Group orbits in garmonic analysis and ergodic theory. Researchers from many areas need a type of mathematical analysis which involves the behaviour of a system - which may be a set of data points - under repeated application of some operation or group of operations. The structures arising from this kind of process are known as group orbits. The project gives information about their nature. Two major types of orbits are considered, coming from actions of discrete groups on measure spaces, and fro ....Group orbits in garmonic analysis and ergodic theory. Researchers from many areas need a type of mathematical analysis which involves the behaviour of a system - which may be a set of data points - under repeated application of some operation or group of operations. The structures arising from this kind of process are known as group orbits. The project gives information about their nature. Two major types of orbits are considered, coming from actions of discrete groups on measure spaces, and from smooth actions of Lie groups on manifolds, where powerful geometric methods are available. The project will yield new understandings of entropy, and new approaches to Fourier analysis.Read moreRead less
Symmetries in analysis. Technical research is like an iceberg. The 10% you see in applications is supported by 90% hidden, long-term, sometimes abstruse or theoretical-sounding work. The area of mathematical analysis has, for over 200 years, proved its worth as part of the unseen 90%, giving us such important tools as Fourier analysis, statistical mechanics and quantum mechanics. Australia is known as a world leader in mathematical analysis, and it is important for the country to maintain that e ....Symmetries in analysis. Technical research is like an iceberg. The 10% you see in applications is supported by 90% hidden, long-term, sometimes abstruse or theoretical-sounding work. The area of mathematical analysis has, for over 200 years, proved its worth as part of the unseen 90%, giving us such important tools as Fourier analysis, statistical mechanics and quantum mechanics. Australia is known as a world leader in mathematical analysis, and it is important for the country to maintain that edge in a number of key disciplines, so we can continue to participate in global technological advance. The project has an international focus which will enable that to happen. It will also provide training for the next generation of mathematicians. Read moreRead less
Dynamical systems: theory and practice. Mathematical science has proven a crucial platform for science and technology: it may have a long lead-time to application but its impacts are more profound than glamorous technical developments. Australia has an economic imperative to maintain investment in fundamental mathematics. Dynamical systems underpin a wide range of applications in physics, engineering, information science, finance and economics. This project will improve our capacity to model sy ....Dynamical systems: theory and practice. Mathematical science has proven a crucial platform for science and technology: it may have a long lead-time to application but its impacts are more profound than glamorous technical developments. Australia has an economic imperative to maintain investment in fundamental mathematics. Dynamical systems underpin a wide range of applications in physics, engineering, information science, finance and economics. This project will improve our capacity to model systems and to study their evolution, giving us better predictive power. It will keep Australia in the forefront of international research, providing a basis of expertise not otherwise available to Australian researchers and industry. Read moreRead less
Non-commutative analysis and differential calculus. This project is in an area of central mathematical importance and will lead to important scientific advances that will keep Australia at the forefront internationally in this field of research. There is an emphasis on international networking and we will collaborate with leading researchers in USA and France.
Constrained and Stable Solutions of Nonlinear and Semismooth Equations. In this project, comprehensive models for designing safe power system parameters will be proposed, efficient algorthms for solving these models will be constructed. The new models and algorithms in this project will provide efficient tools to prevent catastrophic events in power systems, which is related with national security. This project will also strengthen collaboration of Australian applied
mathematians with inter ....Constrained and Stable Solutions of Nonlinear and Semismooth Equations. In this project, comprehensive models for designing safe power system parameters will be proposed, efficient algorthms for solving these models will be constructed. The new models and algorithms in this project will provide efficient tools to prevent catastrophic events in power systems, which is related with national security. This project will also strengthen collaboration of Australian applied
mathematians with international researchers and engineering scientists. This is important for the advance of science and technology in
Australia.Read moreRead less
Evolutionary algorithms for problems in functional genomics data analysis. Skin cancer has a high incidence in the Australian population. Schizophrenia is a psychiatric disorder that affects a significant proportion of the population worldwide. Both illnesses have genetic roots and can be triggered by environmental factors. We will uncover genetic relationship to disease and their responses to environmental conditions using computational methods and mathematical algorithms that can aid in the de ....Evolutionary algorithms for problems in functional genomics data analysis. Skin cancer has a high incidence in the Australian population. Schizophrenia is a psychiatric disorder that affects a significant proportion of the population worldwide. Both illnesses have genetic roots and can be triggered by environmental factors. We will uncover genetic relationship to disease and their responses to environmental conditions using computational methods and mathematical algorithms that can aid in the determination of function, especially in disease states. Understanding the complex genetic interactions that trigger these illnesses would give great benefits in preventive health care, skin cancer and schizophrenia genetic basis, and may lay the ground for building new methods for "personalized medicine".
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Functional and harmonic analysis of function spaces: synthesis, development and applications. Recent advances in mathematics are on the borderlines of its branches. This interdisciplinary project develops and binds the research areas attracting growing interest of prominent mathematicians during the last 30 years because of not only its theoretical value, but also its ties with the key equations describing a multitude of physical phenomena and the theoretical foundation of numerical methods. Th ....Functional and harmonic analysis of function spaces: synthesis, development and applications. Recent advances in mathematics are on the borderlines of its branches. This interdisciplinary project develops and binds the research areas attracting growing interest of prominent mathematicians during the last 30 years because of not only its theoretical value, but also its ties with the key equations describing a multitude of physical phenomena and the theoretical foundation of numerical methods. The Euler, Helmholtz, Lamb, Navier-Stokes and acoustic equations, studied in terms of function spaces, govern incompressible viscous fluid flows and wave propagations. Contributing to both pure mathematics and, particularly, Short-Term Tsunami Prediction, the project will enhance Australia's research reputation.Read moreRead less
A genetic analysis of the role of an atypical hexokinase in gene regulation. This project addresses a question which is relevant to all living things-how do changes in the environment of a cell bring about a change in gene expression? The aim of this project is to investigate the role of hexokinases in gene regulation by studying the Aspergillus nidulans xprF gene, which encodes an an unusual hexokinase. Hexokinases are thought to be the glucose sensors in plants, animals and fungi, and play a ....A genetic analysis of the role of an atypical hexokinase in gene regulation. This project addresses a question which is relevant to all living things-how do changes in the environment of a cell bring about a change in gene expression? The aim of this project is to investigate the role of hexokinases in gene regulation by studying the Aspergillus nidulans xprF gene, which encodes an an unusual hexokinase. Hexokinases are thought to be the glucose sensors in plants, animals and fungi, and play a role in the development of diabetes in humans. In plants, sugars affect many processes including growth, flowering, photosynthesis, nitrogen metabolism, starch synthesis, pigmentation and response to pathogens.Read moreRead less
Structure and states of operator-algebraic dynamical systems. This project is in the general area of functional analysis, and more specifically operator theory, an area in which the University of Wollongong has an active research group and a strong international reputation. The investigators will study dynamical systems arising in combinatorial and number-theoretic situations, where the analogue of the "dynamics'' is provided by an action of the real line on an operator algebra. Thus the project ....Structure and states of operator-algebraic dynamical systems. This project is in the general area of functional analysis, and more specifically operator theory, an area in which the University of Wollongong has an active research group and a strong international reputation. The investigators will study dynamical systems arising in combinatorial and number-theoretic situations, where the analogue of the "dynamics'' is provided by an action of the real line on an operator algebra. Thus the project will involve ideas and techniques from a wide range of mathematical disciplines, and will help to broaden Australia's expertise across these disciplines.Read moreRead less
Endomorphisms, transfer operators and Hilbert modules. This project is in the general area of functional analysis, an area where both Newcastle University and the University of New South Wales have strong international reputations. The aim of the project is to study irreversible dynamics in the presence of transfer operators, as recently introduced by Professor Exel. The motivation comes from a variety of examples arising in different areas of mathematics, including number theory and graph theor ....Endomorphisms, transfer operators and Hilbert modules. This project is in the general area of functional analysis, an area where both Newcastle University and the University of New South Wales have strong international reputations. The aim of the project is to study irreversible dynamics in the presence of transfer operators, as recently introduced by Professor Exel. The motivation comes from a variety of examples arising in different areas of mathematics, including number theory and graph theory. It is hoped that the results will give new understanding of the algebraic and analytic structure underlying the multi-resolution analyses used in approximation theory and Fourier analysis. This project will help ensure that Australia has a strong foundation in mathematics which will foster innovation.Read moreRead less