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
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
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