Novel geometric invariants. Quantum theory is the language of fundamental physics, it describes the small scale structure of matter and possibly space-time. Sophisticated models in condensed matter physics and string theory have exposed geometric and topological structure as basic building blocks of the theory. Issues thrown up by quantum theory are very similar to, and have provided techniques to solve, problems in the geometry of three and four dimensional manifolds. Exciting two way exchanges ....Novel geometric invariants. Quantum theory is the language of fundamental physics, it describes the small scale structure of matter and possibly space-time. Sophisticated models in condensed matter physics and string theory have exposed geometric and topological structure as basic building blocks of the theory. Issues thrown up by quantum theory are very similar to, and have provided techniques to solve, problems in the geometry of three and four dimensional manifolds. Exciting two way exchanges of methods, problems and solutions have emerged. This project aims to settle fundamental questions in the interaction between these two fields.Read moreRead less
New approaches to index theory. The laws of nature are often expressed by differential equations, involving their rates of change. If 'elliptic,' they have an 'index,' which is the number of solutions minus the number of constraints imposed. The Atiyah-Singer index theorem gives a striking calculation of this "index'. An extension is Fractional Index Theory, which has received international attention, having solved a fundamental open problem. A central aim is to investigate this further. I will ....New approaches to index theory. The laws of nature are often expressed by differential equations, involving their rates of change. If 'elliptic,' they have an 'index,' which is the number of solutions minus the number of constraints imposed. The Atiyah-Singer index theorem gives a striking calculation of this "index'. An extension is Fractional Index Theory, which has received international attention, having solved a fundamental open problem. A central aim is to investigate this further. I will assist beginners to navigate to the cutting edge of research through workshops, spring-schools and supervision. Benefits include the enhancement of Australia's position in the forefront of international research.Read moreRead less
Operator Integrals and Derivatives. The project is a contribution to the study of non-commutative differential and integral calculus. The novelty of the present project lies in the study of smoothness properties of functions whose domains and ranges are spaces of unbounded, non-commuting operators on some Hilbert space. Our general approach will be based on a detailed investigation of properties of double operator integrals, which permit smoothness estimates of operator-functions. It can be expe ....Operator Integrals and Derivatives. The project is a contribution to the study of non-commutative differential and integral calculus. The novelty of the present project lies in the study of smoothness properties of functions whose domains and ranges are spaces of unbounded, non-commuting operators on some Hilbert space. Our general approach will be based on a detailed investigation of properties of double operator integrals, which permit smoothness estimates of operator-functions. It can be expected that the new techniques generated will find further application in areas of mathematical physics and non-commutative geometry related to quantized calculus.
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Non-commutative analysis and differential calculus. This project is in an area of central mathematical importance and will lead to important scientific advances that will keep Australia at the forefront internationally in this field of research. There is an emphasis on international networking and we will collaborate with leading researchers in USA and France.
Preventing biological growth – a new generation anti-biofouling coatings. The project aims to improve anti-biofouling technology by developing a ‘smart and green’ coating that requires no toxic biocides and makes use of copper already present in the water. Biofouling is the unwanted attachment and growth on surfaces in water; it causes significant problems on ships and in drinking water systems, and damages infrastructure and capital investment. Biofouling also carries a significant risk of spre ....Preventing biological growth – a new generation anti-biofouling coatings. The project aims to improve anti-biofouling technology by developing a ‘smart and green’ coating that requires no toxic biocides and makes use of copper already present in the water. Biofouling is the unwanted attachment and growth on surfaces in water; it causes significant problems on ships and in drinking water systems, and damages infrastructure and capital investment. Biofouling also carries a significant risk of spreading diseases and environmental damage through the introduction of invasive marine species. Existing coatings release highly toxic substances into the water, causing untold environmental damage. This project offers a single, comprehensive solution for all of the above problems.Read moreRead less
Precision-engineered hybrid core-shell materials . This project aims to develop new platform technologies for making nanostructured hybrid core-shell materials with exceptionally high drug loading and programmed release. Building on this research team's recent breakthrough in the precision engineering of core-shell materials, this research will revolutionise current approaches for making drug-loaded polymer and inorganic particles. Significant outcomes will include a novel sequential nanoprecipi ....Precision-engineered hybrid core-shell materials . This project aims to develop new platform technologies for making nanostructured hybrid core-shell materials with exceptionally high drug loading and programmed release. Building on this research team's recent breakthrough in the precision engineering of core-shell materials, this research will revolutionise current approaches for making drug-loaded polymer and inorganic particles. Significant outcomes will include a novel sequential nanoprecipitation platform technology for making drug-core polymer-shell nanoparticles, and a new bio-inspired approach for making hybrid drug-core silica-shell nanocomposites, and new materials for applications in programmed release and delivery systems.Read moreRead less
Nanostructured Electrocatalysts for Clean Fuels Production. This project aims to develop single-component and hybrid transition-metal and metal-free electrocatalysts with controllable nanostructures to efficiently and selectively catalyse carbon dioxide reduction and hydrogen evolution reactions for clean fuels production including hydrogen and low-carbon organic molecules. By combining experimental and theoretical modelling, this project plans to reveal the origins, mechanism and pathway of the ....Nanostructured Electrocatalysts for Clean Fuels Production. This project aims to develop single-component and hybrid transition-metal and metal-free electrocatalysts with controllable nanostructures to efficiently and selectively catalyse carbon dioxide reduction and hydrogen evolution reactions for clean fuels production including hydrogen and low-carbon organic molecules. By combining experimental and theoretical modelling, this project plans to reveal the origins, mechanism and pathway of these reactions, and the effect of catalyst composition and morphology on their performance. The resulting nanostructured catalysts are of great importance for feasible clean fuel generation and carbon dioxide reduction.Read moreRead less
There and back again: operator algebras, algebras and dynamical systems. The aim of this project is to develop mathematics that enables us to transfer information back and forth between dynamical systems and algebras, including operator algebras. Dynamical systems - systems that change over time - are ubiquitous, and central to modern mathematics and its applications. In mathematics, dualities allow us to translate questions from one context to another in which they are easier to solve and then ....There and back again: operator algebras, algebras and dynamical systems. The aim of this project is to develop mathematics that enables us to transfer information back and forth between dynamical systems and algebras, including operator algebras. Dynamical systems - systems that change over time - are ubiquitous, and central to modern mathematics and its applications. In mathematics, dualities allow us to translate questions from one context to another in which they are easier to solve and then translate the answer back again. Expected outcomes include increased understanding of the relationship between operator algebras and the dynamical systems that they represent. Benefits include enhanced international collaboration, and increased Australian capacity in pure mathematics, particularly operator algebras.Read moreRead less
Batteries of the future-a new strategy for CO2 fixation and energy storage. This project aims to develop metal-carbon dioxide batteries with high specific energy densities for carbon dioxide capture as well as energy conversion and storage. Metal-carbon dioxide batteries are promising not only for conversion of waste carbon dioxide to value-added chemicals, but also for storage of electricity from renewable power and balancing of the carbon cycle. By combining experimental work and theoretical m ....Batteries of the future-a new strategy for CO2 fixation and energy storage. This project aims to develop metal-carbon dioxide batteries with high specific energy densities for carbon dioxide capture as well as energy conversion and storage. Metal-carbon dioxide batteries are promising not only for conversion of waste carbon dioxide to value-added chemicals, but also for storage of electricity from renewable power and balancing of the carbon cycle. By combining experimental work and theoretical modelling, this study will explore novel electrode materials via catalyst design and understanding of the underlying reaction mechanisms. The outcomes will revolutionize battery technology and position Australia as a global leader in the critical transition to a decarbonized economy.Read moreRead less
Solar-thermal desalination system for parallel water-electricity generation. This project aims to develop a multi-functional solar-thermal desalination device to simultaneously produce clean water and electricity. Interfacial solar evaporation-based desalination technology has the unique advantage of using solar light as the sole energy source for affordable clean water production. However, its absolute evaporation rate is still too low for practical application and all of the latent heat releas ....Solar-thermal desalination system for parallel water-electricity generation. This project aims to develop a multi-functional solar-thermal desalination device to simultaneously produce clean water and electricity. Interfacial solar evaporation-based desalination technology has the unique advantage of using solar light as the sole energy source for affordable clean water production. However, its absolute evaporation rate is still too low for practical application and all of the latent heat released from vapor condensation during desalination is wasted. Solving these two critical issues by the study of energy nexus, design and fabrication of advanced photothermal materials and desalination devices could accelerate practical adoption of this technology and benefit millions of people who desperately need clean water. Read moreRead less