiers in Belief Revision,
MaryAnne Williams and
Hans Rott
(Eds.),
Applied Logic Series,
22,
Kluwer Academic Publishers, 2001.
[PDF]

I. Raeburn,
A. Sims and
D. P. Williams,
Twisted actions and obstructions in group cohomology,
in C*algebras: Proceedings of the SFB Workshop on C*algebras,
Münster, Germany, March 8–12,
1999,
J. Cuntz and
S. Echterhoff
(Eds.),
Springer,
2000.
[PDF]

A. Sims,
C*algebras associated to higherrank graphs,
PhD Thesis,
University of Newcastle Australia,
2003.
[PDF]

A. Sims
Graphs and C*algebras,
invited technical article, Gazette of the Australian Mathematical Society
39
(2012),
35–39.
[PDF]

A. Sims
Hausdorff étale groupoids and their C*algebras,
to appear in “Operator algebras and dynamics: groupoids, crossed products
and Rokhlin dimension” (F. Perera, Ed.) in Advanced Courses in Mathematics. CRM Barcelona, Birkhäuser.
[http://arxiv.org/abs/1710.10897]
[PDF]
Research Interests and Affiliations
I am broadly interested in functional analysis, more specifically in the area of operator algebras and its applications in related fields.
Much of my research is concerned with C*algebras associated to directed graphs, to higherrank graphs and to other combinatorial structures.
These can be regarded as special cases of the theory of C*algebras associated to Hilbert bimodules and to product systems of Hilbert
bimodules, and I have a longstanding interest in these as well. More recently I have developed interests in C*algebras associated to
groupoids and to Fell bundles over groupoids, and also to the interplay between operator algebras and algebraic topology: in particular in
Dixmier–Douady theory and in deformations of C*algebras by cohomological data. I have also recently developed research programs
studying the structure of equilibrium states, known as KMS states, of C*dynamical systems; particularly in the context of
C*algebras associated to combinatorial structures.
I am a professor of pure mathematics in the School of Mathematics & Applied Statistics, which belongs to the Faculty of Engineering and Information Sciences, and am a member of the Institute for Noncommutative Analysis (INCA), a research centre of the University of Wollongong's Institute for Mathematics and Its Applications.
Current research students
 Becky Armstrong: Simplicity and structure of twisted C*algebras of topological higherrank graphs.Cosupervised with Nathan Brownlowe.
 Michael Mampusti: Fractal dual tilings and their C*algebras.Cosupervised with Mike Whittaker
 Alex Mundey: Operatoralgebraic invariants for fractal geometry. Cosupervised with Adam Rennie.
 Nick Seaton: Operator algebras and cohomology of groupoids. Cosupervised with David Pask.
 Rhys MacDonald: Twisted groupoid C*algebras and KMS states.
Cosupervised with David Pask.
Previous research students
 James Fletcher: Fredholm theory for graph C*algebras and applications of KKtheory to Cuntz–Pimsner algebras. Cosupervised with Adam Rennie. Graduated 2017.
 James Rout: Actions of graphs on topological spaces and generalised Bunce–Deddens algebras.Cosupervised with Dave Robertson. Graduated 2017.
 Dr Mitchell Hawkins: Applications of compact topological graph C*algebras to noncommutative solenoids. Cosupervised with Nathan Brownlowe. Graduated 2015.
 Dr Hui Li: Twisted C*algebras associated to topological graphs. Cosupervised with David Pask. Graduated 2014.
 Dr Yuxiang Tang: Tiling systems and 2graphs associated to textile systems. Cosupervised with David Pask. Graduated 2014.
 Dr Peter Lewin: The structure and ergodic theory of higherrank graph algebras. Cosupervised with Iain Raeburn. Graduated 2012.
 Dr Samuel B.G. Webster: Directed graphs and kgraphs: topology of the path space and how it manifests in the associated C*algebra. Cosupervised with Iain Raeburn. Graduated 2011.
You can find here a small collection of informal notes that I have developed or that others have allowed me to post at various times.
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