Noncommutative geometry: new frontiers. This project is at the leading edge of fundamental mathematics and will result in important scientific advances. As a result Australian science will be seen to be at the forefront internationally. This area of mathematics is having a high impact at the moment so that research training is an important aspect. There will be PhD students trained as part of the project and honours students exposed to the latest advances. Australians would normally need to go ....Noncommutative geometry: new frontiers. This project is at the leading edge of fundamental mathematics and will result in important scientific advances. As a result Australian science will be seen to be at the forefront internationally. This area of mathematics is having a high impact at the moment so that research training is an important aspect. There will be PhD students trained as part of the project and honours students exposed to the latest advances. Australians would normally need to go to leading international centres such as Paris to partake in projects of this nature. That high profile research of this kind can be done in Australia will enhance our capacity to retain scientific talent.Read moreRead less
Noncommutative geometry and applications. Noncommutative geometry is a new field of mathematical research having its origins in quantum mechanics. The main feature of this theory is that it deals with geoemtric and topological aspects of objects for which the order in which we make measurements or perform operations or observations is relevant to the outcome. This happens with microscopic systems especially those at the atomic or subatomic length scale. The methods have been motivated by and fou ....Noncommutative geometry and applications. Noncommutative geometry is a new field of mathematical research having its origins in quantum mechanics. The main feature of this theory is that it deals with geoemtric and topological aspects of objects for which the order in which we make measurements or perform operations or observations is relevant to the outcome. This happens with microscopic systems especially those at the atomic or subatomic length scale. The methods have been motivated by and found application in condensed matter physics, string theory, random media, algebraic structures and the geometry and topology of manifoldsRead moreRead less
Noncommutative geometry in representation theory and quantum physics. One of the most important problems in natural science is to understand the structure of spacetime at the Planck scale. Mathematical investigations in recent years have predicted that at this scale, spacetime becomes noncommutative. Taking this noncommutativity into account, the project brings together geometry, algebra and quantum mechanics to develop new mathematical theories required for addressing the problem. It promises ....Noncommutative geometry in representation theory and quantum physics. One of the most important problems in natural science is to understand the structure of spacetime at the Planck scale. Mathematical investigations in recent years have predicted that at this scale, spacetime becomes noncommutative. Taking this noncommutativity into account, the project brings together geometry, algebra and quantum mechanics to develop new mathematical theories required for addressing the problem. It promises to make fundamental contributions to both mathematics and theoretical physics. Read moreRead less
New Geometric and Entropy Techniques for Differential Equations. The three main practical outcomes of this mathematical research will be better predictability of salt movement responsible for land degradation, better predictability of surface evolution of microelectronic components in nanoscale technology and an open source computer package that harnesses new and powerful geometrical techniques to solve differential equations. The project will train the next generation of researchers in the math ....New Geometric and Entropy Techniques for Differential Equations. The three main practical outcomes of this mathematical research will be better predictability of salt movement responsible for land degradation, better predictability of surface evolution of microelectronic components in nanoscale technology and an open source computer package that harnesses new and powerful geometrical techniques to solve differential equations. The project will train the next generation of researchers in the mathematical modelling of critical physical processes and it will bring international experts to Australia to work on these vital problems.Read moreRead less
Moduli spaces. This project will offer a great opportunity for Australian researchers and students to engage in internationally competitive research in mathematics. Moduli spaces are fundamental to our understanding of mathematics and modern mathematical physics. It is crucial that Australian scientists and students take active part in these developments. The training of Honours and PhD students in various aspects of moduli spaces, and in the mathematics and mathematical physics that it address ....Moduli spaces. This project will offer a great opportunity for Australian researchers and students to engage in internationally competitive research in mathematics. Moduli spaces are fundamental to our understanding of mathematics and modern mathematical physics. It is crucial that Australian scientists and students take active part in these developments. The training of Honours and PhD students in various aspects of moduli spaces, and in the mathematics and mathematical physics that it addresses, is an integral part of this application.Read moreRead less
Quantum Spectra. Fundamental quantum processes will play a key role in emerging technologies in the twenty-first century across diverse industries including quantum information technology, quantum computers and electronics, quantum optics, nanoscale quantum microscopes and superconductor technology. Australia has a strong base of expertise in the underpinning quantum disciplines. This project in strategic basic research within mathematical physics will develop a comprehensive and consistent math ....Quantum Spectra. Fundamental quantum processes will play a key role in emerging technologies in the twenty-first century across diverse industries including quantum information technology, quantum computers and electronics, quantum optics, nanoscale quantum microscopes and superconductor technology. Australia has a strong base of expertise in the underpinning quantum disciplines. This project in strategic basic research within mathematical physics will develop a comprehensive and consistent mathematical description of quantum processes. This research will lead to a deeper understanding of quantum processes, keep Australia at the leading edge of international developments and increase Australia's capacity to develop and implement these new technologies.Read moreRead less
Low-order dynamical models for non-linear fluid behaviour in quasi two-dimensional plasmas. Two complex systems in which a magnetic field imposes two-dimensional fluid motions are turbulent fusion plasmas and magnetospheric plasmas. A distinctive property of 2D flows is the inverse energy cascade, whereby energy streaming into large-scale vortices, coherent structures, or sheared flows gives a remarkable propensity for self-organizing behaviour. This can be exploited to govern or guide our respo ....Low-order dynamical models for non-linear fluid behaviour in quasi two-dimensional plasmas. Two complex systems in which a magnetic field imposes two-dimensional fluid motions are turbulent fusion plasmas and magnetospheric plasmas. A distinctive property of 2D flows is the inverse energy cascade, whereby energy streaming into large-scale vortices, coherent structures, or sheared flows gives a remarkable propensity for self-organizing behaviour. This can be exploited to govern or guide our response to such systems. We propose to investigate the dynamics of momentum and energy exchange in these plasmas, using reduced dynamical models and bifurcation and stability mathematics. Expected outcomes are improved prediction of magnetospheric substorms and confinement of fusion plasmas.
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Energy, Cosmic Censorship and Black Hole Stability. Human progress is achieved by confronting fundamental questions, at the leading edge of knowledge. This project will lead to better understanding of space-time physics, and of the properties of singular solutions of non-linear hyperbolic equations. Such equations govern a wide range of physical phenomena, including fluid flow, weather and electromagnetic fields.
New frontiers in statistical mechanics. The chiral Potts model has been introduced in 1981 as a model for commensurate-incommensurate phase transitions in a layer of atoms or molecules adsorbed to a solid surface. If the adsorbed atoms all fit to holes between the surface atoms, the added layer is frozen, commensurate with the surface. If the added atoms are unable to fit holes, the added layer is no longer commensurate with the surface and could be in a floating state. A deeper understanding of ....New frontiers in statistical mechanics. The chiral Potts model has been introduced in 1981 as a model for commensurate-incommensurate phase transitions in a layer of atoms or molecules adsorbed to a solid surface. If the adsorbed atoms all fit to holes between the surface atoms, the added layer is frozen, commensurate with the surface. If the added atoms are unable to fit holes, the added layer is no longer commensurate with the surface and could be in a floating state. A deeper understanding of this and similar phenomena in layered systems has nanotechnological implications. This may affect the design of new small electronic devices or could apply to small biological systems and the development of new medicines. The project will surely lead to new applicable mathematics.Read moreRead less
The mathematical analysis of ultracold quantum gases. Ongoing developments in the experimental realisation of ultracold quantum
gases play a leading role in the international effort towards the
eventual realisation of quantum technology. This project brings together Australian
researchers with complementary strengths to develop a sophisticated range of innovative
mathematical tools for understanding these fundamental quantum systems. The expected
outcomes will thus include potentially far r ....The mathematical analysis of ultracold quantum gases. Ongoing developments in the experimental realisation of ultracold quantum
gases play a leading role in the international effort towards the
eventual realisation of quantum technology. This project brings together Australian
researchers with complementary strengths to develop a sophisticated range of innovative
mathematical tools for understanding these fundamental quantum systems. The expected
outcomes will thus include potentially far reaching impacts on downstream quantum technology.
The project will contribute to training mathematically talented students and thus take essential
steps to establish the long term future of mathematical physics in Australia. It will also establish enduring key international research links.Read moreRead less