Joel is a third-year bachelor of computer science student majoring in data science at the University of Queensland. He has a strong interest in machine learning, and is currently working on deep reinforcement learning. He is planning to pursue postgraduate study in machine learning in the future. His hobbies include playing music, such as the cornet in a brass band.

This project aims to perform an in-depth study on Schwarzer et al.’s work on Self- Predictive Representations, and develop improved algorithms for data-efficient reinforcement learning.

Isaac is a third-year student at University of Wollongong, studying the Bachelor of Mathematics, majoring in pure maths. Isaac’s research interests primarily in the connection between geometry and logic, and the use of category theory to study this. He is also interested in automated theorem proving, program synthesis, and how categories can be applied to these problems. Isaac is the founder and organiser of the UOW undergraduate seminar and the current president of the UOW Mathematics and Statistics Society. Outside of Mathematics Isaac enjoys hiking, camping, and gymnastics.

Doctrines are a category-theoretic reformulation of the concept of a theory from mathematical logic. In this project we will focus on the use of doctrines to present fragments of first order logic. Some doctrines have a notion of equality. Work by Fabio Pasquali has shown that doctrines that present first order logic can freely be given a notion of equality. This project seeks to generalise this result from doctrines to fibrations.

Rebecca Milne is a current Queensland University of Technology student studying a Bachelor of Science and Bachelor of Mathematics majoring in Physics and Applied and Computational Mathematics respectively. Rebecca wants to use mathematics to better human health and wellbeing and aspires to do postgraduate research in upon completion of her undergraduate degree.

In her spare time, Rebecca enjoys volunteering at her university as well as being creative with her art.

Bone is a dynamic tissue that optimises its shape to the mechanical loads that it carries. However, what serves as a reference mechanical state (setpoint) in this shape optimisation remains largely unknown – a constant reference state is usually assumed. Instead of a set mechanical state, it has been proposed that a reference point that the mechanical reference state of bone is a mechanical memory of the cellular network living within bone tissue (osteocytes). Mechanical memory can be renewed when bone is replaced during bone resorption and formation.

This new theory of bone mechanobiology has not yet been generalised to a spatiotemporal setting. It is expected to resolve long-standing issues of traditional bone adaptation theories.

This project will develop a new mathematical model of bone shape adaptation to mechanics by including a dynamic mechanical memory that can be set, removed, and reset by bone remodelling processes. The project will investigate how bone shape evolves under this new model of bone mechanobiology in which the mechanical reference state is a renewable mechanical memory.

Liam Barnes is a 3rd year undergraduate student at the University of Newcastle, completing a double degree in Mathematics and Science. His Mathematics major is pure/applied mathematics and his Science major is Physics. His research interests include Solar Physics, Theoretical Physics and Functional Analysis. He is passionate about developing our understanding of the world around us for the betterment of society, and believes mathematics and physics is where he can make the greatest difference. Liam is hopeful that this research project, where he aims to compare the Coriolis and Lorentz forces on plasma flows on the Sun’s surface, will further develop his understanding and knowledge in mathematical physics and prepare him for further research in Honours and postgraduate study.

In his spare time, Liam enjoys working out at the gym, playing videogames and hanging out with mates.

The aim of this project is to compute the effect of the Coriolis effect on all of the flows generated as an active region forms at the surface of the Sun, simulated by three-dimensional magneto-hydrodynamic simulations of the near-surface convective layers including the effects of solar rotation. From the simulations we have access to the full three-dimensional components of the flows and the magnetic field as a function of height.

We will use (pre-computed) state-of-the-art three-dimensional magnetohydrodynamic (MHD) simulations of emerging active regions in the near-surface layers of the Sun to calculate the effect of the Coriolis force on different flows and compare it to the Lorentz force and magnetic tension in the MHD equations.

Elizabeth (Liz) Mabbutt is a 2nd year Bachelor of Mathematics student at the University of Wollongong. She has been interested in statistics since taking an introduction to statistics course in first year, and has also developed an interest in pure mathematics and an enjoyment of writing proofs since taking a real analysis course in second year. She is looking towards starting honours in 2025 and a PhD afterwards.

Liz participated in a 2-week research scholarship in the winter of 2023 focusing on metric spaces and a proof of Hutchinson’s Theorem, where she enjoyed collaborating with other people and learning new concepts. She is looking forward to doing more research in other areas of mathematics she is interested in.

The Navier Stokes equations are a system of DEs used to model fluid dynamics. In Western Australia, they are used to model the vibrations of underwater pipes. However, in this context, they do not have an analytical solution. Numerical solutions can be found, however, this requires a supercomputer, and 6 weeks to evaluate 9 points.Therefore, given a limited number of points, we want to be able to interpelate between them. To do this, we will consider the Gaussian process.

For this research project, I will prove the convergence of the Gaussian process, and write python code to apply it to the points numerically calculated using a supercomputer.

Furthermore, if time allows, I will study the inverse problem, where given “noisy” data, to solve for input values.

Additionally, if time allows, I will study the experimental design problem – determining the optimal points to numerically solve for such that the solution can be best approximated.

Jolyon is a Bachelor of Philosophy (Honours) student at the University of Western Australia, studying a double major in mathematics and physics. In 2021, he undertook an undergraduate research placement in theoretical physics with Dr. Darren Grasso, culminating in a derivation of the action for electromagnetic fields from Maxwell’s equations.

He completed a semester on exchange at the University of Manchester in the second half of 2022, where he was introduced to the field of mathematical logic. His focus is now on pure mathematics, with a particular interest in logic, geometry, and algebra. In his spare time, he enjoys making music: playing piano, singing in choirs, and occasionally composing. Since 2022 he has been President of The Winthrop Singers Ltd, a tertiary student choir and not-for-profit based in Perth. He looks forward to commencing Honours in Pure Mathematics at UWA in 2024.

In recent work by Bamberg and Penttila (2023), Helen Skala’s (1992) elegant firstorder axiom system for plane hyperbolic geometry has been further simplified with the replacement of two assumptions with two simpler axioms, the independence of the second of which, the “perpendicularity axiom”, remains in question. This project aims to determine whether the perpendicularity axiom is necessary for a complete and independent set of axioms for plane hyperbolic geometry. The methodology is to use an algebraic form of the axioms and search for a proof of the perpendicularity axiom by codifying the symbolic statements in an interactive proof solver. The geometric interpretation of all results will be considered, and findings will be visualised.

Joseph Kwong is a third-year mathematics student at the University of Queensland. Joseph is interested in pure mathematics. In particular, he is interested in differential geometry. Joseph plans to do an honours project in differential geometry in 2024.

A Riemannian manifold is called Einstein if its Ricci curvature is a constant multiple of the metric. An example is the n-sphere equipped with the round metric. An interesting question is whether or not we can put other Einstein metrics on n-spheres. In a recent paper, Neinhaus and Wink constructed non-round Einstein metrics on the ten sphere. A crucial step in the construction is by considering doubly warped Einstein metrics on a particular dense open subset M, then extending the metric to the entire sphere.

It is well known that under certain boundary conditions, doubly warped metrics on M can be extended smoothly. Neinhaus and Wink claim in their paper that the Einstein condition significantly simplifies these boundary conditions, but a proof is not given. The main aim of our project is to write a proof of this claim. On the way, we wish to understand the boundary conditions for which doubly warped metrics on M extend smoothly to the entire sphere, and how the Einstein condition changes these boundary conditions.

Jonathan Mavroforas is a third-year Bachelor of Science student majoring in Mathematics and aims to complete his Honours in 2024. Through his studies, he has developed a strong interest in differential equations, probability theory and stochastic processes. Incorporating these fields in his research, he will investigate how stochastic filtering and optimal control can be extended under rough paths. In the future, he also hopes to research applications of rough path theory to mathematical finance.

To investigate the extensions of stochastic optimal control and robust filtering under rough path theory. The research will consist of three parts: 1) a summary of the key results of rough path theory necessary for extending stochastic optimal control and robust filtering; 2) a short exposition on Allan & Cohen’s [1] key findings; 3) exploring Allan & Cohen’s [1] remarks on the convergence of the filter to the true expectation.

[1] A.L. Allan and S. N. Cohen. Pathwise Stochastic Control with Applications to Robust Filtering. arXiv:1902.05434v2, 2019.

Jason is passionate about using maths to explore and solve real world problems. Currently, his interests lie in complex and dynamical systems, and in particular, the modelling of complex networks. However, his interests are always evolving, so he’s always excited to learn new maths.

Jason spent his first three years at The University of Western Australia studying maths and electrical engineering; in 2024, he plans to undertake an honours year with the UWA Complex Systems Group.

Recent work has been done by Jiang et al. to identify key cycles in networks. This project will apply this work to the transition networks produced by applying time delay embedding and state space partitioning to time-series data, with the goal of identifying generating or high-information partitions. This project will research the relationship between key cycles in transition networks, and the possibly generating or high-information nature of the partitions from which the networks are produced.

Jason is a third-year student at the University of Sydney studying mathematics and statistics, who expects to continue his studies in the Master of Mathematical Sciences program. He has had a bit of an unusual journey, having rekindled his passion for maths after studying accounting and finance. On the side, he enjoys drumming, underground comics, and gaming (with world records in a traffic management game).

Supersingular Isogeny Key Encapsulation (SIKE) is a cryptographic algorithm expected to be safe from quantum computing, yet was recently broken. This project aims to extend aspects of the SIKE algorithm by considering the mapping of pencils of elliptic curves by translation in their symmetry group.