Harmonic analysis and spectral analysis of differential operators. Harmonic analysis has had a profound influence in many areas of mathematics, including partial differential equations. This project is at the frontier of research, closely related to theoretical work of applied technology such as signal processing, financial modelling and it ensures that Australia maintains a high research profile in this field.
Geometric transforms and duality. This Proposal is fundamental, basic research at the forefront of modern differential geometry and its application to physics. It will ensure that Australia is involved in today's mathematical and physical advances and that we have Australian mathematicians trained to take advantage of the future benefits of these advances.
Heat kernel and Riesz transform on non-compact metric measure spaces. This project will develop new techniques in heat kernel theory, with applications to such important topics as Schrodinger model for quantum mechanics. The proposed research is at the forefront of research in harmonic analysis and partial differential equations and will further enhance Australia's high international standing in these research fields.
Harmonic analysis of rough oscillations. This project intends to explore new perspectives in harmonic analysis. Harmonic analysis is a set of mathematical techniques used in many branches of science and engineering to analyse complex signals (functions). It is highly effective in modelling phenomena such as the propagation of electromagnetic waves, but it is currently limited to propagation occurring in a simple-enough medium. An intense international research effort in harmonic analysis is curr ....Harmonic analysis of rough oscillations. This project intends to explore new perspectives in harmonic analysis. Harmonic analysis is a set of mathematical techniques used in many branches of science and engineering to analyse complex signals (functions). It is highly effective in modelling phenomena such as the propagation of electromagnetic waves, but it is currently limited to propagation occurring in a simple-enough medium. An intense international research effort in harmonic analysis is currently under way to lift this limitation. This project is part of that effort, and aims to unite two of its fundamental directions of development: one focusing on the roughness of the medium; and one focusing on the interaction between highly oscillatory aspects of the function and the geometry of the medium.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