Jonathan Taylor, Ph. D.

Research Interests

I am broadly interested in C*-algebras arising from algebraic objects and dynamical systems, as well as the broader category theoretic structures surrounding them. Some more specific interests include:

  • analysis and classification of inclusions of C*-algebras;
  • Fell bundles over étale non-Hausdorff groupoids and their C*-algebras;
  • inverse semigroup actions and their crossed products, noncommutative dynamical systems;
  • geometric semigroup theory and non-commutative Stone duality;
  • functoriality for C*-algebra constructions.

My previous research projects focus heavily on the analysis of groupoid C*-algebras, including classifying inclusions of regular maximal commutative C*-subalgebras (called essential Cartan inclusions) with detection of ideals as groupoid C*-algebras. This expands upon the results of Renault and Kumjian using a different approach to Exel and Pitts with different advantages. Another major project was describing morphisms between étale groupoids that induce *-homomorphisms between the C*-algebras of the groupoids. This research frames entwining of conditional expectations and injectivity of the induced homomorphisms on the level of groupoids, as well showing that all homomorphisms between essential Cartan pairs that preserve the Cartan structure must arise from morphisms between the underlying groupoids.

Professional Affiliations

I am currently a postdoctoral researcher at the University of Potsdam in Germany, working in the research group of Prof. Dr. Sven Raum (Professor for algebra).

I began my doctoral candidacy at University of Göttingen in October 2019 as part of the Research Training Group RTG2491 in Fourier Analysis and Spectral Theory. I worked notably with Prof. Dr. Ralf Meyer as my main doctoral advisor, as well as with Prof. Dr. Thomas Schick and Prof. Dr. Chenchang Zhu, who together form my Thesis Advisory Committee. I defended my PhD in September of 2022, graduating magna cum laude. My thesis was titled “Aperiodic dynamical inclusions of C*-algebras”.

I previously completed my Bachelor with Honours at the University of Wollongong, with my thesis “Graded K-homology for Graph C*-algebras”, under the supervision of Snr. Prof. Aidan Sims and Dr. Adam Sierakowski.