I am currently a visiting research fellow at the Institute for Geometry and its Applications in the School of Mathematical Sciences at the University of Adelaide.
For the period July-December 2017 I will be a Lecturer at the University of Adelaide.
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.
I was a Research Associate (i.e. a postdoc) at the University of Adelaide from October 2013 to April 2015.
You may also find me on: MathOverflow|Google+|arXiv|ORCiD|Publons
If you need it, here is my email: droberts.[fifth and largest-known Fermat prime]@gmail.[etc]
The smooth Hom-stack of an orbifold, Joint with Raymond Vozzo, arXiv:1610.05904. To appear in the proceedings of Higher Structures:Advances at the MATRIX institute. (Accepted 13 December 2016)
Equivariant bundle gerbes, Advances in Theoretical and Mathematical Physics 21 (2017) no. 4 (to appear) 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), arXiv:1302.7019. Journal of Homotopy and Related Structures Volume 11, Issue 4 (2016) pp 923–942 doi:10.1007/s40062-016-0160-0, ReadCube.
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 arXiv:1402.7108.
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.
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). [email protected]
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
Strict 2-sites, $J$-spans and localisations.
Two rational maps that generate $\pi_1^s$ (working title)
Homogeneous 2-bundles
From code loops to 2-groups
String structures and string connections on homogeneous spaces, joint with Raymond Vozzo
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)
Smooth mapping stacks of differentiable stacks and orbifolds, Functional analysis seminar, University of Colorado, Boulder. 1 December 2016.
Low-dimensional higher geometry by examples, Kempner Colloquium, University of Colorado, Boulder. 29 November 2016.
Smooth mapping orbifolds, Differential geometry seminar, University of Adelaide. 20 May 2016.
Class forcing and topos theory, Topos a IHES, IHES, 27 November 2015. (Abstract), (Video)
Homogeneous string connections, 2015 Annual Meeting of the Australian Mathematical Society, 1 October 2015. (Abstract)
Homogeneous bundles and higher geometry, Eduard Čech Institute for Algebra, Geometry and Physics, 24 February 2015 (notes)
A new String group model from LG, Infinite-dimensional Structures in Higher Geometry and Representation Theory, Universität Hamburg, February 2015
String structures on homogeneous bundles, 8th Australia New Zealand Mathematics Convention, 12 December 2014 (Abstract)
A geometric proof of a theorem of Serre, Algebra and Topology seminar, Australian National University, 23 September 2014. (Abstract)
Explicit string bundles, Workshop on Higher Gauge Theory and Higher Quantization, Heriot-Watt University, June 2014. (notes from talk)
An explicit string bundle, Algebra/Geometry/Topology seminar University of Melbourne, 22 November 2013.
An explicit string bundle, AustMS 2013, 3 October 2013 (slides in WriteLaTeX).
Proper class forcing, Category Theory 2013, July 2013.
The complete list is here.
See here for a list of 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.