Research

Research interests

My research focuses on operator algebras, particularly C*-algebras. These mathematical structures, analogous to infinite-dimensional matrices, were originally introduced to provide a rigorous framework for describing quantum physical phenomena that emerged in the early 20th century. While operator algebras are studied in their own right, they have since found widespread applications in fields such as representation theory, harmonic analysis, geometry, mathematical physics, and more. Additionally, techniques from various branches of mathematics have been employed to address problems in operator algebras. I am particularly interested in the interactions between C*-algebras, groups, and topological dynamics. Specifically, I explore how the structural and approximation properties of C*-algebras relate to the underlying groups or dynamics from which they arise. My recent work has focused on investigating a generalised notion of dimension for C*-algebras known as stable rank.

Publications

1. Nina Rynne, Geneva Birtles, Jamie Bell, Mung Suan Pau Duhlian, Samuel McNeil, Adel Mehrpooya, Blake Noske, Yadursha Vakeesan, and Michael Bode. "Complex patch geometry promotes species coexistence through a reverse competition–colonization trade-off." Proc. R. Soc. B 290, no. 2010 (2023): 20231554. DOI: 10.1098/rspb.2023.1554

Theses 

1. "The classification of approximately finite-dimensional C*-algebras" 

Honour's thesis (equivalent of Master's) at the University of Wollongong, 2022. Supervised by Prof. Dr. Aidan Sims.