nLab
David Michael Roberts

I am currently a Research Associate (that is, a postdoc) at the Institute for Geometry and its Applications in the School of Mathematical Sciences 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.

Previous to this, for July-2017 to February 2018 I was a Lecturer (=Assistant Professor in the US system) in the School of Mathematical Sciences. I was also a Research Associate at the University of Adelaide from October 2013 to April 2015.

You may also find me on: 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

Writing

Preprints/Notes

• Topological sectors for heterotic M5-brane charges under Hypothesis H (2020), arXiv:2003.09832. Submitted.

• The formal construction of formal anafunctors (2018), arXiv:1808.04552 doi:10.25909/5b6cfd1a73e55 (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) Submitted.

• Extending Whitney’s extension theorem: nonlinear function spaces, arXiv:1801.04126. Joint with Alexander Schmeding. Submitted.

• 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)

Papers

• (Re)constructing code loops, arXiv:1903.02748. Accepted to appear, American Mathematical Monthly, 11 March 2020. Joint with Ben Nagy.

• 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

In preparation

• String structures and string connections on homogeneous spaces, joint with Raymond Vozzo

Other

• A Crisis of Identification, Inference: International Review of Science 4 Issue 3 (2019) (link)

• 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)

Selected Talks

• Groupoids, spans and cospans, Groupoids, Graphs, and Algebras, University of Sydney. 2 July 2019.

• From cows to inductive types; or, What are numbers?, School of Mathematical Sciences Undergraduate Seminar, University of Adelaide. 5 September 2018.

• The stack of smooth maps from a manifold to a differentiable stack is differentiable, Topology in Australia and South Korea, POSTECH. 23 April 2018. (Video, requires flash)

• Constructions in lower dimensional higher geometry, Gauge theory and higher geometry, University of Adelaide. 29 November 2017.

• Constructing differential string structures, Differential geometry seminar, University of Adelaide. 7 June 2017.

• 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), (Notes)

• 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.

Supervision and teaching

See here for a list of student projects I have supervised and courses I have taught.

Copyright statement

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.