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
Discovery Early Career Researcher Award - Grant ID: DE230100054
Funder
Australian Research Council
Funding Amount
$432,000.00
Summary
Spectral estimates in the presence of a magnetic field. Estimates on eigenvalues of integral operators are at the core of numerous results in the study of quantum phenomena and in associated mathematical fields. This project aims to establish detailed spectral properties of the integral operators arising in quantum models incorporating magnetic fields. An anticipated goal is the generation of new and significant theoretical results in analysis that will open novel approaches to the use of magnet ....Spectral estimates in the presence of a magnetic field. Estimates on eigenvalues of integral operators are at the core of numerous results in the study of quantum phenomena and in associated mathematical fields. This project aims to establish detailed spectral properties of the integral operators arising in quantum models incorporating magnetic fields. An anticipated goal is the generation of new and significant theoretical results in analysis that will open novel approaches to the use of magnetic differential operators. This is expected to benefit Australian science by invigorating collaboration between mathematics and theoretical physics, by providing research training relevant to emerging quantum science based technology and strengthening research collaborations with world leading scientists.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
Early Career Industry Fellowships - Grant ID: IE230100048
Funder
Australian Research Council
Funding Amount
$466,097.00
Summary
Ammonium-selective membranes to shift water industry into circular economy. The project aims to develop ammonium-selective membranes which are urgently needed in Australian key industries for sustainable ammonia recovery. The project expects to construct the membranes to achieve desirable pore size and surface functionality for fast and selective ammonia transport. The developed membranes should make ammonia recovery from wastewater more effective and sustainable, leading to the healthy waterway ....Ammonium-selective membranes to shift water industry into circular economy. The project aims to develop ammonium-selective membranes which are urgently needed in Australian key industries for sustainable ammonia recovery. The project expects to construct the membranes to achieve desirable pore size and surface functionality for fast and selective ammonia transport. The developed membranes should make ammonia recovery from wastewater more effective and sustainable, leading to the healthy waterway and reduced energy for both ammonia production and removal. Recovered ammonia expects to produce valuable products, supporting agriculture industry and hydrogen economy. The developed membranes should enable water industry's shift into circular economy, providing significant economic and environmental benefits to Australia.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
Perovskite-silicon tandem solar cells: a pathway to 30 per cent efficiency. This project aims to develop a new type of solar cell that is much more efficient than today’s commercial silicon solar cells. Increasing cell efficiency is one of the most effective ways to reduce the cost of solar electricity, but silicon cells are approaching practical and theoretical limits. This project expects to boost the efficiency of silicon solar cells by adding a low-cost solar cell on top to create a tandem d ....Perovskite-silicon tandem solar cells: a pathway to 30 per cent efficiency. This project aims to develop a new type of solar cell that is much more efficient than today’s commercial silicon solar cells. Increasing cell efficiency is one of the most effective ways to reduce the cost of solar electricity, but silicon cells are approaching practical and theoretical limits. This project expects to boost the efficiency of silicon solar cells by adding a low-cost solar cell on top to create a tandem device. The expected outcome is a solar cell that can convert more than 30 per cent of incident sunlight into electricity, compared to 20-25 per cent for current cells. Developing cheap, high efficiency solar cells should further reduce the cost of solar electricity, and accelerate the uptake of clean energy.Read moreRead less