David Roberts

School of Computer and Mathematical Sciences

Faculty of Sciences, Engineering and Technology

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.

Career
Publications
Supervision
Contact

Appointments

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

Education

Date Institution name Country Title

2005 - 2010 University of Adelaide Australia PhD

2001 - 2004 University of Adelaide Australia BSc(hons)
Research Interests

Algebraic and Differential Geometry Category Theory Mathematical Logic

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

Journals

Year	Citation
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 Scopus1
2022	Roberts, D. M. (2022). Explicit String bundles.
2022	Roberts, D. M. (2022). Many finite-dimensional lifting bundle gerbes are torsion. Bulletin of the Australian Mathematical Society, 105(2), 323-338. DOI
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 WoS1
2021	Roberts, D. M. (2021). The elementary construction of formal anafunctors. Categories and General Algebraic Structures with Applications, 15(1), 183-229. DOI Scopus3
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 WoS3
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 WoS2
2017	Murray, M., Roberts, D., Stevenson, D., & Vozzo, R. (2017). Equivariant bundle gerbes. Advances in Theoretical and Mathematical Physics, 21(4), 921-975. DOI Scopus6 WoS6
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 WoS2
2016	Roberts, D., & Stevenson, D. (2016). Simplicial principal bundles in parametrized spaces. New York Journal of Mathematics, 22, 405-440. Scopus4
2015	Roberts, D. (2015). A topological fibrewise fundamental groupoid. Homology, Homotopy and Applications, 17(2), 37-51. DOI Scopus1 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 WoS3
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. Scopus17 WoS14
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 WoS3
-	Roberts, D. M. (n.d.). A Crisis of Identification. Inference: International Review of Science, 4(3). DOI

Book Chapters

Year	Citation
2017	Roberts, D., & Vozzo, R. (2017). The smooth Hom-stack of an orbifold. In D. Wood, J. de Gier, C. Praeger, & T. Tao (Eds.), 2016 MATRIX Annals (Vol. 1, pp. 43-47). Switzerland: Springer, Cham. DOI

Working Paper

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

Software

Year Citation

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

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

Preprint

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.

Other Supervision Activities

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 - ongoing	Principal Supervisor	Topos theory	The University of Adelaide	-	Honours	Full Time	Blake Donnelly

Email: david.roberts@adelaide.edu.au

David Roberts

Appointments

Education

Research Interests

Journals

Book Chapters

Working Paper

Software

Preprint

Other Supervision Activities

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