Harmonic analysis of Laplacians in curved spaces. Harmonic Analysis is a branch of mathematics which is interrelated to other fields of mathematics like complex analysis, number theory and partial differential equations (pdes) with many applications in engineering and technology. This project aims to solve a number of difficult fundamental problems at the frontier of harmonic analysis in understanding Laplacians in curved spaces. Such Laplacians control the propagation of heat and waves on manif ....Harmonic analysis of Laplacians in curved spaces. Harmonic Analysis is a branch of mathematics which is interrelated to other fields of mathematics like complex analysis, number theory and partial differential equations (pdes) with many applications in engineering and technology. This project aims to solve a number of difficult fundamental problems at the frontier of harmonic analysis in understanding Laplacians in curved spaces. Such Laplacians control the propagation of heat and waves on manifolds and Lie groups, arising in mathematical physics and quantum mechanics. Expected outcomes are the solutions of dispersive equations and the framework of singular integrals in curved spaces; new ideas and techniques in harmonic analysis developed; and training of Australian future mathematicians.Read moreRead less
Real groups, Hodge theory, and the Langlands program. This mathematics project aims to settle open questions in real groups. The real groups are the fundamental symmetries occurring in nature and are important both in number theory and in the physical sciences. In particular, this project aims to reach a comprehensive understanding of Langlands duality for real groups, investigate how Hodge theory can be used to describe the unitary dual, and investigate the micro-local structure of systems of d ....Real groups, Hodge theory, and the Langlands program. This mathematics project aims to settle open questions in real groups. The real groups are the fundamental symmetries occurring in nature and are important both in number theory and in the physical sciences. In particular, this project aims to reach a comprehensive understanding of Langlands duality for real groups, investigate how Hodge theory can be used to describe the unitary dual, and investigate the micro-local structure of systems of differential equations. Potential benefits include increasing the international stature of mathematics in Australia and improving the quality of the workforce.Read moreRead less
Indigenous mathematical transforms. A class of mathematical transforms, or systematic conversions between related spaces or objects, was practised by some Aboriginal and Torres Strait Islander groups. Such transforms from ground to night sky were used in long-distance route-recording and wayfinding techniques. This project aims to elucidate these transforms, and to use this knowledge to extend the mathematical framework and applications of Fourier analysis. There is significant potential for new ....Indigenous mathematical transforms. A class of mathematical transforms, or systematic conversions between related spaces or objects, was practised by some Aboriginal and Torres Strait Islander groups. Such transforms from ground to night sky were used in long-distance route-recording and wayfinding techniques. This project aims to elucidate these transforms, and to use this knowledge to extend the mathematical framework and applications of Fourier analysis. There is significant potential for new mathematics to emerge at this exciting interface of Indigenous/non-Indigenous knowledge. Expected outcomes are interdisciplinary research training for Indigenous students and new understanding of Indigenous sciences. Emerging big data technologies such as holography may benefit. Read moreRead less
TSuNAMi: Time Series Network Animal Modelling. Our proposal is motivated by and based upon the successful representation of time series as a network (or graph). We construct an abstract representation of a system from measurements of its changing behaviour over time. Properties of that structure (the network) then allow us to infer diagnostic information of the system. Specifically, we propose to apply this to livestock welfare during transport. By measuring the biological and environment condi ....TSuNAMi: Time Series Network Animal Modelling. Our proposal is motivated by and based upon the successful representation of time series as a network (or graph). We construct an abstract representation of a system from measurements of its changing behaviour over time. Properties of that structure (the network) then allow us to infer diagnostic information of the system. Specifically, we propose to apply this to livestock welfare during transport. By measuring the biological and environment condition of the animal we construct a network representation of that system. Geometric features of that network can then be used to infer health or duress of the subject. This proposal will develop the generic mathematical machinery to connect geometric features of the network with system behaviour. Read moreRead less
Metaphotonics and metasurfaces for disruptive sensing technologies. This project aims to address a big challenge in nanophotonics by developing revolutionary methods for efficient chiral sensing of molecules without the need for spectrometry, frequency scanning, or moving mechanical parts, and to enhance chiroptical signals a hundredfold with the help of metasurface structures. Resonant metasurfaces are arrays of engineered dielectric nanoparticles with extraordinary characteristics, and they wo ....Metaphotonics and metasurfaces for disruptive sensing technologies. This project aims to address a big challenge in nanophotonics by developing revolutionary methods for efficient chiral sensing of molecules without the need for spectrometry, frequency scanning, or moving mechanical parts, and to enhance chiroptical signals a hundredfold with the help of metasurface structures. Resonant metasurfaces are arrays of engineered dielectric nanoparticles with extraordinary characteristics, and they would allow to overcome current limitations of chiral sensing analytical tools. Detecting chiral molecules in low concentrations is crucially important to many fields of biology, chemistry, and pharmacy, as well as to the food and cosmetics industries, constituting a market of tens of billions of dollars.Read moreRead less
High-resolution multiscale modelling of pandemics: COVID-19 and beyond. The project aims to develop high-resolution computational models for pandemic mitigation and control, focussing on the novel coronavirus and its emerging variants, and leveraging demographic, genomic and epidemiological data. It expects to rigorously compare multi-scale effects of complex vaccination and social distancing strategies and quantify optimal responses under the COVID-19 induced uncertainty. The intended outcomes ....High-resolution multiscale modelling of pandemics: COVID-19 and beyond. The project aims to develop high-resolution computational models for pandemic mitigation and control, focussing on the novel coronavirus and its emerging variants, and leveraging demographic, genomic and epidemiological data. It expects to rigorously compare multi-scale effects of complex vaccination and social distancing strategies and quantify optimal responses under the COVID-19 induced uncertainty. The intended outcomes include computational models of how the most infectious viral variants emerge and spread in presence of interventions, how to predict the outbreaks, and which are the most vulnerable communities. This should make a significant economic and social impact, improving population health while maintaining a resilient economy.Read moreRead less
Quantifying emergence and dynamics of foodborne epidemics in Australia. The project aims to greatly improve the accuracy and scope of computational epidemiological models predicting emergence and evolution of foodborne diseases in Australia. It expects to reveal key pathways for both biological evolution of microorganisms, and their spread though food supply chains and human interactions. The intended outcomes include discovering how the most dominant strains of foodborne infection emerge and se ....Quantifying emergence and dynamics of foodborne epidemics in Australia. The project aims to greatly improve the accuracy and scope of computational epidemiological models predicting emergence and evolution of foodborne diseases in Australia. It expects to reveal key pathways for both biological evolution of microorganisms, and their spread though food supply chains and human interactions. The intended outcomes include discovering how the most dominant strains of foodborne infection emerge and self-organise in complex networks, how to predict and contain the epidemics closer to their source, and which are the most vulnerable groups and communities. This should make a significant economic and social impact, improving health of the population, while also safeguarding national and international supply chains.Read moreRead less
Learning the meso-scale organization of complex networks. This project aims to model and learn the organization of online social networks. We will combine mathematical models, inference, and domain knowledge from computational social sciences to obtain interpretable descriptions of the role groups of users play in the network. The expected outcomes are new mathematical models and computational methods that learn from data how to best decompose a complex network into building blocks and their int ....Learning the meso-scale organization of complex networks. This project aims to model and learn the organization of online social networks. We will combine mathematical models, inference, and domain knowledge from computational social sciences to obtain interpretable descriptions of the role groups of users play in the network. The expected outcomes are new mathematical models and computational methods that learn from data how to best decompose a complex network into building blocks and their interactions, linking connectivity to function. This should provide benefits to industries and policy makers interested in how information spreads in social media, including the critical questions of understanding the mechanisms contributing to political polarization and fragmentation.Read moreRead less
Variable Structure Complex Network Systems with Smart Grid Applications. This project aims to establish a breakthrough theory and technology to help deliver reliability and security of complex network systems, which are subject to structure changes, against faults and cyberattacks. Expected outcomes include a new theory that lays the foundation for understanding such systems, innovative algorithms and tools for their design, and a practical software platform used for ensuring reliability and sec ....Variable Structure Complex Network Systems with Smart Grid Applications. This project aims to establish a breakthrough theory and technology to help deliver reliability and security of complex network systems, which are subject to structure changes, against faults and cyberattacks. Expected outcomes include a new theory that lays the foundation for understanding such systems, innovative algorithms and tools for their design, and a practical software platform used for ensuring reliability and security of such systems. It will be applied directly to critical infrastructure such as the national power grid to help maintain lifeline resilience and achieve economic benefits. It will also provide an opportunity to train the next generation engineers in this cutting-edge technology for Australia.Read moreRead less
Feature Learning for High-dimensional Functional Time Series. This project aims to develop new methods and theories for common features on high-dimensional functional time series observed in empirical applications. The significance includes addressing a key gap in adaptive and efficient feature learning, improving forecasting accuracy and understanding forecasting-driven factors comprehensively for empirical data. Expected outcomes involve advances in big data theory and easy-to-implement algori ....Feature Learning for High-dimensional Functional Time Series. This project aims to develop new methods and theories for common features on high-dimensional functional time series observed in empirical applications. The significance includes addressing a key gap in adaptive and efficient feature learning, improving forecasting accuracy and understanding forecasting-driven factors comprehensively for empirical data. Expected outcomes involve advances in big data theory and easy-to-implement algorithms for applied researchers. This project benefits not only advanced manufacturing by finding optimal stopping time for wood panel compression, but also superior forecasting for mortality in demography, climate data in environmental science, asset returns in finance, and electricity consumption in economics. Read moreRead less