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
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.
Pacific Partners? The Australia-New Zealand alliance in the Pacific Islands. This project aims to investigate how alliances operate and why they endure using an in-depth analysis of the Australia-New Zealand alliance in the Pacific Islands, the region where the alliance has focused and in which there is growing strategic and policy interest. It intends to build a micro-level analysis of the influence of the behaviors and beliefs of individuals onto existing conceptual accounts. Informed by exten ....Pacific Partners? The Australia-New Zealand alliance in the Pacific Islands. This project aims to investigate how alliances operate and why they endure using an in-depth analysis of the Australia-New Zealand alliance in the Pacific Islands, the region where the alliance has focused and in which there is growing strategic and policy interest. It intends to build a micro-level analysis of the influence of the behaviors and beliefs of individuals onto existing conceptual accounts. Informed by extensive interviews, it expects to advance understanding of how the two states negotiate differences in approaches and interests while working together to preserve their security. It anticipates pinpointing strengths and vulnerabilities in the alliance and contributing to a more informed policy debate about how it should operate.Read moreRead less
Ubiquity of K-theory and T-duality. An abstract mathematical tool, called K-theory, has recently found application in two, not obviously related, areas of physics: the classification of D-branes in String Theory, and topological phases in Condensed Matter Theory. This project aims to advance the development of K-theory using ideas from physics. In particular, the project aims to generalise previous constructions, such as T-duality, to loop spaces, and to develop the K-theory relevant to the clas ....Ubiquity of K-theory and T-duality. An abstract mathematical tool, called K-theory, has recently found application in two, not obviously related, areas of physics: the classification of D-branes in String Theory, and topological phases in Condensed Matter Theory. This project aims to advance the development of K-theory using ideas from physics. In particular, the project aims to generalise previous constructions, such as T-duality, to loop spaces, and to develop the K-theory relevant to the classification of topological phases in strongly interacting systems. This project involves postgraduate training as a crucial tool in achieving its aims and enhances Australia's position at the forefront of international research.Read moreRead less
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'.
Diversification and conservation of Australian frogs. Australia's 216 known species of frogs are exceptionally diverse, 98 per cent are found nowhere else in the world and many of them are in trouble. This project will test ideas concerning the tempo of Australian frog diversification, identify previously cryptic new species and provide information critical to the conservation of Australia's declining frogs.