Alexander Mundey
Research
Research Interests
I'm broadly interest in the interplay between dynamical systems and operator algebras. My research focuses on C*algebraic approaches to studying topological and algebraic dynamical systems, often by computing invariants (KKtheory, KMSstates, cohomology) and determining how these invariants help to understand the underlying dynamical systems.
A lot of my work focuses on CuntzPismner algberas and groupoid C*algebras. I have used these constructions model a range of dynamical systems including iterated function systems, graph dynamics, selfsimilar actions, and more general actions of groups on trees.
I am currently employed as an Associate Research Fellow as the University of Wollongong on an ARC Discovery Project grant under Senior Professor Aidan Sims.
I also organise the Wollongong OANCG Seminar. If you have any inquires about the seminar, please send me an email.
Publications

K. Brix, A. Mundey and A. Rennie,
Morphisms of CuntzPimsner algebras from completely positive maps,
preprint (2023) [arXiv]  A. Mundey and A. Sims,
Homology and twisted C*algebras for selfsimilar actions and ZappaSzép products,
preprint (2023) [arXiv] 
K. Brix, A. Mundey and A. Rennie,
Splittings for C*correspondences and strong shift equivalence,
preprint (2023) [arXiv] 
A. Mundey,
A Closed Graph Theorem for hyperbolic iterated function systems,
J. Fractal Geom. 9 (2022), no. 34, 325–336. [DOI] [arXiv] 
A. Mundey and A. Rennie,
A CuntzPimsner Model for the C*algebra of a Graph of Groups,
J. Math. Anal. Appl. 496 (2021), no.2, 36pp. [DOI] [arXiv] 
N. Brownlowe, A. Mundey, D. Pask, J. Spielberg and A. Thomas,
C*algebras associated to graphs of groups,
Adv. Math. 316 (2017), 114–186. [DOI] [arXiv]
Grants
 AEGis CONNECT  University of Wollongong (20232024)
Fractals Unleashed: Discovering New Invariants through Operator Algebras
with Adam Rennie  RevITAlising (RITA) Research Grant – University of Wollongong (20212022)
A quantum approach to the emergence of selfsimilarity
PhD Thesis:
"The Noncommutative Dynamics and Topology of Iterated Function Systems", University of Wollongong, 2020
 Principal Supervisor: Adam Rennie
 Cosupervisor: Aidan Sims
Recent Talks:
 “Perfecting noncommutative topology” Australian Mathematical Society Annual Conference, University of Newcastle, Dec 2021
 “Attaining perfection in noncommutative topology” University of Wollongong Operator Algebras and Noncommutative Geometry Seminar, Nov 2021
 “From BassSerre Theory to CuntzPimsner Algebras” Arizona State University C*seminar, Jan 2021
 “From BassSerre Theory to CuntzPimsner Algebras” Australian Mathematical Society Annual Conference, University of New England, Dec 2020
 “A CuntzPimsner Model for the C*algebra of a Graph of Groups” University of Wollongong Operator Algebras and Noncommutative Geometry Seminar, Oct 2019