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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What predictions can I trust? Stability of chaotic random dynamical systems. This project aims to make significant progress on the intricate question of global stability of non-autonomous chaotic dynamical systems. Using ergodic theory, this project expects to determine when and how errors in dynamical models that are small and frequent, or large and infrequent, can cause dramatic changes in meaningful mathematical model outputs. Expected outcomes include the discovery of mathematical mechanisms ....What predictions can I trust? Stability of chaotic random dynamical systems. This project aims to make significant progress on the intricate question of global stability of non-autonomous chaotic dynamical systems. Using ergodic theory, this project expects to determine when and how errors in dynamical models that are small and frequent, or large and infrequent, can cause dramatic changes in meaningful mathematical model outputs. Expected outcomes include the discovery of mathematical mechanisms underlying large-scale (in)stability for time-dependent dynamical systems, and reliable numerical methods for detecting instabilities. This research is expected to lead to improved characterisations of shocks or collapse in externally driven dynamical systems and assist scientists to gauge which predictions they can trust.Read moreRead less
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.
Regional resilience to economic shocks: Australia’s COVID Economic slowdown. This project is designed to analyse how employment outcomes in Australian regions respond to economic shocks such as that caused by COVID-19. Set within the emerging literature dealing with employment resilience, the project uses unique data (Payroll Jobs index) to measure employment resilience and understand the factors that impact diverse regional outcomes. Understanding these patterns is significant as a region's ec ....Regional resilience to economic shocks: Australia’s COVID Economic slowdown. This project is designed to analyse how employment outcomes in Australian regions respond to economic shocks such as that caused by COVID-19. Set within the emerging literature dealing with employment resilience, the project uses unique data (Payroll Jobs index) to measure employment resilience and understand the factors that impact diverse regional outcomes. Understanding these patterns is significant as a region's economic performance has the potential to impact the well being of individuals and their families, as well as the sustainability of local economies and communities. The project will result in a nuanced understanding of regional employment performance that will inform policy in both government and non-government sectors. Read moreRead less
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