Geometric variational problems and nonlinear partial differential systems. We will investigate several important problems on non-linear partial differential systems, bridging analysis, differential geometry and mathematical physics. Harmonic maps are the prototype of maps minimizing the Dirichlet energy. The liquid crystal configuration generalizes the harmonic map with values into two dimensional spheres. The Yang-Mills equations originated from particle physics. We will make fundamental contri ....Geometric variational problems and nonlinear partial differential systems. We will investigate several important problems on non-linear partial differential systems, bridging analysis, differential geometry and mathematical physics. Harmonic maps are the prototype of maps minimizing the Dirichlet energy. The liquid crystal configuration generalizes the harmonic map with values into two dimensional spheres. The Yang-Mills equations originated from particle physics. We will make fundamental contributions to these topics: Regularity problem and energy minimality of weakly harmonic maps, Weak solutions of the liquid crystal equilibrium system, Yang-Mills heat flow and singular Yang-Mills connections.
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New mathematics to quantify fluctuations and extremes in dynamical systems. Many problems in the natural world result from the cumulative effect of extreme events in complex dynamical systems. Dynamical models of ecological and physical processes have internal variables that can combine to produce large observable changes. Quantitative estimation of the variability of these chaotic models is difficult because of the time dependence of the dynamics and their “long memory” due to significant deter ....New mathematics to quantify fluctuations and extremes in dynamical systems. Many problems in the natural world result from the cumulative effect of extreme events in complex dynamical systems. Dynamical models of ecological and physical processes have internal variables that can combine to produce large observable changes. Quantitative estimation of the variability of these chaotic models is difficult because of the time dependence of the dynamics and their “long memory” due to significant deterministic components. This project aims to develop mathematics and numerics to accurately quantify and assess these complicated variations. The project expects to provide powerful tools to predict harmful outcomes in biogeophysical systems, and assist with the development of mitigation strategies.Read moreRead less
ARC Financial Integrity Research Network. The integrity of the financial system is constantly under stress because of the development of ever more complex financial instruments, structures and strategies, and the associated research technologies that continues to accelerate worldwide. FIRN's vision is to harness the considerable strengths of Australia's internationally renowned finance, accounting and economics researchers into a research agenda to address issues concerning the integrity of the ....ARC Financial Integrity Research Network. The integrity of the financial system is constantly under stress because of the development of ever more complex financial instruments, structures and strategies, and the associated research technologies that continues to accelerate worldwide. FIRN's vision is to harness the considerable strengths of Australia's internationally renowned finance, accounting and economics researchers into a research agenda to address issues concerning the integrity of the financial system. It will enable Australian research in this area to match the scale and impact of similar research in other major international financial centres, and play an essential role in placing Australia among the world's leaders in financial markets related research.Read moreRead less
Investigation of Demand Diversity and Appropriate New Generation Entry into Electricity Market Simulation Tools. The power industry is currently facing a great challenge in providing
better market operation and management following recent devastating blackouts in North America, UK and Italy. This project aims at investigating major mechanisms of market simulation techniques including impacts from load diversity and approaches to defining appropriate new generation entry into the market. From th ....Investigation of Demand Diversity and Appropriate New Generation Entry into Electricity Market Simulation Tools. The power industry is currently facing a great challenge in providing
better market operation and management following recent devastating blackouts in North America, UK and Italy. This project aims at investigating major mechanisms of market simulation techniques including impacts from load diversity and approaches to defining appropriate new generation entry into the market. From the outcome of this project the National Electricity Market will be able to manage the uncertainties of load diversity (one of the most common blackout causes), and efficiently minimise risk associated with decisions on new generation entry to enhance electricity supply infrastructure.
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The presentation of expert evidence in Australian criminal trials: the role of lawyers and experts. This project will shed light on how courts, lawyers and experts can work effectively together to deliver expert evidence in the courtroom. Improving the provision and effective use of expert evidence will benefit the Australian community by providing a better quality criminal justice system.
Change Detection in Causal Relationships and Measurement of Systemic Risk. Empirical measures of interconnectedness between financial institutions based on tests of Granger causality are currently used in detecting systemic risk. However, researchers need to define periods of calm and stress exogenously in order to implement these tests appropriately. This project aims to develop a new procedure to identify changes in causal relationships and the timing of these changes. The new approach has the ....Change Detection in Causal Relationships and Measurement of Systemic Risk. Empirical measures of interconnectedness between financial institutions based on tests of Granger causality are currently used in detecting systemic risk. However, researchers need to define periods of calm and stress exogenously in order to implement these tests appropriately. This project aims to develop a new procedure to identify changes in causal relationships and the timing of these changes. The new approach has the potential to be a significant improvement in the real-time identification of emerging turmoil in financial markets and provide an improved method for the detection of systemic risk. The new test procedure will be implemented using data for financial and non-financial institutions across Europe, the US and Australia.Read moreRead less
Centre for Mathematical and Statistical Modelling of Complex Systems. This Centre, formed by a group of high-profile researchers, brings expertise from linked but hitherto disparate areas together. It will place Australia at the forefront of research into complex systems.
The mission of the Centre is to stimulate research in mathematical and statistical modelling of complex systems and to encourage cross-fertilisation of ideas and techniques. The specific objectives are
- to formulate and ana ....Centre for Mathematical and Statistical Modelling of Complex Systems. This Centre, formed by a group of high-profile researchers, brings expertise from linked but hitherto disparate areas together. It will place Australia at the forefront of research into complex systems.
The mission of the Centre is to stimulate research in mathematical and statistical modelling of complex systems and to encourage cross-fertilisation of ideas and techniques. The specific objectives are
- to formulate and analyse mathematical and statistical models for natural and artificial complex systems,
- to use these models to develop an understanding of the behaviour of these systems
- to incorporate this understanding into strategies for management and control.Read moreRead less
An econometric analysis of the effects of family benefit policies on fertility, saving and labour force participation in Australia. This project will help to 'strengthen Australia's economic fabric' by improving our understanding of the effect of family benefit policies on fertility, saving and labour force participation. This is important because boosting fertility and labour force participation are both seen as ways of mitigating the economic burden of population ageing, thereby helping Austra ....An econometric analysis of the effects of family benefit policies on fertility, saving and labour force participation in Australia. This project will help to 'strengthen Australia's economic fabric' by improving our understanding of the effect of family benefit policies on fertility, saving and labour force participation. This is important because boosting fertility and labour force participation are both seen as ways of mitigating the economic burden of population ageing, thereby helping Australia to 'age well, age productively' in a national sense. Also, achieving a desired level of national saving is a medium term goal of government economic policy. Hence it is important to understand the interaction of saving, fertility and labour force participation in order to develop compatible and effective economic policies.Read moreRead less
Local Government and Housing in Australia for the 21st Century. This project plans to analyse survey data, qualitative interviews and detailed case studies to investigate and theorise trends in the relationship between local government and housing supply and demand. It aims to answer a number of questions: What is the role of local government in housing Australians in the 21st century? How have changing economic, social, demographic and political processes affected the interaction between local ....Local Government and Housing in Australia for the 21st Century. This project plans to analyse survey data, qualitative interviews and detailed case studies to investigate and theorise trends in the relationship between local government and housing supply and demand. It aims to answer a number of questions: What is the role of local government in housing Australians in the 21st century? How have changing economic, social, demographic and political processes affected the interaction between local government and housing over the past decades, and what are the likely impacts in the future? How might a reshaped Australian Federation recast the role of local government in this area of social and economic policy? The research aims to consider inner urban, suburban and regional and rural areas; and to contribute to a healthier and more productive Australia by providing local governments with evidence on their role in the housing market and how they can prepare for the future.Read moreRead less