Global wavefront propagation and non-elliptic Fredholm theory. Many significant phenomena in the natural world are described by partial differential equations that involve evolution in time. This project aims to develop new mathematical methods, involving recently discovered global wavefront set analysis and Fredholm theory, to solve such equations. These methods aim to extend the range of equations that can be solved as well as yield more information about solutions, in particular, their long-t ....Global wavefront propagation and non-elliptic Fredholm theory. Many significant phenomena in the natural world are described by partial differential equations that involve evolution in time. This project aims to develop new mathematical methods, involving recently discovered global wavefront set analysis and Fredholm theory, to solve such equations. These methods aim to extend the range of equations that can be solved as well as yield more information about solutions, in particular, their long-time asymptotics.Read moreRead less
Curvature flows and spectral estimates. Curvature flows are a class of geometrically motivated equations, modelled on the heat equation. Recently, researchers have developed new methods for studying the regularity of solutions to these equations, and applied them to a different problem, that of estimating quantities depending on the smaller eigenvalues of a Schroedinger operator. This project builds on the early success of this research and will produce a new understanding of the behaviour of ei ....Curvature flows and spectral estimates. Curvature flows are a class of geometrically motivated equations, modelled on the heat equation. Recently, researchers have developed new methods for studying the regularity of solutions to these equations, and applied them to a different problem, that of estimating quantities depending on the smaller eigenvalues of a Schroedinger operator. This project builds on the early success of this research and will produce a new understanding of the behaviour of eigenvalues, establish sharp estimates for spectral quantities, particularly on manifolds with curvature bounds, and find optimal conditions under which non-compact solutions to curvature flows are stable.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