Alexander Mundey
Research
Research Interests
I have a broad interest in the interplay between dynamical systems and operator algebras with my research focusing on C*algebraic approaches to studying topological and algebraic dynamical systems. I am driven towards constructing dynamical invariants that arise from C*algebraic constructions—for example via KKtheory or KMSstates—and how these invariants manifest as classifying invariants of the underlying dynamical systems.
My expertise is in CuntzPismner algberas associated to C*correspondences and groupoid C*algebras. I have used these constructions model a range of dynamical systems including iterated function systems, dynamical systems arising from graphs, 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 run the Operator Algebras & Noncommutative Geometry seminar at the University of Wollongong. If you have any inquries about the seminar, please send me an email.
Publications

Mundey A.,
A Closed Graph Theorem for hyperbolic iterated function systems, To appear: Journal of Fractal Geometry.
[arXiv] 
Mundey A., Rennie A.,
A CuntzPimsner Model for the C*algebra of a Graph of Groups, J. Math. Anal. Appl. 496 (2021), no.2, 36pp.
[DOI][arXiv] 
Brownlowe N., Mundey A., Pask D., Spielberg J., Thomas A.,
C*algebras associated to graphs of groups, Adv. Math. 316 (2017), 114–186.
[DOI] [arXiv]
Grants
 RevITAlising (RITA) Research Grant – University of Wollongong (2021)
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