Harmonic analysis in rough contexts. Harmonic analysis is a set of mathematical techniques aimed at decomposing complex signals into simple pieces in a way that is reminiscent of the decomposition of sounds into harmonics. It is highly efficient in analysing signals in homogeneous media such as wave propagation through the air that underpins wireless communication technology. However, wave propagation through inhomogeneous media, such as the human body in medical imaging or the Earth in geophysi ....Harmonic analysis in rough contexts. Harmonic analysis is a set of mathematical techniques aimed at decomposing complex signals into simple pieces in a way that is reminiscent of the decomposition of sounds into harmonics. It is highly efficient in analysing signals in homogeneous media such as wave propagation through the air that underpins wireless communication technology. However, wave propagation through inhomogeneous media, such as the human body in medical imaging or the Earth in geophysical imaging, is much harder to model. Phenomena with random components, as considered in finance for instance, are also problematic. This project is an important part of an intense international research effort to develop harmonic analysis in such rough contexts.Read moreRead less
Socio-spatial implications of smart city development in India. The project aims to generate extensive new knowledge on the complex socio-spatial implications of smart city development; and the ways in which they have been further consolidated, expedited, and elevated in response to COVID, and to stimulate the pandemic-hit economies. It makes a significant contribution to smart urbanism discourse globally with a focus on equity and its special role at times of crisis. The outcomes include a Smart ....Socio-spatial implications of smart city development in India. The project aims to generate extensive new knowledge on the complex socio-spatial implications of smart city development; and the ways in which they have been further consolidated, expedited, and elevated in response to COVID, and to stimulate the pandemic-hit economies. It makes a significant contribution to smart urbanism discourse globally with a focus on equity and its special role at times of crisis. The outcomes include a Smart City Roadmap for advising diverse stakeholders on how to negotiate for and build inclusive smart cities - with significant benefits in strengthening existing, and building new connections between India and Australia in an area of bilateral national significance.Read moreRead less
The Spectral Theory and Harmonic Analysis of Geometric Differential Operators. The project will involve mathematical research of the highest international standard in two very active and far-reaching field of mathematics: quantum chaos, and harmonic analysis. Progress in these fields will have implications in areas such as communications technology (e.g. image compression), quantum theory, and mathematical analysis (e.g. partial differential equations).
Transforming tobacco policy to deliver societal benefits. This project aims to develop new regulatory options for tobacco to minimise the legal market while avoiding the adverse societal and economic impacts of transferring consumer demand to illegal tobacco products. It addresses a significant current concern about a growing illegal tobacco market and seeks to improve understanding of the impact of tobacco control policies on the illegal market, and the societal impacts. The project also seeks ....Transforming tobacco policy to deliver societal benefits. This project aims to develop new regulatory options for tobacco to minimise the legal market while avoiding the adverse societal and economic impacts of transferring consumer demand to illegal tobacco products. It addresses a significant current concern about a growing illegal tobacco market and seeks to improve understanding of the impact of tobacco control policies on the illegal market, and the societal impacts. The project also seeks to draw insights from illicit drug policy to understand potential consequences of greater restrictions on the legal tobacco market. The expected outcomes include an enhanced monitoring system for illicit tobacco and policy recommendations to achieve government goals of reducing smoking rates.Read moreRead less
Predictability in evolution: From behaviour to genome. This project aims to determine whether evolution is primarily unpredictable and stochastic, or predictable and constrained along certain pathways. By using a natural experiment that caused wood-feeding cockroaches to evolve into soil-burrowing cockroaches in response to climate change millions of years ago, this project will determine how the genomes of these organisms responded. This will show whether the same molecular changes are repeated ....Predictability in evolution: From behaviour to genome. This project aims to determine whether evolution is primarily unpredictable and stochastic, or predictable and constrained along certain pathways. By using a natural experiment that caused wood-feeding cockroaches to evolve into soil-burrowing cockroaches in response to climate change millions of years ago, this project will determine how the genomes of these organisms responded. This will show whether the same molecular changes are repeatedly used in the evolution of complex traits, including burrow construction. This will contribute to the understanding of how predictable evolution is at the molecular level, and provide insights into how genomes change in response to prolonged climate change.Read moreRead less
Operator algebras as models for dynamics and geometry. Operator algebra is the mathematical theory which describes quantum physics and predicts how quantum systems will behave. Through this project, the researcher's recent discoveries in operator algebra will give us new insight into the dynamics and geometry - that is, the behaviour and shape - of the quantum world.
Optimal Control of Multi-Object System. Better understanding of multi-object systems developed from this research, in particular, optimal control algorithms for multi-object systems have several significant socio-economic benefits. Application areas that benefits from our research include aerospace applications such as radar, sonar, guidance, navigation, and air traffic control and non-aerospace areas such as image processing, oceanography autonomous vehicles and robotics, remote sensing, and bi ....Optimal Control of Multi-Object System. Better understanding of multi-object systems developed from this research, in particular, optimal control algorithms for multi-object systems have several significant socio-economic benefits. Application areas that benefits from our research include aerospace applications such as radar, sonar, guidance, navigation, and air traffic control and non-aerospace areas such as image processing, oceanography autonomous vehicles and robotics, remote sensing, and biomedical research. The sensor network discipline also stand to benefit from the understanding of multi-object system and control framework. Read moreRead less
Regularisation methods of inverse problems: theory and computation. This project aims to investigate regularisation methods for inverse problems which are ill-posed in the sense that their solutions depend discontinuously on the data. When only noisy data is available, regularisation methods define stable approximate solutions by replacing the original inverse problem with a family of well-posed neighbouring problems monitored by a so-called regularisation parameter. The project expects to devel ....Regularisation methods of inverse problems: theory and computation. This project aims to investigate regularisation methods for inverse problems which are ill-posed in the sense that their solutions depend discontinuously on the data. When only noisy data is available, regularisation methods define stable approximate solutions by replacing the original inverse problem with a family of well-posed neighbouring problems monitored by a so-called regularisation parameter. The project expects to develop purely data-driven rules to choose the regularisation parameter and show how they work in theory, and in practice. It will also develop convex framework, acceleration strategies as well as preconditioning and splitting ideas to design efficient regularisation solvers.Read moreRead less
Partial differential equation: Schrodinger operator and long-time dynamics. This project aims to develop new analysis methods associated to the Schrodinger operator, and to solve several challenging problems regarding dispersive partial differential equations (PDE). Long-time dynamics of PDE solutions are a key goal in both pure and applied mathematics, and have been extensively studied by leading mathematicians and mathematical physicists. However, it is unknown how to investigate large soluti .... Partial differential equation: Schrodinger operator and long-time dynamics. This project aims to develop new analysis methods associated to the Schrodinger operator, and to solve several challenging problems regarding dispersive partial differential equations (PDE). Long-time dynamics of PDE solutions are a key goal in both pure and applied mathematics, and have been extensively studied by leading mathematicians and mathematical physicists. However, it is unknown how to investigate large solutions when the order of the PDE's nonlinearity is low. This project expects to develop new methods to attack such problems. The results of the project will be of great importance in mathematics and physics, as many fundamental physical models in areas such as optics, fluid mechanics and quantum mechanics fit the paradigm.Read moreRead less
City Living: Urban consolidation and the social sustainability of cities. This project will investigate the dynamic tensions that arise in cities between individual and communal rights and requirements through a detailed examination of the lived experiences of urban apartment residents and owners. It will provide ground-breaking data on the influence of socio-economic mix on the governance and management of apartment buildings, residents’ perceptions of home and the broader implications for the ....City Living: Urban consolidation and the social sustainability of cities. This project will investigate the dynamic tensions that arise in cities between individual and communal rights and requirements through a detailed examination of the lived experiences of urban apartment residents and owners. It will provide ground-breaking data on the influence of socio-economic mix on the governance and management of apartment buildings, residents’ perceptions of home and the broader implications for the social sustainability of cities and will further current academic debates on these issues. It will open new opportunities for inter-disciplinary and international collaboration and provide evidence to inform planning and urban development policy nationally and internationally.Read moreRead less