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
Special Research Initiatives - Grant ID: SR0354466
Funder
Australian Research Council
Funding Amount
$20,000.00
Summary
Mathematics in Contemporary Science. The Mathematics in Contemporary Science Research Network brings contemporary methods of non-linear analysis and differential equations, geometric reasoning and relevant algebraic and topological ideas to enrich six application areas in modern science: Complex Systems, Computer Vision, Optimal Transportation, Nanotechnology, Physics and Shortest Networks. MiCS will develop both the mathematics and the application areas in parallel. It will focus on postgradu ....Mathematics in Contemporary Science. The Mathematics in Contemporary Science Research Network brings contemporary methods of non-linear analysis and differential equations, geometric reasoning and relevant algebraic and topological ideas to enrich six application areas in modern science: Complex Systems, Computer Vision, Optimal Transportation, Nanotechnology, Physics and Shortest Networks. MiCS will develop both the mathematics and the application areas in parallel. It will focus on postgraduate training through workshops, summer schools and web based resources and build long-term international collaborations with EU networks and NSERC, NSF and EPSRC institutes as well as bringing together academic and industry leaders.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.
Using 3D printing to improve access to graphics by vision-impaired people. This project aims to investigate the possible benefits of 3D printing for production of accessible materials for vision-impaired people. Currently tactile graphics are used to provide severely vision-impaired adults and children with access to graphical content used in education and in orientation and mobility training. This project is expected to clarify the kinds of graphics for which 3D prints are better suited than ta ....Using 3D printing to improve access to graphics by vision-impaired people. This project aims to investigate the possible benefits of 3D printing for production of accessible materials for vision-impaired people. Currently tactile graphics are used to provide severely vision-impaired adults and children with access to graphical content used in education and in orientation and mobility training. This project is expected to clarify the kinds of graphics for which 3D prints are better suited than tactile graphics, and to build capacity within the national accessible format provision sector for the production and use of 3D prints. Benefits will include increased educational opportunities and quality of life for Australians with severe vision impairment, through improved access to graphic materials used in education and orientation and mobility training.
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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
Discovery Early Career Researcher Award - Grant ID: DE160101293
Funder
Australian Research Council
Funding Amount
$350,000.00
Summary
Nanoporous Iron-Based Oxygen Evolution Electrocatalysts for Water Splitting. This project aims to develop high-performance water splitting devices based on nanoporous iron-based oxygen evolution electrocatalysts. The devices, which will produce hydrogen to relieve the energy shortage in Australia, can be powered by photovoltaic and wind-generated electricity or directly use solar energy. The development of new energy materials that can be used to make renewable and clean fuels from abundant and ....Nanoporous Iron-Based Oxygen Evolution Electrocatalysts for Water Splitting. This project aims to develop high-performance water splitting devices based on nanoporous iron-based oxygen evolution electrocatalysts. The devices, which will produce hydrogen to relieve the energy shortage in Australia, can be powered by photovoltaic and wind-generated electricity or directly use solar energy. The development of new energy materials that can be used to make renewable and clean fuels from abundant and easily accessible resources is among the most challenging and demanding tasks today. The combination of iron doping and nanoporous structure are intended to improve both the intrinsic and extrinsic catalytic activities of the electrocatalysts to be developed in the project.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE200101244
Funder
Australian Research Council
Funding Amount
$417,276.00
Summary
Advanced zinc-ion batteries with high voltage and high energy density. Zinc-ion battery is not only cheaper than current lithium-ion battery (LIB), but it is safer due to a neutral aqueous electrolyte. However, its grid-scale development is plagued by limited output voltage and inadequate energy density compared with more mainstream LIB. This project aims to solve the discharge-voltage problem by fabricating atomic-level structure engineered manganese (Mn)-based cathode and a new stable solid-st ....Advanced zinc-ion batteries with high voltage and high energy density. Zinc-ion battery is not only cheaper than current lithium-ion battery (LIB), but it is safer due to a neutral aqueous electrolyte. However, its grid-scale development is plagued by limited output voltage and inadequate energy density compared with more mainstream LIB. This project aims to solve the discharge-voltage problem by fabricating atomic-level structure engineered manganese (Mn)-based cathode and a new stable solid-state electrolyte, and improve the device energy density by zinc (Zn) anode interface nanotechnology. The success of this project will benefit Australia’s access to new markets and introduce a new low-cost and safe energy storage technology for the long-term viability of Australia’s abundant Zn and Mn resources.Read moreRead less