Harmonic analysis and dispersive partial differential equations. This project aims to develop theoretical results and practical techniques in the study of Partial Differential Equations. Harmonic analysis is used to study these equations; in which a system’s local behaviour is used to analyse global properties, using techniques such as the Fourier transform. The project will investigate central problems in the area, revealing deep connections between analysis and geometry, and apply these to stu ....Harmonic analysis and dispersive partial differential equations. This project aims to develop theoretical results and practical techniques in the study of Partial Differential Equations. Harmonic analysis is used to study these equations; in which a system’s local behaviour is used to analyse global properties, using techniques such as the Fourier transform. The project will investigate central problems in the area, revealing deep connections between analysis and geometry, and apply these to study the solutions’ long-term behaviour to non-linear equations. Expected outcomes include theoretical results and practical techniques to solve non-linear dispersive equations, which arise in quantum and fluid mechanics.Read moreRead less
Nonlinear harmonic analysis and dispersive partial differential equations. This proposal is devoted to linear and nonlinear harmonic analysis. It aims to unify the most significant attributes of harmonic analysis such as restriction estimates, dispersive properties of differential operators, spectral multipliers, uniform Sobolev estimates and sharp Weyl formula. Such unification will strongly improve tools for mathematical modelling in all areas of technology and science. Notable applications in ....Nonlinear harmonic analysis and dispersive partial differential equations. This proposal is devoted to linear and nonlinear harmonic analysis. It aims to unify the most significant attributes of harmonic analysis such as restriction estimates, dispersive properties of differential operators, spectral multipliers, uniform Sobolev estimates and sharp Weyl formula. Such unification will strongly improve tools for mathematical modelling in all areas of technology and science. Notable applications include medical imaging, fluid dynamics and subatomic modelling using quantum interpretation.
It will solve several important open problems in spectral analysis of partial differential operators and develop new cutting-edge techniques in harmonic analysis with application to nonlinear partial differential equations.Read moreRead less
Reducing the social, economic and health burden associated with obesity-related chronic diseases among socio-economically disadvantaged populations. This project will develop new methods and approaches for reducing obesity-related chronic diseases (OCDs) among socially disadvantaged populations in Australia, using prevention models. These prevention models will improve the evidence base in this field as well as inform public health policy and practice in Australia (and other industrialised count ....Reducing the social, economic and health burden associated with obesity-related chronic diseases among socio-economically disadvantaged populations. This project will develop new methods and approaches for reducing obesity-related chronic diseases (OCDs) among socially disadvantaged populations in Australia, using prevention models. These prevention models will improve the evidence base in this field as well as inform public health policy and practice in Australia (and other industrialised countries).Read moreRead less
Finite dimensional integrable systems and differential geometry. Mathematical models of many processes in science (physics, engineering) and in the real world (nature, economics) are governed by complicated systems of differential equations. An important, distinguished class of such models is described by integrable systems, the systems for which one can provide a comprehensive qualitative picture, and in many cases, a complete solution. Using recently developed, powerful methods of integrable s ....Finite dimensional integrable systems and differential geometry. Mathematical models of many processes in science (physics, engineering) and in the real world (nature, economics) are governed by complicated systems of differential equations. An important, distinguished class of such models is described by integrable systems, the systems for which one can provide a comprehensive qualitative picture, and in many cases, a complete solution. Using recently developed, powerful methods of integrable systems and differential geometry, this project will focus on a range of important, interconnected theoretical problems in both disciplines. The expected outcomes will provide new, deep, mathematically and physically significant results which will lead to applications and developments across a range of fields.Read moreRead less
Theory and applications of symmetries of relational structures. Relational structures underpin information science, and symmetries of the structures determine their behaviour. This project exploits the interplay between several distinct branches of mathematics concerned with symmetries of relational structures, and will lead to new understandings and breakthroughs of high theoretical interest.
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.
Investing in the Future of Children in Multicultural Australia - Cultural Competence in Families First (CULCOFAM). Healthy start to life - Discovering how to use valuable parenting knowledge of parents from culturally different backgrounds will help us to draw on them and achieve their childrens' potential (National Agenda for Early Childhood initiative). Preventive healthcare - Knowing how to use cultural resources will help us to promote parenting in culturally appropriate ways, and strengthen ....Investing in the Future of Children in Multicultural Australia - Cultural Competence in Families First (CULCOFAM). Healthy start to life - Discovering how to use valuable parenting knowledge of parents from culturally different backgrounds will help us to draw on them and achieve their childrens' potential (National Agenda for Early Childhood initiative). Preventive healthcare - Knowing how to use cultural resources will help us to promote parenting in culturally appropriate ways, and strengthen capacity for children to grow in best health (Focus on Prevention Initiative). Strengthening Australia's social fabric - The results will help to ensure that child services strengthen local community cohesion, and families can make culturally acceptable choices to better look after their children (National welfare reform and participation agendas). Read moreRead less
Settlement service literacy among migrants in two states: Victoria and New South Wales. This project aims to assess the level of and need for settlement service literacy (SSL) among newly-arrived migrants. The project will explore and transform understandings of the relationship between migrants’ SSL and cultural integration. This will provide significant benefits, such as producing a theory-driven model to better address migrants’ needs and thus contribute to conceptual advances in theory, res ....Settlement service literacy among migrants in two states: Victoria and New South Wales. This project aims to assess the level of and need for settlement service literacy (SSL) among newly-arrived migrants. The project will explore and transform understandings of the relationship between migrants’ SSL and cultural integration. This will provide significant benefits, such as producing a theory-driven model to better address migrants’ needs and thus contribute to conceptual advances in theory, research and practice in relation to resettlement in Australia.Read moreRead less
Settling well in regional Australia: Experiences of people from refugee backgrounds. Regional humanitarian settlement is a key priority across all levels of government in Australia. This study aims to provide the first longitudinal assessment of the impacts of regional settlement for humanitarian migrants and destination communities. Its innovative, mixed-method and multi-sited approach will generate new knowledge of the opportunities and challenges for sustainable regional settlement. Expected ....Settling well in regional Australia: Experiences of people from refugee backgrounds. Regional humanitarian settlement is a key priority across all levels of government in Australia. This study aims to provide the first longitudinal assessment of the impacts of regional settlement for humanitarian migrants and destination communities. Its innovative, mixed-method and multi-sited approach will generate new knowledge of the opportunities and challenges for sustainable regional settlement. Expected outcomes include enhanced community, organisational and government decision-making capacity. By guiding end-users’ current and future actions, the study has strong potential to support the wellbeing of humanitarian migrants and to contribute to healthy and resilient regional communities.Read moreRead less