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:
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.
Quinn Patterson, Adam Sierakowski, Aidan Sims, Jonathan Taylor, "Graded K-theory and K-homology of relative Cuntz--Pimsner algebras and graph C*-algebras." Journal of Mathematical Analysis and Applications, 2021.
Jonathan Taylor, "Aperiodic dynamical inclusions of $C^*$-algebras." arXiv Preprint, 2023.
Jonathan Taylor, "Essential commutative Cartan subalgebras of $C^*$-algebras." arXiv Preprint, 2023.
Jonathan Taylor, "Functoriality for groupoid and Fell bundle $C^*$-algebras." arXiv Preprint, 2023.
Ralf Meyer, Ali Raad, Jonathan Taylor, "Inductive limits of noncommutative Cartan inclusions." Proceedings of the American Mathematical Society, 2024.