My main research interests are the representation theory of groupoid C*-algebras and algebras associated with labeled graphs.
ARTICLES
Properties preserved by groupoid equivalence (with Dana Williams).
Accepted to Journal of Operator Theory.
Preprint: https://arxiv.org/abs/2203.15620
The primitive ideal space of groupoid C∗-algebras for groupoids with Abelian
isotropy (with Dana Williams).
Indiana University Mathematics Journal 70 (2022), no.1, 359–390. Preprint: https://arxiv.org/abs/2108.02277.pdf
Ultragraph algebras via labelled graph groupoids, with applications to generalized
uniqueness theorems (with Gilles de Castro and Daniel Gonçalves).
Journal of Algebra 579 (2021), 456–495. Preprint: https://arxiv.org/pdf/2009.01357.pdf
Topological full groups of ultragraph groupoids as an isomorphism invariant (with
Gilles de Castro and Daniel Gonçalves).
Münster Journal of Mathematics 14 (2021), no.1, 165–189. Preprint: https://arxiv.org/pdf/1912.10465.pdf
Labelled space C∗-algebras as partial crossed products and a simplicity
characterization (with Gilles de Castro).
Journal of Mathematical Analysis and Applications 491 (2020), no.1, 124-290. Preprint: https://arxiv.org/pdf/1909.04456.pdf
GCR and CCR Steinberg algebras (with Lisa O. Clark and Benjamin Steinberg).
Canadian Journal of Mathematics 72 (2020), no.6, 1581–1606. Preprint: https://arxiv.org/pdf/1901.06056.pdf
The orbit spaces of groupoids whose C*-algebras are CCR.
Journal of Mathematical Analysis and Applications 478 (2019), no.1, 304–319. Preprint: https://arxiv.org/pdf/1806.05623.pdf
The orbit spaces of groupoids whose C∗-algebras are GCR.
Journal of Operator Theory 80 (2018), no.1, 167–185. Preprint: https://arxiv.org/abs/1806.05623.
PREPRINTS
Leavitt Path Algebras of Labelled Graphs (with Giuliano Boava, Gilles de Castro and
Daniel Gonçalves).
Preprint: https://arxiv.org/pdf/2106.06036.pdf.
Algebras of one-sided subshifts over arbitrary alphabets (with Giuliano Boava, Gilles de Castro and Daniel Gonçalves).
PHD THESIS
Van Wyk, D.W. 2017. The structure of GCR and CCR groupoid C*-algebras. (Ph.D. thesis, University of Otago).
CONTRIBUTIONS
Weideman, A.J. & Van Dyk, T.J. (editors) with Van Wyk, D.W., Burmeister, T., Steyn, S., Hsuan Wu, M. 2014. Academic literacy: Test your competence [Section on quantitative literacy]. Bloemfontein: ICELDA.
SELECTED TALKS
The primitive ideal space of groupoid C*-algebras for groupoids with abelian isotropy [Joint work with Dana Williams]. Joint Mathematics Meeting, AMS Contributed Paper Session on Differential and Metric Geometry, Geometric Analysis, and Algebras of Operators, Virtual, April 2022.
Introductory workshop on groupoids and Steinberg algebras. Cimpa School – From Dynamics to Algebra and Representation Theory and Back, Florianópolis, Brazil, February 2022.
The primitive ideal space of groupoid C*-algebras for groupoids with abelian isotropy. South African Mathematical Society annual meeting, South Africa, December 2021.
The primitive ideal space of groupoid C*-algebras for groupoids with abelian isotropy. Web-seminar on Operator Algebras, Universidade Federal de Santa Catarina, Florianópolis, Brazil, August 2021.
GCR groupoids C*-algebras. Dartmouth College, Hanover, USA, October 2020.
Realizing labelled space C*-algebras as partial crossed products. Dartmouth College, Hanover, USA, July 2020.
Labelled space C*-algebras as partial crossed products. IV Workshop on Dynamics, Numeration and Tilings, Florianópolis, Brazil, 29 April – 3 May, 2019.
The orbit space of groupoids whose C*-algebras GCR or CCR, ICM. Operator Algebras Satellite Conference, Florianópolis, Brazil, July 2018.
Groupoids whose C*-algebras are CCR. University of São Paulo, Brazil, October 2018.
GCR groupoids C*-algebras. Federal University of Santa Catarina, Florianópolis, Brazil, March 2018.
Type I groupoid C*-algebras. Australian Mathematical Society annual meeting, Canberra, Australia, December 2016.