Alexander Mundey

Research

Research Interests

I am broadly interested 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 and determining how these invariants help to understand the underlying dynamics.

On the dynamical side of things, the systems I look at tend to be "self-similar" in one way or another. This includes—but is not limited to—iterated function systems, (topological) graph dynamics, self-similar actions (and more general actions of groups on trees) and semigroups. On the C*-algebraic side of things I use groupoids and C*-correspondences to provide noncommutative models of dynamical systems, and use invariants of the associated algebras to understand properties of the dynamics.

I am currently employed as an Associate Research Fellow as the University of Wollongong on an ARC Discovery Project grant under Distinguished Professor Aidan Sims.

I also organise the Wollongong OANCG Seminar. If you have any inquires about the seminar, please send me an email.

• ORCID Profile
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• Math Genealogy

Publications

1. K. Brix, A. Mundey and A. Rennie,
   Morphisms of Cuntz-Pimsner algebras from completely positive maps,
   preprint (2023) [arXiv]
2. A. Mundey and A. Sims,
   Homology and twisted C*-algebras for self-similar actions and Zappa-Szép products,
   preprint (2023) [arXiv]
3. K. Brix, A. Mundey and A. Rennie,
   Splittings for C*-correspondences and strong shift equivalence,
   Math. Scand, 130 (2024) [article] [arXiv]
4. A. Mundey,
   A Closed Graph Theorem for hyperbolic iterated function systems,
   J. Fractal Geom. 9 (2022), no. 3-4, 325–336. [article] [arXiv]
5. A. Mundey and A. Rennie,
   A Cuntz-Pimsner Model for the C*-algebra of a Graph of Groups,
   J. Math. Anal. Appl. 496 (2021), no.2, 36pp. [article] [arXiv]
6. N. Brownlowe, A. Mundey, D. Pask, J. Spielberg and A. Thomas,
   C*-algebras associated to graphs of groups,
   Adv. Math. 316 (2017), 114–186. [article] [arXiv]

Grants

1. AEGis CONNECT - University of Wollongong (2023-2024)
   Fractals Unleashed: Discovering New Invariants through Operator Algebras
   Lead CI: A. Mundey | Other CIs: Adam Rennie
2. RevITAlising (RITA) Research Grant – University of Wollongong (2021-2022)
   A quantum approach to the emergence of self-similarity
   Lead CI: A. Mundey

PhD Thesis

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

• Principal Supervisor: Adam Rennie
• Cosupervisor: Aidan Sims

Bonus Facts

I have an Erdős number of 3.

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