Unraveling ocean mixing and air-sea forcing along the Indo-Pacific exchange. This project aims to collect unprecedented observations and develop high resolution model simulations to examine changes in the Indonesian Throughflow (ITF) north of Australia. This project expects to develop new knowledge of ocean-atmosphere interactions along the path of the ITF from the Pacific to the Indian Ocean, which are the powerhouse that drives changes in winds and rainfall around Australia and the entire Indo ....Unraveling ocean mixing and air-sea forcing along the Indo-Pacific exchange. This project aims to collect unprecedented observations and develop high resolution model simulations to examine changes in the Indonesian Throughflow (ITF) north of Australia. This project expects to develop new knowledge of ocean-atmosphere interactions along the path of the ITF from the Pacific to the Indian Ocean, which are the powerhouse that drives changes in winds and rainfall around Australia and the entire Indo-Pacific region. Expected outcomes include a 1000-fold increase in the observations of mixing in the Indonesian seas and new understanding of the ocean-atmosphere processes that control water property change along the ITF. This should lead to strong improvement in the skill of climate forecast models in the Australian region.Read moreRead less
Free parafermions: a challenge for non-Hermitian physics. This project aims to calculate and understand the physical properties of free parafermions. Parafermions have attracted interest in topological schemes for quantum computation because they are computationally more powerful than Majorana fermions. The core of this project is a fundamental model of free parafermions, which has been shown to exhibit unexplained puzzling properties. The project outcomes include an in-depth understanding of th ....Free parafermions: a challenge for non-Hermitian physics. This project aims to calculate and understand the physical properties of free parafermions. Parafermions have attracted interest in topological schemes for quantum computation because they are computationally more powerful than Majorana fermions. The core of this project is a fundamental model of free parafermions, which has been shown to exhibit unexplained puzzling properties. The project outcomes include an in-depth understanding of this model by taking the non-Hermitian features into account, establishing a connection with open quantum systems. Non-Hermitian systems are also of increasing relevance in physics, especially in quantum optics. The project also aims to contribute to training researchers in the mathematical sciences.
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New approaches and applications of integrable quantum field theory. This project aims to develop new mathematical approaches to the theory of integrable systems to obtain exact solutions of various non-linear models of two-dimensional quantum field theory. The project is based on an unexpected correspondence between classical and quantum systems which provides a powerful method for describing physically interesting models of integrable quantum field theory. Expected outcomes include exact soluti ....New approaches and applications of integrable quantum field theory. This project aims to develop new mathematical approaches to the theory of integrable systems to obtain exact solutions of various non-linear models of two-dimensional quantum field theory. The project is based on an unexpected correspondence between classical and quantum systems which provides a powerful method for describing physically interesting models of integrable quantum field theory. Expected outcomes include exact solutions to non-linear sigma-models which have important applications in many areas, including condensed matter physics, string and field theories and Riemannian geometry. The project expects to provide significant benefit to the advancement of knowledge in physics and mathematics.Read moreRead less
Topological insulators and free fermions: from Hermitian to non-Hermitian. This project aims to develop and fully understand a class of mathematical models describing fundamental interacting systems of particles of central importance in the physics of topological insulators. This will include the extension of exact solutions to more complicated models and the development and application of topological data analysis for detecting topological phase transitions in these and more general materials. ....Topological insulators and free fermions: from Hermitian to non-Hermitian. This project aims to develop and fully understand a class of mathematical models describing fundamental interacting systems of particles of central importance in the physics of topological insulators. This will include the extension of exact solutions to more complicated models and the development and application of topological data analysis for detecting topological phase transitions in these and more general materials. The project will also apply diagrammatic methods to address a long-standing challenge in solving a particular model. The project aims to contribute to training researchers in an area of the mathematical sciences of benefit to the future development of new concepts for next-generation electronic devices and smart materials.Read moreRead less
Towards a superannuation system fit for the future. Towards a superannuation system fit for the future. This project aims to develop a stochastic superannuation model and propose alternative post retirement solutions, using data-led understanding of savings habits. Funding for the increasing cost of the growing older population will, if not modelled, forecast and managed adequately, swamp all other welfare and state funded costs. To manage older age costs adequately, governments need to encourag ....Towards a superannuation system fit for the future. Towards a superannuation system fit for the future. This project aims to develop a stochastic superannuation model and propose alternative post retirement solutions, using data-led understanding of savings habits. Funding for the increasing cost of the growing older population will, if not modelled, forecast and managed adequately, swamp all other welfare and state funded costs. To manage older age costs adequately, governments need to encourage people to save and provide ways people can save—but need to better understand how people save money for their old age. This research is expected to enable the “superannuation change“ necessary for the superannuation system to remain sustainable and fund retirees to live well.Read moreRead less
Reaching new frontiers of quantum fields and gravity through deformations. This project aims to reach new frontiers in quantum field and gravity theories. These underpin systems ranging from semi-conductors to particle collisions and the quantum behavior of black holes. An obstacle is that these theories are notoriously hard to solve. This project proposes to tackle this longstanding problem by using new deformations, symmetries and dualities that have attracted widespread attention. Expected ou ....Reaching new frontiers of quantum fields and gravity through deformations. This project aims to reach new frontiers in quantum field and gravity theories. These underpin systems ranging from semi-conductors to particle collisions and the quantum behavior of black holes. An obstacle is that these theories are notoriously hard to solve. This project proposes to tackle this longstanding problem by using new deformations, symmetries and dualities that have attracted widespread attention. Expected outcomes will include innovative techniques that will greatly enhance and interconnect our knowledge of field theories and quantum gravity, together with new discoveries in quantum-corrected geometries. A new network of domestic and international experts will largely benefit the fields of theoretical and mathematical physics.Read moreRead less
The Ricci curvature of homogeneous spaces. The geometry of homogeneous spaces is an area of research with applications in numerous fields, including topology, harmonic analysis, relativity and quantum theory. This project aims to resolve a fundamental problem in this area, known as the prescribed Ricci curvature problem for homogeneous metrics, and to settle the important and closely related question of Ricci iteration existence and convergence. Moreover, the project aims to exploit the interpla ....The Ricci curvature of homogeneous spaces. The geometry of homogeneous spaces is an area of research with applications in numerous fields, including topology, harmonic analysis, relativity and quantum theory. This project aims to resolve a fundamental problem in this area, known as the prescribed Ricci curvature problem for homogeneous metrics, and to settle the important and closely related question of Ricci iteration existence and convergence. Moreover, the project aims to exploit the interplay between geometry and algebra to provide new insight into the physically significant problem of classifying unitary Lie algebra representations. This project is expected to facilitate interdisciplinary interaction leading to exciting developments across a range of fields.Read moreRead less
Indigenous mathematical transforms. A class of mathematical transforms, or systematic conversions between related spaces or objects, was practised by some Aboriginal and Torres Strait Islander groups. Such transforms from ground to night sky were used in long-distance route-recording and wayfinding techniques. This project aims to elucidate these transforms, and to use this knowledge to extend the mathematical framework and applications of Fourier analysis. There is significant potential for new ....Indigenous mathematical transforms. A class of mathematical transforms, or systematic conversions between related spaces or objects, was practised by some Aboriginal and Torres Strait Islander groups. Such transforms from ground to night sky were used in long-distance route-recording and wayfinding techniques. This project aims to elucidate these transforms, and to use this knowledge to extend the mathematical framework and applications of Fourier analysis. There is significant potential for new mathematics to emerge at this exciting interface of Indigenous/non-Indigenous knowledge. Expected outcomes are interdisciplinary research training for Indigenous students and new understanding of Indigenous sciences. Emerging big data technologies such as holography may benefit. Read moreRead less
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
Singularity and regularity for Monge-Ampere type equations. The Monge-Ampere equation, as a premier nonlinear partial differential equation, arises in several areas including geometry, physics, and optimal transportation. Many important problems and applications are related to the regularity of solutions, which are obstructed by singularities. This project aims to classify the geometry of the singular sets, and to establish a comprehensive regularity theory for general Monge-Ampere type equation ....Singularity and regularity for Monge-Ampere type equations. The Monge-Ampere equation, as a premier nonlinear partial differential equation, arises in several areas including geometry, physics, and optimal transportation. Many important problems and applications are related to the regularity of solutions, which are obstructed by singularities. This project aims to classify the geometry of the singular sets, and to establish a comprehensive regularity theory for general Monge-Ampere type equations by using innovative approaches and developing cutting-edge technologies in partial differential equations. Expected outcomes include the resolution of outstanding open problems. This project will significantly enhance Australia’s leadership and expertise in a major area of mathematics and applications.Read moreRead less