Geometric problems from quantum theory. This Proposal is fundamental, basic research at the forefront of the application of mathematics to physical theories. The problems that will be worked on are central to much of the research activity which is presently occuring in leading centres and institutes internationally. By being a part of that research we ensure that not only is Australia involved in todays mathematical and physical advances but that we also have Australian mathematicians trained ....Geometric problems from quantum theory. This Proposal is fundamental, basic research at the forefront of the application of mathematics to physical theories. The problems that will be worked on are central to much of the research activity which is presently occuring in leading centres and institutes internationally. By being a part of that research we ensure that not only is Australia involved in todays mathematical and physical advances but that we also have Australian mathematicians trained to take advantage of the benefits those advances will bring in the future.Read moreRead less
Novel geometric invariants. Quantum theory is the language of fundamental physics, it describes the small scale structure of matter and possibly space-time. Sophisticated models in condensed matter physics and string theory have exposed geometric and topological structure as basic building blocks of the theory. Issues thrown up by quantum theory are very similar to, and have provided techniques to solve, problems in the geometry of three and four dimensional manifolds. Exciting two way exchanges ....Novel geometric invariants. Quantum theory is the language of fundamental physics, it describes the small scale structure of matter and possibly space-time. Sophisticated models in condensed matter physics and string theory have exposed geometric and topological structure as basic building blocks of the theory. Issues thrown up by quantum theory are very similar to, and have provided techniques to solve, problems in the geometry of three and four dimensional manifolds. Exciting two way exchanges of methods, problems and solutions have emerged. This project aims to settle fundamental questions in the interaction between these two fields.Read moreRead less
Stress Evaluation with Non-Linear Guided Waves. This project plans to investigate a novel approach for in situ measurement of stress in structures based on an internal resonance phenomenon for nonlinear guided waves. Monitoring the stress level of critical structural components is important to ensure structural safety. The project plans to derive the requirements for this internal resonance and its dependence on stress analytically and verify them experimentally for both simple waveguides and mo ....Stress Evaluation with Non-Linear Guided Waves. This project plans to investigate a novel approach for in situ measurement of stress in structures based on an internal resonance phenomenon for nonlinear guided waves. Monitoring the stress level of critical structural components is important to ensure structural safety. The project plans to derive the requirements for this internal resonance and its dependence on stress analytically and verify them experimentally for both simple waveguides and more realistic structures. The expected outcome is the demonstration of the feasibility of a new inexpensive method for continuous monitoring of applied or thermally-induced stresses, which is of great importance in several engineering contexts, such as modern railway track rails, pipelines or pre-stressed strands in concrete structures.Read moreRead less
Dualities in String Theory and Conformal Field Theory in the context of the Geometric Langlands Program. The Langlands program ties together seemingly unrelated areas of Mathematics. Recently, in the context of the Geometric Langlands correspondence, novel connections with Theoretical Physics have emerged, thus becoming one of the most active areas of research in both Mathematics and Theoretical Physics. Australia has a number of world-renowned experts, including the two CI's, in various aspect ....Dualities in String Theory and Conformal Field Theory in the context of the Geometric Langlands Program. The Langlands program ties together seemingly unrelated areas of Mathematics. Recently, in the context of the Geometric Langlands correspondence, novel connections with Theoretical Physics have emerged, thus becoming one of the most active areas of research in both Mathematics and Theoretical Physics. Australia has a number of world-renowned experts, including the two CI's, in various aspects of the Langlands program, and is therefore well-placed to make seminal contributions. Being involved in these new developments is of crucial importance to the health of Mathematics and Theoretical Physics in Australia. An integral part of this proposal is student involvement and postgraduate training.Read moreRead less
Trade and investment in the face of declining international cooperation. This project aims to investigate the impact and policy implications of trade and investment policies in a world trade system facing increasing uncertainty. The project intends to gain an improved understanding of investment regulations like Investor State Dispute Settlement (ISDS) agreements and their impact on trade and foreign direct investment. Expected outcomes include new theories for the breakdown of international agr ....Trade and investment in the face of declining international cooperation. This project aims to investigate the impact and policy implications of trade and investment policies in a world trade system facing increasing uncertainty. The project intends to gain an improved understanding of investment regulations like Investor State Dispute Settlement (ISDS) agreements and their impact on trade and foreign direct investment. Expected outcomes include new theories for the breakdown of international agreements and their effects on third world countries as well as empirical methods that allow for a quantification of the welfare and employment effects of investment policies like ISDS. This project should provide benefits by informing government policy makers to improve Australia’s trade and investment policies.Read moreRead less
Big-Picture Bioethics: policy-making and liberal democracy. We live an era of rapid growth in biotechnology generating new and difficult ethical questions that need to be tackled by bioethicists and politicians. This project goes beyond typical approaches in bioethics to explore the "big picture": how policies are generated in ethically-contentious domains. It is important to examine how the values of different stakeholders are reflected in such processes to ensure that they are in accordance wi ....Big-Picture Bioethics: policy-making and liberal democracy. We live an era of rapid growth in biotechnology generating new and difficult ethical questions that need to be tackled by bioethicists and politicians. This project goes beyond typical approaches in bioethics to explore the "big picture": how policies are generated in ethically-contentious domains. It is important to examine how the values of different stakeholders are reflected in such processes to ensure that they are in accordance with Australia's commitment to fostering a multicultural, pluralistic, democratic society. This project will produce practical recommendations for refining public consultation in healthcare policy-making through an examination of three relevant contentious case studies in Australia with comparison to Canada.Read moreRead less
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.
Applications of generalised geometry to duality in quantum theory. This project will undertake research into mathematics at the forefront of modern physics. The aim of the project is to develop a mathematical theory of T-duality, a phenomenon in quantum physics, using generalised geometry.
Supersymmetric quantum field theory, topology and duality. Supersymmetry is universally considered as one of the most fundamental concepts in physics, playing an increasingly central role in recent studies of quantum field theory and string theory. There is a corresponding development of supersymmetry in mathematics and this project will make advances both in 'superphysics' and 'supermathematics'.