Papers/Research/Writing

Preprints

• 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)

Published

• Homotopy types of topological stacks of categories, New York Journal of Mathematics, Volume 30 (2024) 940–955, journal version, arXiv:2204.02778. (Blog post)
• Substructural fixed-point theorems and the diagonal argument: theme and variations, Compositionality 5, 8 (2023), 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, 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, 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, doi:10.1007/978-3-319-72299-3_3 MATRIX hosted version, arXiv:1610.05904. 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.
• Simplicial principal bundles in parameterized spaces, New York Journal of Mathematics Volume 22 (2016) 405-440, journal version, arXiv:1203.2460, joint with Danny Stevenson.
• On certain 2-categories admitting localisation by bicategories of fractions, Applied Categorical Structures (2015) doi:10.1007/s10485-015-9400-4, ReadCube, arXiv:1402.7108.
• A topological fibrewise fundamental groupoid, Homology, Homotopy and Applications, Volume 17 (2015) Number 2, 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 (2015) Issue 5, 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

Notes not for publication

• Comments on Mochizuki’s 2018 Report (2018) doi:10.25909/5c5ce1fda4b7c, (blog post)
• Class forcing and topos theory, notes from my 2015 talk at IHES, doi:10.4225/55/5b2252e3092af
• 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)

Non-technical

• A Crisis of Identification, Inference: International Review of Science 4 Issue 3 (2019) doi:10.37282/991819.19.2, Subsequently reprinted for the special collection “A Christmas Chrestomathy, 2014–2020”, in vol 5, Issue 4.