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Jonathan Taylor

Doctoral Candidate
Georg-August-Universität Göttingen

Research Interests

I am interested in Noncommutative Geometry and Dynamics. My current research is in étale groupoids and their C*-algebras, as well as analysis of noncommutative Cartan pairs. In studying these, I have been motivated to study local multplier algebras, and define a construction analogous to this for Hilbert bimodules.

I am also interested in investigating the types of morphisms that arise between twisted groupoids associated to commutative Cartan Pairs: when one has a *-homomorphism between two Cartan pairs preserving all the relevant struture, what kinda of morphisms does one acqure between the underlying twisted groupoids (if any).

Another interest of mine is in the noncommutative Stone duality and geometric semigroup theory, as well as dynamics of these objects acting on C*-algebras.


Previously I have worked with computation of KK-theory for graph C*-algebras and more generally Cuntz-Pimsner algebras of graded Hilbert bimodules, using a generalised version of Pimsner’s 6-term exact sequence from Kumjian, Pask, and Sims. This work is related to my thesis and was later published with Quinn Patterson, Adam Sierakowski, and Aidan Sims.

Affiliations

I began my doctoral candidacy at Georg-August-Universität Göttingen in October 2019 as part of the Research Training Group (RTG) in Fourier Analysis and Spectral Theory. I work 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 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.

Articles and Presentations

Localised Hilbert modules and weak noncommutative Cartan pairs: arXiv

Graded K-theory and K-homology of relative Cuntz-Pimsner algebras and graph C*-algebras: ScienceDirect arXiv

Presentiation Recording: Essential groupoid C*-algebras of non-Hausdorff groupoids

Inductive Limits of Noncommutative Cartan Inclusions (with Ralf Meyer, Ali I. Raad): arXiv

Essential commutative Cartan subalgebras of C*-algebras: arXiv

Contact Me

University of Göttingen Mathematical Institute
Bunsenstraße 3-5
37073
Göttingen
Germany

University email: jonathan.taylor “at” mathematik “dot” uni-goettingen “dot” de

Personal-Professional email: jtaylor.math “at” outlook “dot” com

Orcid ID: 0000-0002-6951-999X

arXiv: arxiv.org/a/taylor_j_5

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