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.
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
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.
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
Development of Advanced Fracture Mechanics Models and Novel Technical Tools for Integrity, Durability and Safety Assessment. The proposed project will lead to the new understanding of fracture phenomena and structural integrity. It will create a range of novel computer based technical tools for life and integrity assessment of structures in the presence of cracks and other defects, so as to meet the high safety standards across a wide range of industries. The project will result in technology th ....Development of Advanced Fracture Mechanics Models and Novel Technical Tools for Integrity, Durability and Safety Assessment. The proposed project will lead to the new understanding of fracture phenomena and structural integrity. It will create a range of novel computer based technical tools for life and integrity assessment of structures in the presence of cracks and other defects, so as to meet the high safety standards across a wide range of industries. The project will result in technology that will help to make Australian products stronger and more durable so they become more competitive with low cost overseas imports. All the research outcomes will have a direct benefit to Australian interests, including both public and private industries.Read moreRead less
Unravelling the neutron lifetime puzzle with lattice quantum chromodynamics. This project will perform supercomputer simulations to confront one of the outstanding puzzles of nuclear and particle physics, the neutron lifetime. New knowledge will be generated through the development of novel theoretical and numerical techniques to increase the precision of the leading theoretical inputs required to predict the neutron lifetime. The outcomes will provide crucial theoretical guidance into understan ....Unravelling the neutron lifetime puzzle with lattice quantum chromodynamics. This project will perform supercomputer simulations to confront one of the outstanding puzzles of nuclear and particle physics, the neutron lifetime. New knowledge will be generated through the development of novel theoretical and numerical techniques to increase the precision of the leading theoretical inputs required to predict the neutron lifetime. The outcomes will provide crucial theoretical guidance into understanding the neutron; helping to guide the next-generation neutron experiments, from particle physics to applications in advanced materials science. The results will have immediate benefit by resolving the neutron lifetime puzzle, while enabling Australian scientists to take a leadership role in this area of fundamental science.Read moreRead less
ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. The ARC Centre for the Mathematical Analysis of Cellular Systems aims to deliver the mathematics required to compute life. The Centre will deliver innovation in computational and mathematical biology and establish in silico biology alongside in vivo and in vitro biology. These models will allow us to understand the complexity of life at the cellu ....ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. The ARC Centre for the Mathematical Analysis of Cellular Systems aims to deliver the mathematics required to compute life. The Centre will deliver innovation in computational and mathematical biology and establish in silico biology alongside in vivo and in vitro biology. These models will allow us to understand the complexity of life at the cellular level and enable new ways of combining diverse and heterogenous data. This will allow us to understand the mechanisms underlying cellular behaviour, and to apply rational design engineering methods in order to control the dynamics of biological systems. 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
Structure of Hadronic Excitations from Lattice Quantum Chromodynamics. Quantum chromodynamics describes the fundamental strong interactions between quarks and gluons as they compose hadrons such as the proton or neutron. Beyond these lowest-energy systems, the quantum mechanical excitation spectra display a rich and complex structure. Remarkably, little is known about the internal structure of these states. The central goal of this project is to unveil the nature of hadrons and their excited sta ....Structure of Hadronic Excitations from Lattice Quantum Chromodynamics. Quantum chromodynamics describes the fundamental strong interactions between quarks and gluons as they compose hadrons such as the proton or neutron. Beyond these lowest-energy systems, the quantum mechanical excitation spectra display a rich and complex structure. Remarkably, little is known about the internal structure of these states. The central goal of this project is to unveil the nature of hadrons and their excited states using the first principles approach of lattice gauge theory. By elucidating aspects of hadron structure in terms of the most fundamental non-perturbative quark and gluon fields, the project will create new knowledge impacting on renowned experimental programs at international facilities.Read moreRead less
Electromagnetic structure of hadronic excitations from lattice quantum chromodynamics. Just as quantum electrodynamics describes the quantum mechanical excitation spectra of atomic systems, quantum chromodynamics (QCD) describes the excitation spectra of quark and gluon systems, such as the proton. This project will resolve the internal structure of the low-lying excitations of QCD, as being investigated at international facilities.