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 KK-theory or KMS-states—and how these invariants manifest as classifying invariants of the underlying dynamical systems.

My expertise is in Cuntz-Pismner 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, self-similar 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.

• ORCID Profile
• UOW Scholars

Publications

1. Mundey A., A Closed Graph Theorem for hyperbolic iterated function systems, To appear: Journal of Fractal Geometry.
   [arXiv]
2. Mundey A., Rennie A., A Cuntz-Pimsner Model for the C*-algebra of a Graph of Groups, J. Math. Anal. Appl. 496 (2021), no.2, 36pp.
   [DOI][arXiv]
3. 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 self-similarity

PhD Thesis:

"The Noncommutative Dynamics and Topology of Iterated Function Systems", University of Wollongong, 2020

• Principal Supervisor: Adam Rennie
• Cosupervisor: Aidan Sims

Recent Talks:

1. “Perfecting noncommutative topology” Australian Mathematical Society Annual Conference, University of Newcastle, Dec 2021
2. “Attaining perfection in noncommutative topology” University of Wollongong Operator Algebras and Noncommutative Geometry Seminar, Nov 2021
3. “From Bass-Serre Theory to Cuntz-Pimsner Algebras” Arizona State University C*-seminar, Jan 2021
4. “From Bass-Serre Theory to Cuntz-Pimsner Algebras” Australian Mathematical Society Annual Conference, University of New England, Dec 2020
5. “A Cuntz-Pimsner Model for the C*-algebra of a Graph of Groups” University of Wollongong Operator Algebras and Noncommutative Geometry Seminar, Oct 2019

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