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).
Geometric methods in mathematical physiology. This project will develop new geometric methods for the analysis of multiple-scales models of physiological rhythms and patterns, and will design diagnostic tools to identify key parameters that cause and control these signals. Thus, this project will deliver powerful mathematics for detecting and understanding fundamental issues of physiological systems.
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
A geometric theory for modern optimisation problems in control and estimation. Linear-quadratic and spectral factorisation problems play a crucial role in system and control theory as well as many important application areas. The success of the project will represent a significant advancement of state-of-the-art in these broad areas.
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
A probabilistic and geometric understanding of transport and metastability in mathematical geophysical flows. Complicated fluid flow is at the heart of physical oceanography and atmospheric science. This project will develop new mathematical technologies to reveal hidden transport barriers around which complicated fluid flow is organised. This project will lead to more accurate circulation predictions from ocean and atmosphere models.
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