Developing mathematical models and statistical methods to understand the dynamics of infectious diseases: stochasticity, structure and inference. Infectious diseases remain a major contributor to mortality and illness worldwide. The potential for future severe pandemics also continues to present a substantial threat to our health and well-being. Mathematics and statistics are increasingly becoming part of the arsenal used by governments to combat the invasion and spread of infectious diseases. I ....Developing mathematical models and statistical methods to understand the dynamics of infectious diseases: stochasticity, structure and inference. Infectious diseases remain a major contributor to mortality and illness worldwide. The potential for future severe pandemics also continues to present a substantial threat to our health and well-being. Mathematics and statistics are increasingly becoming part of the arsenal used by governments to combat the invasion and spread of infectious diseases. In such work, three themes have emerged as having the potential to revolutionise the modelling of infectious diseases: stochasticity, structure (both age and spatial), and inference. This project will develop state-of-the-art techniques, at the interface of these themes, of critical importance to understanding the dynamics of infectious diseases.Read moreRead less
From individuals to mass organisation: aggregation, synchronisation and collective movement in locusts. By combining field biology, robotics and mathematics, this project will determine how animals flock or swarm and, in particular, how locust nymphs control their collective movement over their lifetime. The mathematical models derived during the project will be directly applied to controlling outbreaks of locusts in Australia, South and North Africa.
New techniques and invariants in low-dimensional topology. The aim of this project is to introduce and apply new methods and invariants in the field of low-dimensional topology by developing parametrised and equivariant enhancements of Seiberg-Witten theory and Floer homology. These new refined invariants, made possible by recent advances in gauge theory, will be more powerful than existing ones, enabling the detection of new exotic phenomena. Expected outcomes include effective means for distin ....New techniques and invariants in low-dimensional topology. The aim of this project is to introduce and apply new methods and invariants in the field of low-dimensional topology by developing parametrised and equivariant enhancements of Seiberg-Witten theory and Floer homology. These new refined invariants, made possible by recent advances in gauge theory, will be more powerful than existing ones, enabling the detection of new exotic phenomena. Expected outcomes include effective means for distinguishing families of spaces, measuring their complexity and new obstructions for their existence. The new invariants and techniques will lead to the resolution of some open problems in low-dimensional topology and enhance Australia's reputation as a world leader in this field.Read moreRead less
Integrating rifts and swell in the mathematics of ice shelf disintegration. Antarctic ice-shelf disintegrations have the alarming potential to cause rapid sea level rise, through accelerated discharge of the Antarctic Ice Sheet and initiating runaway Ice Sheet destabilisations. The project aims to develop a mathematical model of swell-induced ice-shelf vibrations in a coupled ocean–shelf 3D framework, focusing on interactions between vibrations and the rift networks that characterise outer shelf ....Integrating rifts and swell in the mathematics of ice shelf disintegration. Antarctic ice-shelf disintegrations have the alarming potential to cause rapid sea level rise, through accelerated discharge of the Antarctic Ice Sheet and initiating runaway Ice Sheet destabilisations. The project aims to develop a mathematical model of swell-induced ice-shelf vibrations in a coupled ocean–shelf 3D framework, focusing on interactions between vibrations and the rift networks that characterise outer shelf margins before disintegration. Accurate, efficient solutions will be developed by fusing powerful approximation theories, and validated by numerical solutions. The model will be combined with state-of-the-art data to predict trends in Antarctica’s remaining ice shelves and indicate potential future disintegrations.Read moreRead less
Flow structures and transport: predictability and control. Moving flow structures (the boundary of an eddy, the flow interface between two fluids) are crucial in fluid mixing and in the transport of heat, pollutants and nutrients. This project will analyse their roles in improving predictions of spreading extents and rates for geophysical-scale problems, and in controlling transport at the micro-scale. Inaccuracies in currently available numerical diagnostics for transport prediction will be com ....Flow structures and transport: predictability and control. Moving flow structures (the boundary of an eddy, the flow interface between two fluids) are crucial in fluid mixing and in the transport of heat, pollutants and nutrients. This project will analyse their roles in improving predictions of spreading extents and rates for geophysical-scale problems, and in controlling transport at the micro-scale. Inaccuracies in currently available numerical diagnostics for transport prediction will be comprehensively evaluated via comparison with recent exact models. Analytical methods for quantifying transport under unsteady flow protocols will be developed, and used to answer questions on controlling transport in microfluidic applications in conjunction with experimentalists.Read moreRead less
Holonomy groups and special structures in pseudo-Riemannian geometry. The project studies mathematical models used in physical theories, such as general relativity and string theory, to create a global picture of the universe. The outcomes will enhance the role that Australia plays in these developments and contribute to the mathematical knowledge which lies at the foundations of modern technologies.
Mathematics the key to modern glass and polymer fibre technology. This project aims to develop fully coupled flow and energy models to determine the preform structure and fibre-drawing parameters needed to fabricate a desired microstructured optical fibre by stretching of the preform to a fibre. It will focus on polymer to develop a non-Newtonian flow model, which can handle the subset of Newtonian glass fibre drawing. It will develop fast, powerful three-dimensional predictive tools to solve th ....Mathematics the key to modern glass and polymer fibre technology. This project aims to develop fully coupled flow and energy models to determine the preform structure and fibre-drawing parameters needed to fabricate a desired microstructured optical fibre by stretching of the preform to a fibre. It will focus on polymer to develop a non-Newtonian flow model, which can handle the subset of Newtonian glass fibre drawing. It will develop fast, powerful three-dimensional predictive tools to solve the models and experimentally validate solutions. This work will direct future design of microstructured optical fibres to empower next-generation optical-fibre technologies. Expected outcomes are fibre designs for telecommunications, medicine, biotechnology, sensing and imaging.Read moreRead less
The Standard Model and beyond on supercomputers. Using the latest advances in supercomputing, the researcher will confront some of the most challenging problems facing nuclear and particle physicists.