Special Research Initiatives - Grant ID: SR0354716
Funder
Australian Research Council
Funding Amount
$10,000.00
Summary
Energetically Open Systems Research Network Study. Conceptual frameworks arising in the physical sciences, such as non-equilibrium statistical mechanics and thermodynamics, synergetics, chaos and dynamical systems theory, are seminal in the emerging science of complexity. This study will lay the groundwork for a network to link Australian and overseas research on these fundamental concepts, and their application within the context of entropy-producing systems vital to the long-term sustainabilit ....Energetically Open Systems Research Network Study. Conceptual frameworks arising in the physical sciences, such as non-equilibrium statistical mechanics and thermodynamics, synergetics, chaos and dynamical systems theory, are seminal in the emerging science of complexity. This study will lay the groundwork for a network to link Australian and overseas research on these fundamental concepts, and their application within the context of entropy-producing systems vital to the long-term sustainability of the earth - oceans, atmosphere, biosphere, CO2-free energy production, space and solar environment. The network would facilitate the development of young investigators and be linked into wider complex systems networks such as the CSIRO Centre for Complex Systems Science.Read moreRead less
Polynomial representations of the Hecke algebra. This project will offer a great opportunity for talented students to engage in internationally competitive research in mathematics. In addition, through international collaboration, this project will be able to deliver an online database with software libraries which will be a world benchmark for computation with multivariate polynomials.
Statistical Topology and its Application to Deriving New Geometric Invariants. This project will offer a great opportunity for talented students to engage in internationally competitive research. Statistical topology, which combines ideas in topology, geometry and statistical mechanics is becoming a rapidly increasing branch of mathematics, with many emerging applications in bio-informatics, computer science and theoretical physics.
Quantum Spectra. Fundamental quantum processes will play a key role in emerging technologies in the twenty-first century across diverse industries including quantum information technology, quantum computers and electronics, quantum optics, nanoscale quantum microscopes and superconductor technology. Australia has a strong base of expertise in the underpinning quantum disciplines. This project in strategic basic research within mathematical physics will develop a comprehensive and consistent math ....Quantum Spectra. Fundamental quantum processes will play a key role in emerging technologies in the twenty-first century across diverse industries including quantum information technology, quantum computers and electronics, quantum optics, nanoscale quantum microscopes and superconductor technology. Australia has a strong base of expertise in the underpinning quantum disciplines. This project in strategic basic research within mathematical physics will develop a comprehensive and consistent mathematical description of quantum processes. This research will lead to a deeper understanding of quantum processes, keep Australia at the leading edge of international developments and increase Australia's capacity to develop and implement these new technologies.Read moreRead less
Energy, Cosmic Censorship and Black Hole Stability. Human progress is achieved by confronting fundamental questions, at the leading edge of knowledge. This project will lead to better understanding of space-time physics, and of the properties of singular solutions of non-linear hyperbolic equations. Such equations govern a wide range of physical phenomena, including fluid flow, weather and electromagnetic fields.
Geometry of manifolds of non-negative scalar curvature. This proposal will benefit Australia in several ways: Its outcomes will make Australia a world leader in research on scalar curvature, and consequently help Australia secure its position among world leaders in research on differential geometry and differential equations; Overseas world-class experts will be attracted to Australia by the impact of this research to develop further collaboration; More and more talented Australian students will ....Geometry of manifolds of non-negative scalar curvature. This proposal will benefit Australia in several ways: Its outcomes will make Australia a world leader in research on scalar curvature, and consequently help Australia secure its position among world leaders in research on differential geometry and differential equations; Overseas world-class experts will be attracted to Australia by the impact of this research to develop further collaboration; More and more talented Australian students will be motivated to pursue science-based and mathematics based studies, thereby improving the mathematical skills of the Australian workforce.Read moreRead less
Moduli spaces. This project will offer a great opportunity for Australian researchers and students to engage in internationally competitive research in mathematics. Moduli spaces are fundamental to our understanding of mathematics and modern mathematical physics. It is crucial that Australian scientists and students take active part in these developments. The training of Honours and PhD students in various aspects of moduli spaces, and in the mathematics and mathematical physics that it address ....Moduli spaces. This project will offer a great opportunity for Australian researchers and students to engage in internationally competitive research in mathematics. Moduli spaces are fundamental to our understanding of mathematics and modern mathematical physics. It is crucial that Australian scientists and students take active part in these developments. The training of Honours and PhD students in various aspects of moduli spaces, and in the mathematics and mathematical physics that it addresses, is an integral part of this application.Read moreRead less
Topics on 3- and 4-dimensional manifolds. - to develop practical algorithms for recognising surfaces, knots and 3-dimensional spaces. These will be very useful for experimentation
and to understand the computational complexity of such questions.
- to understand the properties of minimal surfaces in 3-dimensional spaces of constant negative curvature, with applications to the complexity of knots and the structure of these spaces.
- to develop a theory of 4-dimensional spaces which are covered ....Topics on 3- and 4-dimensional manifolds. - to develop practical algorithms for recognising surfaces, knots and 3-dimensional spaces. These will be very useful for experimentation
and to understand the computational complexity of such questions.
- to understand the properties of minimal surfaces in 3-dimensional spaces of constant negative curvature, with applications to the complexity of knots and the structure of these spaces.
- to develop a theory of 4-dimensional spaces which are covered by
Euclidean 4-space. New techniques will be utilised, since the powerful methods of Freedman-Quinn do not apply to most such spaces. Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE180100957
Funder
Australian Research Council
Funding Amount
$339,328.00
Summary
Partial differential equations, free boundaries and applications. This project aims to investigate fundamental problems in the analysis of partial differential equations and free boundary theory, to develop advanced mathematical theories with the possibility of important applications. The expected outcome is the establishment of a regularity and classification theory for nonlocal equations and for free boundary problems in linear and nonlinear settings. The benefit of the project lies in a concr ....Partial differential equations, free boundaries and applications. This project aims to investigate fundamental problems in the analysis of partial differential equations and free boundary theory, to develop advanced mathematical theories with the possibility of important applications. The expected outcome is the establishment of a regularity and classification theory for nonlocal equations and for free boundary problems in linear and nonlinear settings. The benefit of the project lies in a concrete advancement of the mathematical research with advantages for a deeper understanding of complex phenomena in physics and biology. Some of the problems also provide results useful for industrial applications.Read moreRead less
Three-dimensional geometry and topology. This project will carry out important fundamental research into the geometry and topology of 3-dimensional manifolds, an area of intense activity over the last 30 years.
The work has direct applications to physics, for example recent work in cosmology aimed at determining the global structure of our universe. Our work on knotting and symmetries of molecular graphs will also be of considerable interest in chemistry and biology.
The project will also ....Three-dimensional geometry and topology. This project will carry out important fundamental research into the geometry and topology of 3-dimensional manifolds, an area of intense activity over the last 30 years.
The work has direct applications to physics, for example recent work in cosmology aimed at determining the global structure of our universe. Our work on knotting and symmetries of molecular graphs will also be of considerable interest in chemistry and biology.
The project will also provide high quality training of undergraduate and graduate students in geometry and topology, and will increase international cooperation by developing closer links with colleagues and institutions overseas.Read moreRead less