I am a Research Fellow in the Mathematical Institute at Oxford University, as part of the Quantum Mathematics and Computation research group. I am on leave from my position as Lecturer in Mathematics in the Department of Mathematical Sciences at Stellenbosch University, South Africa.

My research is about low-dimensional topology and mathematical physics, with a focus on topological quantum field theory (TQFT).

- From the finite Fourier transform to topological quantum field theory,

North-meets-South colloquium, Mathematical Institute, Oxford, 6 May 2016. - String-net descriptions of TQFTs and the lifting map.

Edinburgh Mathematical Physics Group (EMPG) seminar, 16 March 2016. - Three-dimensional bordism representations,

Edinburgh Geometry seminar (EDGE), 17 March 2016. - Two different graphical descriptions of 3d TQFTs,

Sheffield topology seminar, 17 November 2015. - Graphical calculus for 3d TQFTs,

Oxford topology seminar, 2 November 2015.

- Spin-net formalism for 3-dimensional toplogical quantum field theories,

Higher Structures in Geometry and Physics conference, Max Planck Institute, Bonn, 12-16 October 2015. - The centre of a fusion category, the adjoint representation, and the tube algebroid.

Higher topological quantum field theory and categorical quantum mechanics workshop, ESI Institute, Vienna, 19-23 October 2015. - Three-dimensional bordism representations from generators and relations,

Parameterized Morse Theory and Low-Dimensional and Symplectic Topology workshop, Banff, March 2014. - Three-dimensional bordism representations from generators and relations,

Structures on Tensor Categories and Topological Field Theories workshop, Erlangen, March 2014.

- Lagrangian subspaces and Fourier transforms,

Seminar on Contextuality and Noncommutative Geometry, Oxford, 9 Mar 2016. - More geometry of the Ising model,

Pizza seminar on mathematical physics, geometry and topology, Oxford, 4 Nov 2015. - The geometry of the Ising model,

Oxford Junior Geometry and Topology seminar, 7 May 2015. - The geometry of force,

Stellenbosch Theoretical Physics Seminar, 19 Sep 2013. - Transformation optics and cloaking devices,

VLS Seminar, 3 August 2012. - Filling space with knotted circles (write-up, some slides)

Stellenbosch colloquium talk, 22 Nov 2010.

Talk given in the Stellenbosch postgraduate seminar, 5 March 2009.

- Modular categories as representations of the 3-dimensional bordism 2-category (with Chris Douglas, Chris Schommer-Pries and Jamie Vicary), Sep 2015.
- Extended 3-dimensional bordism as the theory of modular objects (with Chris Douglas, Chris Schommer-Pries and Jamie Vicary), Nov 2014.
- Quasistrict symmetric monoidal 2-categories via wire diagrams, Sep 2014.

- Fusion categories via string diagrams,

Communications in Contemporary Mathematics, to appear (2015). [arXiv] - The Geometry of Unitary 2-Representations of Finite Groups and their 2-Characters,

Applied Categorical Structures, Vol 19, Issue 1, pp 175-232 (2011). [arXiv]

- Flow equations for Hamiltonians from Continuous Unitary Transformations

Masters thesis in Theoretical Physics, Stellenbosch, 2003. - Categorical Aspects of Topological Quantum Field Theories

Masters thesis in Theoretical Physics, Utrecht University, 2005. - On unitary 2-representations of finite groups and topological quantum field theory

PhD thesis in Pure Mathematics, University of Sheffield, 2009

- Non-perturbative flow equations from running expectation values (with FG Scholtz, HB Geyer),

Physics Review Letters 91 (2003). - Mode identification in the delta-Scuti star 1 Mon (with L. A. Balona et al)

Monthly notices of the Royal Astronomical Society, Vol 321 Issue 2, pg 239-246 (2001).

I enjoy teaching. I am interested in all the various teaching methods, from "chalk and talk" to using technology. Here are some videos of me explaining a limit problem from James Stewart's Calculus, or the memo for a tutorial test. Here is a sample exam I set for Multivariable Calculus.

I try to keep classes interesting by adding bits and bobs of enrichment. For instance, illustrating the difference betweeen rational and irrational numbers by going over Pyhtagoras' original proof of the irrationality of √2, or by learning about the difference between equal temperament and Pythagorean tuning in music. Or, learning about conic sections using Mathematica demonstrations.

Students studying math also need some inspiration. For instance, a speech by Jim Simons, or by Tim Gowers. Or that being a mathematician was rated the best job in America in 2009!

- Multivariable calculus tutorials, Merton College
- Differential equations II tutorial, Merton College

- Introduction to De Rham Cohomology (Graduate Course)

- First year Mathematics for Biology Students (W124)
- Second year Multivariable Calculus (W244).
- Introduction to De Rham Cohomology (Graduate Course)

- First year Engineering Mathematics (IW115).
- Second year Multivariable Calculus (W244).
- Fourth year Real and Complex Analysis 713
- Introduction to De Rham Cohomology (Graduate Course)

- First year Engineering Mathematics (IW115 and 145).

- First year Engineering Mathematics (IW115 and 145).

Courses given at the African Institute for Mathematical Sciences:

- 2012 - Representations of finite groups (with Arnold Keet)

- Gerrit Goosen. Gerrit's project is to implement a string-net (in the sense of Kirillov) version of the isomorphism (due to Balsam-Kirllov and Turaev-Virelizier) between the Reshetikhin-Turaev and Turaev-Viro-Barrett TQFTs.

- Ihechukwu Chinwere, Computer simulation of the modular fibration, May 2012.
- Michael Ajani, Fermionic integration and the Mathai-Quillen form, May 2010.
- Solomon Owerre, Maxwell's equations in terms of differential forms, May 2010.

- Jan Louw, Visualizing the planar three body problem by stereographic projection, Oct 2014.

Some blog posts in recent years:

- Feynman's Fabulous Formula, n-Category Café, 29 Jun 2015.
- The Modular Flow on the Space of Lattices, n-Category Café, 7 April 2014.
- Quasistrict Symmetric Monoidal 2-Categories via Wire Diagrams, n-Category Café, 10 Sep 2014.