New methods in spectral geometry. This project aims to use methods from mathematical scattering theory to resolve problems in the spectral analysis and index theory of differential operators. Both areas underpin the theoretical understanding of physical materials at micro length scales where quantum phenomena dominate. The project will develop new mathematical results in spectral analysis and geometry, and apply its results to theoretical models of quantum phenomena whose spectral properties are ....New methods in spectral geometry. This project aims to use methods from mathematical scattering theory to resolve problems in the spectral analysis and index theory of differential operators. Both areas underpin the theoretical understanding of physical materials at micro length scales where quantum phenomena dominate. The project will develop new mathematical results in spectral analysis and geometry, and apply its results to theoretical models of quantum phenomena whose spectral properties are at the limit of the range of mathematical techniques. Solving these problems is expected to influence non-commutative analysis.Read moreRead less
Physical realisation of enriched quantum symmetries. This project aims to investigate fundamental mathematical structures in modern category theory, providing an algebraic description of physical systems including topological order and conformal field theory. The project will study quantum symmetry, and classify and construct new classes of conformal field theories, using novel tools from enriched category theory, modular forms, and lattice gauge theory.
The main goal is to understand the lands ....Physical realisation of enriched quantum symmetries. This project aims to investigate fundamental mathematical structures in modern category theory, providing an algebraic description of physical systems including topological order and conformal field theory. The project will study quantum symmetry, and classify and construct new classes of conformal field theories, using novel tools from enriched category theory, modular forms, and lattice gauge theory.
The main goal is to understand the landscape of topological and conformal field theories, laying the foundation for new technologies based on topological order. This timely project capitalises on the recent arrival of subfactor experts in Australia, and builds capacity in mathematical research and international links in a cutting edge field.Read moreRead less
Topological stability from spectral analysis. The aim is to use mathematical scattering theory to find and study new topological features of the spectra of linear transformations on Hilbert space. The significance derives from mathematical models of low temperature conducting quantum materials. These have revealed `topological phases of matter' that are stable with respect to a range of variations in the parameters that determine the system. The stability is desired for applications to quantum ....Topological stability from spectral analysis. The aim is to use mathematical scattering theory to find and study new topological features of the spectra of linear transformations on Hilbert space. The significance derives from mathematical models of low temperature conducting quantum materials. These have revealed `topological phases of matter' that are stable with respect to a range of variations in the parameters that determine the system. The stability is desired for applications to quantum devices. Our results will give topological stability from the scattering spectrum, a feature not previously seen. The benefits stem from new results in mathematical scattering theory with a primary novelty being the analysis of ``zero energy resonances'' in mathematical models of graphene.Read moreRead less
Exploiting shear to form new structures of carbon. This project aims to create new, technologically-interesting, materials by combining shear (sliding forces) with high pressure. The work will use both modelling and experiments to understand the pathways to form new materials such as a different form of diamond that is predicted to be harder than regular diamond. Such a material could be used in coatings for cutting tools or ultra-low-scratch surfaces. Expected outcomes include both an understan ....Exploiting shear to form new structures of carbon. This project aims to create new, technologically-interesting, materials by combining shear (sliding forces) with high pressure. The work will use both modelling and experiments to understand the pathways to form new materials such as a different form of diamond that is predicted to be harder than regular diamond. Such a material could be used in coatings for cutting tools or ultra-low-scratch surfaces. Expected outcomes include both an understanding of the importance of shear in the study of high-pressure science, and as a tool to manufacture new functional materials.Read moreRead less
Efficient phylogenetic methods that manage the curse of genomic complexity. This project aims to develop new methods and software to infer the evolutionary history of organisms using genomic data. These new phylogenomic methods need to take account of the complexity of evolutionary processes and/or patterns in time (along the evolutionary tree) and space (along the genome). This project is significant because these methods must merge mathematics and statistics with High-Performance Computing to ....Efficient phylogenetic methods that manage the curse of genomic complexity. This project aims to develop new methods and software to infer the evolutionary history of organisms using genomic data. These new phylogenomic methods need to take account of the complexity of evolutionary processes and/or patterns in time (along the evolutionary tree) and space (along the genome). This project is significant because these methods must merge mathematics and statistics with High-Performance Computing to handle the huge quantities of genetic data and the complexity of evolution itself. An important expected outcome of this project will be the development and release of freely-available software that incorporates these new methods. This project expects to benefit scientists who need to infer phylogenies from genomic data. Read moreRead less
Inequality, Prosperity and the Australian Welfare State. This project aims to clarify contested understandings of Australian inequality and the role of economic and social policies in addressing policy challenges going forward. The objective of the project is to generate significantly improved knowledge of inequality in Australia using innovative approaches of data splicing, decomposition, simulation and backcasting to fill research gaps and resolve contested interpretations. We aim to provide a ....Inequality, Prosperity and the Australian Welfare State. This project aims to clarify contested understandings of Australian inequality and the role of economic and social policies in addressing policy challenges going forward. The objective of the project is to generate significantly improved knowledge of inequality in Australia using innovative approaches of data splicing, decomposition, simulation and backcasting to fill research gaps and resolve contested interpretations. We aim to provide a benchmark and robust framework against which policy development after the current crisis can be evaluated. This project aims to provide significant benefits, keeping Australia at the forefront of research on inequality and public policy, strengthening links between researchers and policy makers.
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Smart materials for atmospheric water management and water harvesting. Fresh water is a scarce resource in many parts of the globe but uncomfortably over-supplied in other regions. Dehumidifying machines, such as air conditioners, are extensively used in humid climates to enhance human comfort, but with great energy costs. Likewise, the production of potable water in remote dry regions is energy intensive. We propose novel hyper-absorbent desiccating polymers combined into sorption-powered engin ....Smart materials for atmospheric water management and water harvesting. Fresh water is a scarce resource in many parts of the globe but uncomfortably over-supplied in other regions. Dehumidifying machines, such as air conditioners, are extensively used in humid climates to enhance human comfort, but with great energy costs. Likewise, the production of potable water in remote dry regions is energy intensive. We propose novel hyper-absorbent desiccating polymers combined into sorption-powered engines inspired by nastic movements in plants to develop extremely efficient dehumidifiers and water harvesting machines. These polymer actuators can help address the auto-acceleration of climate change caused by the increasing use of air conditioners and provide cheap, clean water for remote communities.Read moreRead less
Dynamic evolution of mutation rates: causes and impacts on genomic analysis. This project aims to illuminate the role of variation in mutation rate in driving evolutionary change. Mutation rate is a core parameter in evolutionary analyses in essential applications including epidemiology, conservation and medicine, yet remains a “black box” given arbitrary universal values. This project will take a whole-of-biodiversity approach to understanding the forces shaping mutation rate, impact on evoluti ....Dynamic evolution of mutation rates: causes and impacts on genomic analysis. This project aims to illuminate the role of variation in mutation rate in driving evolutionary change. Mutation rate is a core parameter in evolutionary analyses in essential applications including epidemiology, conservation and medicine, yet remains a “black box” given arbitrary universal values. This project will take a whole-of-biodiversity approach to understanding the forces shaping mutation rate, impact on evolution of biodiversity and effect on accuracy and precision of phylogenetic analyses. Using Australian case studies, the expected outcome of this project will be a greater understanding variation in mutation rate between species, providing significant benefits in developing more sophisticated and reliable phylogenetic analyses.Read moreRead less
Australia's Resilience to Recession. This project aims to study why Australia differs from its OECD peers in that it has not had a recession for 27 years. It intends to generate knowledge by using economic models to solve 3 puzzles relating to Australia’s success: (i) why did foreign financial market shocks not spill over to the economy?; (ii) how has the resource curse that affects economies with a booming resource sector been avoided?; and (iii) what makes Australia special? Expected outcomes ....Australia's Resilience to Recession. This project aims to study why Australia differs from its OECD peers in that it has not had a recession for 27 years. It intends to generate knowledge by using economic models to solve 3 puzzles relating to Australia’s success: (i) why did foreign financial market shocks not spill over to the economy?; (ii) how has the resource curse that affects economies with a booming resource sector been avoided?; and (iii) what makes Australia special? Expected outcomes include the development of theoretical and empirical models that reflect the unique features of the Australian economy. This should provide significant benefits, including guidance to Australian and international policymakers on macroeconomic policies for resource-rich countries.Read moreRead less
Global wavefront propagation and non-elliptic Fredholm theory. Many significant phenomena in the natural world are described by partial differential equations that involve evolution in time. This project aims to develop new mathematical methods, involving recently discovered global wavefront set analysis and Fredholm theory, to solve such equations. These methods aim to extend the range of equations that can be solved as well as yield more information about solutions, in particular, their long-t ....Global wavefront propagation and non-elliptic Fredholm theory. Many significant phenomena in the natural world are described by partial differential equations that involve evolution in time. This project aims to develop new mathematical methods, involving recently discovered global wavefront set analysis and Fredholm theory, to solve such equations. These methods aim to extend the range of equations that can be solved as well as yield more information about solutions, in particular, their long-time asymptotics.Read moreRead less