I work on bundle gerbes, 2-bundles, geometric stacks and internal groupoids and categories, and category theory more generally with a side interest in foundations. I have a particular interest in constructing examples in (low-dimensional) higher geometry.
From May 2022 I am a Visiting Associate Lecturer at the University of Adelaide, in the School of Computer and Mathematical Sciences.
You may also find me on: zbMATH, MathSciNet, Google Scholar, MathOverflow, arXiv, ORCiD, Publons, or my blog, theHigherGeometer.
If you need it, here is my email: droberts.(fifth and largest-known Fermat prime)@gmail.[etc] or [first].[last]@adelaide.edu.au
Classifying bi-invariant 2-forms on infinite-dimensional Lie groups (2023) arXiv:2311.03913. (submitted for publication)
Rigid models for 2-gerbes I: Chern-Simons geometry (2022) arXiv:2209.05521. Joint with Raymond Vozzo. (submitted for publication)
Homotopy types of topological stacks of categories, New York Journal of Mathematics, Volume 30 (2024), 940-955, journal version, arXiv:2204.02778 (this paper was written when I was a PhD student, in 2008/09, but only polished and released on the arXiv in 2022).
Substructural fixed-point theorems and the diagonal argument: theme and variations, Compositionality 5, 8 (2023), doi:10.32408/compositionality-5-8, arXiv:2110.00239.
Many finite-dimensional lifting bundle gerbes are torsion, Bulletin of the Australian Mathematical Society 105 Issue 2 (2022) 323–338, doi:10.1017/S000497272100071X, arXiv:2104.07936.
Extending Whitney’s extension theorem: nonlinear function spaces, Annales de l’Institut Fourier 71 no. 3 (2021) 1241–1286, doi:10.5802/aif.3424, arXiv:1801.04126. Joint with Alexander Schmeding.
The elementary construction of formal anafunctors, Categories and General Algebraic Structures with Applications vol 15 issue 1 (2021) 183–229, doi:10.52547/cgasa.15.1.183, arXiv:1808.04552. (Note that this was cited in Internal Categories, Anafunctors and Localisations with the title Strict 2-sites, J-spans and Localisations, and some paper containing these notes may yet have that title).
(Re)constructing code loops, American Mathematical Monthly 128 Issue 2 (2021) 151–161, doi:10.1080/00029890.2021.1852047, arXiv:1903.02748. Joint with Ben Nagy.
Topological sectors for heterotic M5-brane charges under Hypothesis H J. High Energ. Phys. 2020 no. 52 (2020) doi:10.1007/JHEP06(2020)052 (2020), arXiv:2003.09832.
Smooth loop stacks of differentiable stacks and gerbes, Cahiers de Topologie et Géométrie Différentielle Catégoriques, Vol LIX no 2 (2018) pp 95-141 journal version, arXiv:1602.07973. Joint with Raymond Vozzo.
The smooth Hom-stack of an orbifold, In: Wood D., de Gier J., Praeger C., Tao T. (eds) 2016 MATRIX Annals. MATRIX Book Series, vol 1 (2018) doi:10.1007/978-3-319-72299-3_3, arXiv:1610.05904, MATRIX hosted version. Joint with Raymond Vozzo
Equivariant bundle gerbes, Advances in Theoretical and Mathematical Physics 21 (2017) no. 4 pp 921-975, doi:10.4310/ATMP.2017.v21.n4.a3, arXiv:1506.07931. Joint with Michael Murray, Danny Stevenson and Raymond Vozzo.
Quasi-periodic paths and a string 2-group model from the free loop group, Journal of Lie Theory, 27 (2017), No. 4, 1151-1177. journal version (paywall), arXiv:1702.01514. Joint with Michael Murray and Christoph Wockel.
A bigroupoid’s topology (or, Topologising the homotopy bigroupoid of a space), Journal of Homotopy and Related Structures Volume 11, Issue 4 (2016) pp 923-942, doi:10.1007/s40062-016-0160-0, ReadCube, arXiv:1302.7019.
On certain 2-categories admitting localisation by bicategories of fractions, Applied Categorical Structures Volume 24, Issue 4 (2016) pp 373-384, doi:10.1007/s10485-015-9400-4, ReadCube, arXiv:1402.7108.
Simplicial principal bundles in parametrized spaces, New York Journal of Mathematics Volume 22 (2016) 405-440, journal version, arXiv:1203.2460, joint with Danny Stevenson.
A topological fibrewise fundamental groupoid, Homology, Homotopy and Applications, Volume 17, Number 2 (2015) 37-51, doi:10.4310/HHA.2015.v17.n2.a4, arXiv:1411.5779.
The weak choice principle WISC may fail in the category of sets, Studia Logica Volume 103, Issue 5 (2015) pp 1005-1017, doi:10.1007/s11225-015-9603-6 arXiv:1311.3074.
The universal simplicial bundle is a simplicial group, New York Journal of Mathematics, Volume 19 (2013) 51-60, journal version, arXiv:1204.4886.
On the existence of bibundles, Proc. London Math. Soc. (2012) 105 (6): 1290-1314, doi:10.1112/plms/pds028, arXiv:1102.4388. Joint with Michael Murray and Danny Stevenson
Internal categories, anafunctors and localisations, Theory and Applications of Categories, Vol. 26, 2012, No. 29, pp 788-829, journal version, arXiv:1101.2363
Fundamental bigroupoids and 2-covering spaces, PhD thesis, University of Adelaide (2010). DSpace@Adelaide
The inner automorphism 3-group of a strict 2-group, Journal of Homotopy and Related Structures, vol. 3(1), 2008, pp.193–245, journal version, arXiv:0708.1741. Joint with Urs Schreiber.
Yang-Mills theory for bundle gerbes, Journal of Physics A: Mathematical and Theoretical 39:6039-6044, 2006, doi:10.1088/0305-4470/39/20/027, arXiv:hep-th/0509037. Joint with Mathai Varghese. Sadly, this paper had to be retracted. See also this blog post.
Explicit String bundles (2014/2022) arXiv:2203.04544. (Notes from a talk delivered at Herriot-Watt University on 26 June 2014 at the Workshop on Higher Gauge Theory and Higher Quantization)
A Crisis of Identification, Inference: International Review of Science 4 Issue 3 (2019), doi:10.37282/991819.19.2. This article was subsequently reprinted for the special collection “A Christmas Chrestomathy, 2014–2020”, in vol 5 Issue 4.
Class forcing and topos theory (2018) notes from my 2015 talk at IHES, doi:10.4225/55/5b2252e3092af
Comments on Mochizuki’s 2018 Report (2018) doi:10.25909/5c5ce1fda4b7c, (blog post)
No Ancient Scottish Evidence of Fifth Platonic Solid, Letter to the Editor, Notices of the American Mathematical Society 65 no 6 (2018) p 677 (link)
What do mathematicians think about their journals? Peer review quality tops list of stated issues, LSE Impact Blog, June 22 2016 Blog post (joint with Cameron Neylon and Mark C. Wilson)
Review of Mathematics without apologies: Portrait of a problematic vocation by Michael Harris. (publisher’s page) Appears in: Gazette of the Australian Mathematical Society, Vol. 43 (2016) No. 2 (journal pdf)
Contribution to The “Bounded Gaps between Primes” Polymath Project: A Retrospective Analysis, Newsletter of the European Mathematical Society, No. 94, December 2014. (page 19 of this pdf)
Review of Lectures on real analysis by Finnur Larusson, Australian Mathematical Society Lecture Series, No. 21. (publisher’s page) Appears in: Gazette of the Australian Mathematical Society, Vol. 41 (2014) No. 5 (journal pdf)
See here for a list.
See here for a list of student projects I have supervised and courses I have taught.
My contributions to the nLab are released under a CC0 license. This is essentially public domain, but works in jurisdictions where such matters are difficult. Normal academic standards do apply, so attribution of ideas where they are clearly mine would be nice.
Last revised on April 30, 2025 at 05:52:45. See the history of this page for a list of all contributions to it.