Dr David Roberts

School of Mathematical Sciences

College of Science

Eligible to supervise Masters and PhD (as Co-Supervisor) - email supervisor to discuss availability.


Pure mathematician working on geometry and category theory.See https://thehighergeometer.wordpress.com or https://ncatlab.org/nlab/show/David+Michael+Roberts for more information about my research.

Date Position Institution name
2018 - 2020 Research Associate University of Adelaide
2017 - 2018 Lecturer University of Adelaide
2015 - ongoing Visiting Fellow University of Adelaide
2012 - 2015 Research Associate University of Adelaide
2009 - 2012 Research Officer NCVER

Date Institution name Country Title
2005 - 2010 University of Adelaide Australia PhD
2001 - 2004 University of Adelaide Australia BSc(hons)

Year Citation
2026 Roberts, D. M., & Vozzo, R. F. (2026). Rigid models for 2-gerbes I: Chern–Simons geometry. Journal of Homotopy and Related Structures, 1-66.
DOI
2024 Roberts, D. M. (2024). Homotopy types of topological stacks of categories. The New York Journal of Mathematics, 30, 940-955.
2023 Roberts, D. M. (2023). Substructural fixed-point theorems and the diagonal argument: theme and variations. Compositionality, 5(8), 1-16.
DOI Scopus2
2022 Roberts, D. M., & Schmeding, A. (2022). Extending Whitney's extension theorem: nonlinear function spaces. Annales de l'Institut Fourier, 71(3), 1241-1286.
DOI WoS4
2022 Roberts, D. M. (2022). Many finite-dimensional lifting bundle gerbes are torsion. Bulletin of the Australian Mathematical Society, 105(2), 323-338.
DOI Scopus1 WoS1
2022 Roberts, D. M. (2022). Explicit String bundles.
2021 Roberts, D. M. (2021). The elementary construction of formal anafunctors. Categories and General Algebraic Structures with Applications, 15(1), 183-229.
DOI Scopus4 WoS3
2021 Nagy, B., & Roberts, D. M. (2021). (Re)constructing code loops. American Mathematical Monthly, 128(2), 151-161.
DOI Scopus1 WoS1
2020 Roberts, D. M. (2020). Topological sectors for heterotic M5-brane charges under Hypothesis H. Journal of High Energy Physics, 2020(6), 52-0-52-16.
DOI Scopus5 WoS4
2018 Roberts, D., & Vozzo, R. (2018). Smooth loop stacks of differentiable stacks and gerbes. Cahiers de Topologie et Geometrie Differentielle Categoriques, LIX(2), 95-141.
2018 Roberts, D. M. (2018). No ancient scottish evidence of fifth platonic solid. Notices of the American Mathematical Society, 65(6), 677.
2017 Murray, M., Roberts, D. M., & Wockel, C. (2017). Quasi-periodic paths and a string 2-group model from the free loop group. Journal of Lie Theory, 27(4), 1151-1177.
Scopus3 WoS3
2017 Murray, M., Roberts, D., Stevenson, D., & Vozzo, R. (2017). Equivariant bundle gerbes. Advances in Theoretical and Mathematical Physics, 21(4), 921-975.
DOI Scopus8 WoS9
2016 Roberts, D. (2016). A bigroupoid's topology (or, Topologising the homotopy bigroupoid of a space). Journal of Homotopy and Related Structures, 11(4), 923-942.
DOI
2016 Roberts, D. (2016). On certain 2-categories admitting localisation by bicategories of fractions. Applied Categorical Structures: a journal devoted to applications of categorical methods in algebra, analysis, order, topology and computer science, 24(4), 373-384.
DOI Scopus2 WoS3
2016 Roberts, D., & Stevenson, D. (2016). Simplicial principal bundles in parametrized spaces. New York Journal of Mathematics, 22, 405-440.
Scopus4 WoS1
2015 Roberts, D. (2015). The weak choice principle WISC may fail in the category of sets. Studia Logica, 103(5), 1005-1017.
DOI Scopus5 WoS4
2015 Roberts, D. (2015). A topological fibrewise fundamental groupoid. Homology, Homotopy and Applications, 17(2), 37-51.
DOI Scopus1 WoS1
2013 Roberts, D. (2013). The universal simplicial bundle is a simplicial group. The New York Journal of Mathematics, 19, 51-60.
Scopus1 WoS1
2012 Roberts, D. (2012). Internal categories, anafunctors and localisations. Theory and Applications of Categories, 26(29), 788-829.
Scopus21 WoS22
2012 Murray, M., Roberts, D., & Stevenson, D. (2012). On the existence of bibundles. Proceedings of the London Mathematical Society, 105(6), 1290-1314.
DOI Scopus3 WoS3
2008 Roberts, D., & Schreiber, U. (2008). The inner automorphism 3-group of a strict 2-group. Journal of Homotopy and Related Structures, 3(1), 193-245.
WoS14
2006 Varghese, M., & Roberts, D. (2006). Yang-Mills theory for bundle gerbes. Journal of Physics A: Mathematical and Theoretical (Print Edition), 39(20), 6039-6044.
DOI Scopus3 WoS4
- Roberts, D. M. (2019). A Crisis of Identification. Inference: International Review of Science, 4(3).
DOI

Year Citation
2022 Roberts, D. M., & Vozzo, R. F. (2022). Rigid models for 2-gerbes I: Chern-Simons geometry.
- Roberts, D. (n.d.). Class forcing and topos theory.
DOI
- Roberts, D. (n.d.). Comments on Mochizuki’s 2018 Report.
DOI

Year Citation
2019 Nagy, B., & Roberts, D. (2019). codeloops [Computer Software].

Year Citation
2023 Roberts, D. M. (2023). Classifying bi-invariant 2-forms on infinite-dimensional Lie groups.
2022 Roberts, D. M. (2022). Homotopy types of topological stacks of categories.

Date Role Research Topic Program Degree Type Student Load Student Name
2025 Co-Supervisor Higher Equivariance and String Geometry Master of Philosophy Master Full Time Mr Samuel Lloyd Groocock

Date Role Research Topic Location Program Supervision Type Student Load Student Name
2025 - ongoing Co-Supervisor Higher Equivariance and String Geometry The University of Adelaide - Master Full Time Mr Samuel Lloyd Groocock
2020 - 2020 Principal Supervisor Topos theory The University of Adelaide - Honours Full Time Blake Donnelly

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