Below, I describe some of the research I have done thus far. Copies of two of my bachelor theses are available here.

**Non-linear supersymmetry (particle physics)**

Whenever a symmetry is spontaneously broken, one has to contend with non-linear realisations. The reason is simply that the vacuum is no longer invariant under the former symmetry transformation. At the very least, one must include a constant term, which means that the transformation cannot be represented as a linear map \(\mathbf{v}\mapsto A\mathbf{v}.\) The simplest non-linear realisation is therefore affine.

In general, a subgroup of the original symmetry group may be unbroken and some linear degrees of freedom will remain. The linear and non-linear degrees of freedom can then be extracted, but this procedure crucially depends on the existence of a Haar measure, for which compactness of the unbroken subgroup is required. Unfortunately, this is not the case for supersymmetry breaking. An alternative is to impose a constraint so that only the non-linear degrees remain. This process, which physically corresponds to integrating out the linear modes, can be used to describe the non-linear Volkov-Akulov realisation of the super-PoincarĂ© algebra.

**Topology of reionisation (cosmology)**

During the Epoch of Reionisation, the neutral hydrogen of the Early Universe was transformed into the ionised plasma observed today. This transition, which is closely associated with the birth of the first stars, is currently at the forefront of astrophysical research. Understanding how the process of reionisation occurred is particularly important for the study of large scale structure formation. Theoretical models predict that the initial stage of the reionisation process was characterised by the formation and expansion of bubbles of ionised material surrounding the first galaxies.

One can use concepts from algebraic topology, such as persistent homology, to formally describe the topology of such bubble networks as they develop over time. As an example, Universes with different degrees of galaxy clustering (as depicted) have radically different topologies and reionisation histories. This can be quantified using persistent homology.

**The speed of choice-acclimation (economics)**

An important concept in behavioural economics is that of reference dependent preferences. This is the idea that individuals base their decisions not just on the possible outcomes, but also on comparisons with one or more reference points. In a popular framework used to model such reference-dependent preferences, a distinction is made between decisions whose outcome is realised in the short term (such as travel insurance) or in the long term (such as life insurance), when people have had the time to “acclimate to their choice”. No precise prescription for when to use either model is presently known.

To find out whether the short term or long term model applies for decisions that are only days to weeks away, I tested both models on the decision to attend a professional sports game, using a combination of attendance data and betting prices. Surprisingly, the data imply that the short term model might only be appropriate over a relatively short time interval, at least when it comes to attending an event with an uncertain pay-off. Click here for a preprint of my paper on this topic.