Symmetry in Differential Geometry. Differential geometry is a major branch of mathematics studying shape by using calculus and differential equations. This is a fundamental research project in this area, especially concerned with the interaction between geometry, differential equations, and symmetry. The mathematical notion of symmetry was already formalised early last century and nowadays lies at the very heart of mathematics and physics. Advances in this area provide essential tools in basic s ....Symmetry in Differential Geometry. Differential geometry is a major branch of mathematics studying shape by using calculus and differential equations. This is a fundamental research project in this area, especially concerned with the interaction between geometry, differential equations, and symmetry. The mathematical notion of symmetry was already formalised early last century and nowadays lies at the very heart of mathematics and physics. Advances in this area provide essential tools in basic science and unexpected technological benefits can easily arise (for example, in medical imaging). Fundamental mathematical research is absolutely necessary if Australia is to maintain a presence on the international scientific stage.
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Classification and Invariants in Complex Differential Geometry. Differential geometry is the study of shape using calculus and differential equations. This is a fundamental research project in this area. Complex differential geometry refers to geometry based on the complex numbers, generally a rich and intriguing setting. Geometries will be distinguished by the construction of suitable invariants, both algebraic and analytic. Classification problems will be solved by these means. Of particular i ....Classification and Invariants in Complex Differential Geometry. Differential geometry is the study of shape using calculus and differential equations. This is a fundamental research project in this area. Complex differential geometry refers to geometry based on the complex numbers, generally a rich and intriguing setting. Geometries will be distinguished by the construction of suitable invariants, both algebraic and analytic. Classification problems will be solved by these means. Of particular interest are geometries with a high degree of symmetry, a critical feature that pervades both mathematics and physics. Twistor theory provides the unifying theme for this project.Read moreRead less
Homotopical structures in algebraic, analytic, and equivariant geometry. This is a project for fundamental research in pure mathematics. It is focused on an emerging subfield of complex geometry concerned with spaces and maps that exhibit exceptional flexibility properties, which often go hand-in-hand with a high degree of symmetry. The project aims to develop the foundations of this new area, solve several open problems, and pursue interconnections with and applications to algebraic geometry, c ....Homotopical structures in algebraic, analytic, and equivariant geometry. This is a project for fundamental research in pure mathematics. It is focused on an emerging subfield of complex geometry concerned with spaces and maps that exhibit exceptional flexibility properties, which often go hand-in-hand with a high degree of symmetry. The project aims to develop the foundations of this new area, solve several open problems, and pursue interconnections with and applications to algebraic geometry, complex analysis, geometric invariant theory, and topology.Read moreRead less
Symmetries in real and complex geometry. This project concerns an important area of abstract modern geometry. The results and techniques of the project will lead to significant progress in this area. It will benefit the national scientific reputation, strengthen the research profile of the home institutions, and provide training to young researchers.
Flexibility and symmetry in complex geometry. Differential equations play a fundamental role in science and technology. The aim of the project is to study important differential equations that arise in geometry, their symmetries, and obstructions to solving them.
Global dementias: Examining structural vulnerability and dementia outcomes. This project aims to examine the social and cultural dimensions of dementia by using a comparative ethnographic approach to examine the experiences of people living with dementia in Australia, Malaysia and India. The project expects to generate new anthropological knowledge about structural inequalities by examining how dementia is responded to in diverse geographic, cultural and social settings. Expected outcomes of thi ....Global dementias: Examining structural vulnerability and dementia outcomes. This project aims to examine the social and cultural dimensions of dementia by using a comparative ethnographic approach to examine the experiences of people living with dementia in Australia, Malaysia and India. The project expects to generate new anthropological knowledge about structural inequalities by examining how dementia is responded to in diverse geographic, cultural and social settings. Expected outcomes of this project include the creation of a new evidence-base on dementia and the production of briefing documents to guide global health frameworks. The project should provide significant benefits for people living with dementia by providing locally-relevant strategies to respond to dementia and resultant disability.Read moreRead less
Moving beyond crisis management: Creating a future for people with disabilities living with ageing parents. The needs of thousands of people with disabilities being cared for by ageing parents are beyond the capacity of our existing formal mechanisms for providing care. In order to mitigate this national crisis in support, this research will establish effective, resource efficient support strategies where there are currently no plans in place for future care arrangements. By enhancing the capaci ....Moving beyond crisis management: Creating a future for people with disabilities living with ageing parents. The needs of thousands of people with disabilities being cared for by ageing parents are beyond the capacity of our existing formal mechanisms for providing care. In order to mitigate this national crisis in support, this research will establish effective, resource efficient support strategies where there are currently no plans in place for future care arrangements. By enhancing the capacity of the community to provide support the benefit of existing formal supports will be extended to address the needs of more families. This project will position Australian disability research and support at the forefront of international efforts to legitimize the claim of people with disabilities and their families on community resources.Read moreRead less
Normal forms and Chern-Moser connection in the study of Cauchy-Riemann Manifolds. This research project is aimed at a systematic study of Cauchy-Riemann manifolds, their holomorphic mappings and automorphisms, by means of a unifying approach based on
Chern-Moser type normal forms. The importance of Cauchy-Riemann manifolds stems from the fact that they bridge complex structure and holomorphy with the Riemannian nature of real manifolds. Construction of an analogue of the Chern-Moser normal form ....Normal forms and Chern-Moser connection in the study of Cauchy-Riemann Manifolds. This research project is aimed at a systematic study of Cauchy-Riemann manifolds, their holomorphic mappings and automorphisms, by means of a unifying approach based on
Chern-Moser type normal forms. The importance of Cauchy-Riemann manifolds stems from the fact that they bridge complex structure and holomorphy with the Riemannian nature of real manifolds. Construction of an analogue of the Chern-Moser normal form for multicodimensional Levi-nondegenerate CR-manifolds and extension of CR-mappings between them are major goals in complex analysis. Identification of Chern-Moser chains and equivariant linearisation of isotropy automorphisms are major goals in geometry.Read moreRead less
The impact and cost of short-term health staffing in remote communities. This project aims to examine the impact of the increasing levels of short-term health staffing in remote communities upon service acceptability to patients, workload and attitudes of long-term resident primary health care staff, and the effectiveness and cost of health services. There is a dearth of information about this 'fly in/fly out' (FIFO) workforce in remote communities, which have the worst health outcomes in the co ....The impact and cost of short-term health staffing in remote communities. This project aims to examine the impact of the increasing levels of short-term health staffing in remote communities upon service acceptability to patients, workload and attitudes of long-term resident primary health care staff, and the effectiveness and cost of health services. There is a dearth of information about this 'fly in/fly out' (FIFO) workforce in remote communities, which have the worst health outcomes in the country. The project aims to inform consumers, health practitioners, health service planners and policy-makers about the impact of FIFO, as well as to contribute to the development of strategies designed to stabilise the remote health workforce.Read moreRead less
Staffing practices in Aboriginal primary health care services. This project aims to generate new knowledge about the impact of short-term staffing in remote Aboriginal Community Controlled Health Services on service acceptability to patients, workload and attitudes of long-term staff and the effectiveness and cost of services. The project intends to compare these results to recent findings about the impact of short-term staffing in government-run clinics, in order to quantify and describe the po ....Staffing practices in Aboriginal primary health care services. This project aims to generate new knowledge about the impact of short-term staffing in remote Aboriginal Community Controlled Health Services on service acceptability to patients, workload and attitudes of long-term staff and the effectiveness and cost of services. The project intends to compare these results to recent findings about the impact of short-term staffing in government-run clinics, in order to quantify and describe the potential positive effect of community control. Expected outcomes include rigorous evidence about the 'fly in/fly out' workforce and the impact of community control which can inform new policy that will stabilise the remote health workforce, save money and contribute to 'closing the gap' in health outcomes.Read moreRead less