ARC Complex Open Systems Research Network. Complexity is the common frontier in the physical, biological and social sciences. This Network will link specialists in all three sciences through five generic conceptual and mathematical theme activities. It will promote research into how subsystems self-organise into new emergent structures when assembled into an open, non-equilibrium system. Outcomes will include new technologies and software tools and deeper understanding of fundamental questions i ....ARC Complex Open Systems Research Network. Complexity is the common frontier in the physical, biological and social sciences. This Network will link specialists in all three sciences through five generic conceptual and mathematical theme activities. It will promote research into how subsystems self-organise into new emergent structures when assembled into an open, non-equilibrium system. Outcomes will include new technologies and software tools and deeper understanding of fundamental questions in science. An essential function of the network will be introducing researchers end users to new tools and broadening the horizons of graduate students.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
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
Special Research Initiatives - Grant ID: SR0354466
Funder
Australian Research Council
Funding Amount
$20,000.00
Summary
Mathematics in Contemporary Science. The Mathematics in Contemporary Science Research Network brings contemporary methods of non-linear analysis and differential equations, geometric reasoning and relevant algebraic and topological ideas to enrich six application areas in modern science: Complex Systems, Computer Vision, Optimal Transportation, Nanotechnology, Physics and Shortest Networks. MiCS will develop both the mathematics and the application areas in parallel. It will focus on postgradu ....Mathematics in Contemporary Science. The Mathematics in Contemporary Science Research Network brings contemporary methods of non-linear analysis and differential equations, geometric reasoning and relevant algebraic and topological ideas to enrich six application areas in modern science: Complex Systems, Computer Vision, Optimal Transportation, Nanotechnology, Physics and Shortest Networks. MiCS will develop both the mathematics and the application areas in parallel. It will focus on postgraduate training through workshops, summer schools and web based resources and build long-term international collaborations with EU networks and NSERC, NSF and EPSRC institutes as well as bringing together academic and industry leaders.Read moreRead less
Special Research Initiatives - Grant ID: SR0354693
Funder
Australian Research Council
Funding Amount
$10,000.00
Summary
Australian e-Research Grid. The e-Research Grid program will research and implement core Grid technologies on APAC and partner's deployed HPC resources, to underpin a broad range of Australian research. The computer science CIs will form collaborative links with international programs, adapting developments to local circumstances. The applications-domain CIs will leverage those into their scientific simulations and databases, using grid integrative techniques and portals. Many CIs participate in ....Australian e-Research Grid. The e-Research Grid program will research and implement core Grid technologies on APAC and partner's deployed HPC resources, to underpin a broad range of Australian research. The computer science CIs will form collaborative links with international programs, adapting developments to local circumstances. The applications-domain CIs will leverage those into their scientific simulations and databases, using grid integrative techniques and portals. Many CIs participate in other RNs linking to their motivating applications, enhancing prospects for research and integration. They participate in the APAC Grid program, leveraging 75 HPC staff nationally. A key aim is interoperability with "real-world Grids": eg e-learning & e-health programs.Read moreRead less
Space-based space surveillance with robust computer vision algorithms. Space-based space surveillance with robust computer vision algorithms. This project aims to develop computer vision algorithms to detect man-made objects in space. These algorithms function on nanosatellite platforms, enabling space-based space surveillance. This technology is expected to provide always-on monitoring of the Earth's orbit to enhance existing defence infrastructure and protect vital space assets, including comm ....Space-based space surveillance with robust computer vision algorithms. Space-based space surveillance with robust computer vision algorithms. This project aims to develop computer vision algorithms to detect man-made objects in space. These algorithms function on nanosatellite platforms, enabling space-based space surveillance. This technology is expected to provide always-on monitoring of the Earth's orbit to enhance existing defence infrastructure and protect vital space assets, including communications and navigational satellites, in Earth’s orbit from collisions and covert sabotage. Increased space use by government and civilian agencies opens up opportunities for the space industry. This project is expected to develop Australia’s space surveillance capabilities, protect space assets and capture a growing market.Read moreRead less
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.
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
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'.