I am currently a visiting fellow 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.
I was a research associate (i.e. a postdoc) at the University of Adelaide from October 2013 to April 2015.
If you need it, here is my email:
droberts.[fifth and largest-known Fermat prime]@gmail.blahblah
You may also find me on
A topological fibrewise fundamental groupoid, arXiv:1411.5779. Accepted for publication, Homology, Homotopy and Applications (April 2015)
On certain 2-categories admitting localisation by bicategories of fractions, arXiv:1402.7108. Accepted for publication, Applied Categorical Structures (March 2015)
The weak choice principle WISC may fail in the category of sets, Studia Logica (2015) doi:10.1007/s11225-015-9603-6 arXiv:1311.3074.
A bigroupoid’s topology, arXiv:1302.7019. Submitted for publication.
The universal simplicial bundle is a simplicial group, New York Journal of Mathematics, Volume 19 (2013) 51-60, journal version, arXiv:1204.4886.
Simplicial principal bundles in parameterized spaces, arXiv:1203.2460, joint with Danny Stevenson. Submitted for publication 6 November 2012, rejected 14 November 2012. Resubmitted for publication 15 November 2012, rejected 16 February 2014.
On the existence of bibundles, Proc. London Math. Soc. (2012) 105 (6): 1290-1314, journal version, 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
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, journal version, 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
Smooth loop stacks of differentiable stacks and gerbes, joint with Raymond Vozzo.
Equivariant bundle gerbes, joint with Michael Murray, Raymond Vozzo and Danny Stevenson
String structures and string connections on homogeneous spaces, joint with Raymond Vozzo
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)
Lectures on real analysis by Finnur Larusson, Australian Mathematical Society Lecture Series, No. 21. Appears in: Bulletin of the Australian Mathematical Society, Vol. 41 (2014) No. 5 (journal pdf)
Higher homogeneous bundles, Differential geometry seminar, University of Adelaide. 27 March 2015.
Homogeneous bundles and higher geometry, Eduard Čech Institute for Algebra, Geometry and Physics, 24 February 2015
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)
The Serre-Grothendieck theorem by geometric means, Differential geometry seminar, University of Adelaide, 24 October 2014. (Abstract)
A geometric proof of a theorem of Serre, Algebra and Topology seminar, Australian National University, 23 September 2014. (Abstract)
Mathematics: A castle in the sky?, School of Mathematical Sciences Undergraduate Seminar, University of Adelaide, 25 August 2014. (slides)
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, CT2013, July 2013.
On the Ganter-Kapranov approach to supersymmetry, Strings Journal Club, University of Adelaide. 27 May 2013.
Diffeological spaces and differentiable stacks, Differential Geometry seminar, University of Adelaide. 10 May 2013.
On the Baas-Dundas-Rognes approach to 2-vector bundles, Strings Journal Club, University of Adelaide. 19 February 2013.
Elliptic cohomology - first steps, Strings Journal Club, University of Adelaide. 9 October 2012.
Sheaf cohomology via abelian categories, Strings Journal Club, University of Adelaide. 4 September 2012.
Introduction to 2-groups, Strings Journal Club, University of Adelaide. 5 May 2012.
2-categorical localisation, Australian Category Seminar, Macquarie University. 12 October 2011.
Functorial 2-connected covers, Differential Geometry seminar, University of Adelaide. 21 May 2010.
2-covering spaces, 2009 Annual Meeting of the Australian Mathematical Society, at the University of South Australia. 30 September 2009.
Fundamental 2-groups and 2-covering spaces, slides prepared for talk accepted for the Categorical groups workshop, Barcelona. June 2008. Due to lack of funding at the last minute, I wasn’t able to attend this conference, and my speaking slot was given up. See also this blog post.
Of inner automorphisms and universal bundles, Differential Geometry seminar, University of Adelaide. 26 October 2007.
Bundle gerbes, higher Yang-Mills and Kalb-Ramond, 2006 Annual Meeting of the Australian Mathematical Society, at Macquarie University. September 2006.
Bundle gerbe Yang-Mills, Erwin Schrodinger Institute, May 2006.
Jayden Redden - Explicit formulas for connections, Summer 2014/15
Diclehan Erdal - Coequalisers from minimal ETCS axioms, Summer 2014/15
2015
2014
2013
2007
Semester 2 : Maths 1B, Tutor
Semester 1: Maths 1A, Tutor
2006
Semester 2 : Maths 1B, Tutor
Semester 1: Maths 1A, Tutor
2005
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.