Ethics and risk. This project aims to develop a theory of risk. From the extreme to the everyday, from warfare to the drive to work, the modern world is unimaginable without mutual imposition of risk. Philosophers must explain how risks can be justified, or risk irrelevance. This project will use the tools of ethics (the study of right and wrong action) and decision theory (the study of rational decision-making under uncertainty) to develop a comprehensive theory of the ethics of risk. This proj ....Ethics and risk. This project aims to develop a theory of risk. From the extreme to the everyday, from warfare to the drive to work, the modern world is unimaginable without mutual imposition of risk. Philosophers must explain how risks can be justified, or risk irrelevance. This project will use the tools of ethics (the study of right and wrong action) and decision theory (the study of rational decision-making under uncertainty) to develop a comprehensive theory of the ethics of risk. This project is expected to improve understanding of the risks people impose on others as individuals and as a society.Read moreRead less
A Unified Theory of 'If's. This project aims to develop a unified theory of ‘if’s. Our understanding of an uncertain and risky world requires hypothetical reasoning involving ‘if’s. They are significant theoretically: in science, history, politics, economics, psychology, computer science, linguistics, and philosophy. They are significant practically: in our planning, decision-making, policy priorities, legal judgments, environmental and medical interventions. Yet we lack a comprehensive, readily ....A Unified Theory of 'If's. This project aims to develop a unified theory of ‘if’s. Our understanding of an uncertain and risky world requires hypothetical reasoning involving ‘if’s. They are significant theoretically: in science, history, politics, economics, psychology, computer science, linguistics, and philosophy. They are significant practically: in our planning, decision-making, policy priorities, legal judgments, environmental and medical interventions. Yet we lack a comprehensive, readily implementable theory of ‘if’s. The project expects to provide such a theory, based on probability, improving on approaches from philosophy and linguistics, and benefitting both these fields. It also promises significant benefits for artificial intelligence/machine learning.
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Formal approaches to legal reasoning. This project aims to use formal epistemology to improve understanding of existing legal practices and to propose recommendations for improving the consistency and accuracy of legal proceedings. Since judges and juries rarely know all the relevant facts, they must make the best decision possible in the face of uncertainty. Formal epistemology employs probabilistic reasoning to advance understanding of how to form beliefs and make decisions in response to unce ....Formal approaches to legal reasoning. This project aims to use formal epistemology to improve understanding of existing legal practices and to propose recommendations for improving the consistency and accuracy of legal proceedings. Since judges and juries rarely know all the relevant facts, they must make the best decision possible in the face of uncertainty. Formal epistemology employs probabilistic reasoning to advance understanding of how to form beliefs and make decisions in response to uncertain evidence. The project has potential to influence the relevant policy and will result in improved legal reasoning and risk reduction in legal decision making.Read moreRead less
Improving novice drivers' speed and hazard management. The aim of the study is to extend the evidence-based approach we have developed for speed management (cognitive integration speed management training) to hazard management, thereby developing cognitive integration hazard management training for young drivers. Hence, this study is specifically designed to curb the alarming trend in young driver fatalities on Australian roads. The results of the research will provide clear direction to road au ....Improving novice drivers' speed and hazard management. The aim of the study is to extend the evidence-based approach we have developed for speed management (cognitive integration speed management training) to hazard management, thereby developing cognitive integration hazard management training for young drivers. Hence, this study is specifically designed to curb the alarming trend in young driver fatalities on Australian roads. The results of the research will provide clear direction to road authorities and driver training providers as to effective training strategies to improve young driver training, and ultimately improve road safety with this vulnerable population.Read moreRead less
Topics in triangulated categories. This project in pure mathematics, more specifically in modern homological algebra, builds on work started by the chief investigator in the last five years. What has already been done has achieved striking results, solving very different problems that have been open for two decades. And there seem to be many directions in which it could be pursued further.
The international mathematical community seems intrigued by what the chief investigator has achieved recen ....Topics in triangulated categories. This project in pure mathematics, more specifically in modern homological algebra, builds on work started by the chief investigator in the last five years. What has already been done has achieved striking results, solving very different problems that have been open for two decades. And there seem to be many directions in which it could be pursued further.
The international mathematical community seems intrigued by what the chief investigator has achieved recently - judging by invitations to give prestigious talks and the feedback at these events. The expected outcome is major progress in our understanding of derived categories, as well as diverse applications. The benefit will be to enhance the international stature of Australian science.Read moreRead less
Groups, piecewise linear representations, and linear 2-representations. This project aims to address fundamental questions at the interface of two central areas of modern mathematics, geometric group theory and higher representation theory. Higher representation theory is a relatively new field, but its tools have already had a tremendous impact on mathematics. The project is expected to use these tools to address outstanding questions in geometric group theory. The expected outcomes of this pr ....Groups, piecewise linear representations, and linear 2-representations. This project aims to address fundamental questions at the interface of two central areas of modern mathematics, geometric group theory and higher representation theory. Higher representation theory is a relatively new field, but its tools have already had a tremendous impact on mathematics. The project is expected to use these tools to address outstanding questions in geometric group theory. The expected outcomes of this project include resolutions of open problems in the theory of Artin groups and the creation of a new subject, the dynamical theory of two-linear groups.Read moreRead less
Moduli, invariants, and algebraisation. This project is in pure mathematics. It aims to address gaps in our
knowledge in the modern geometries and their associated algebraic structures that arise in classification problems that pervade mathematics and its applications.
This project expects to generate new knowledge in modern algebra and geometry.
Expected outcomes of this project include major progress in our
understanding of invariants of derived categories of algebraic stacks and the
relat ....Moduli, invariants, and algebraisation. This project is in pure mathematics. It aims to address gaps in our
knowledge in the modern geometries and their associated algebraic structures that arise in classification problems that pervade mathematics and its applications.
This project expects to generate new knowledge in modern algebra and geometry.
Expected outcomes of this project include major progress in our
understanding of invariants of derived categories of algebraic stacks and the
relationship between algebraic and other geometries.
The benefit will be to enhance the international stature of Australian science.Read moreRead less
Banking System Competition and the Macro-economy. Australia has one of the most concentrated banking sectors in the world, generating concerns regarding its efficiency. This project aims to develop unified frameworks to understand and evaluate quantitatively how the structure of the banking industry affects the macro-economy and provide policy recommendations for establishing a healthy and efficient banking industry. This project expects to improve understanding of the welfare trade-off between ....Banking System Competition and the Macro-economy. Australia has one of the most concentrated banking sectors in the world, generating concerns regarding its efficiency. This project aims to develop unified frameworks to understand and evaluate quantitatively how the structure of the banking industry affects the macro-economy and provide policy recommendations for establishing a healthy and efficient banking industry. This project expects to improve understanding of the welfare trade-off between bank competition and economic well-being to enable policymakers to better determine the optimal concentration of banking sector in Australia. This will enhance the productivity and international competitiveness of Australia’s financial system and the broader economy.Read moreRead less
Stability conditions: their topology and applications. This project aims to answer questions about the topology of the space of stability conditions, which has emerged as a central object in a number of different mathematical areas in the past two decades. The proposed work will have important consequences in representation theory, group theory, and algebraic geometry. The project shows that tools from previously unrelated areas, including discontinous differential equations and discrete dynam ....Stability conditions: their topology and applications. This project aims to answer questions about the topology of the space of stability conditions, which has emerged as a central object in a number of different mathematical areas in the past two decades. The proposed work will have important consequences in representation theory, group theory, and algebraic geometry. The project shows that tools from previously unrelated areas, including discontinous differential equations and discrete dynamical systems, are crucial in the theory of stability conditions. Potential benefits include the resolution of outstanding conjectures in mathematics, the initiation of new connections between different areas of mathematics, and the introduction of machine learning techniques into mathematical research.Read moreRead less
Physical realisation of enriched quantum symmetries. This project aims to investigate fundamental mathematical structures in modern category theory, providing an algebraic description of physical systems including topological order and conformal field theory. The project will study quantum symmetry, and classify and construct new classes of conformal field theories, using novel tools from enriched category theory, modular forms, and lattice gauge theory.
The main goal is to understand the lands ....Physical realisation of enriched quantum symmetries. This project aims to investigate fundamental mathematical structures in modern category theory, providing an algebraic description of physical systems including topological order and conformal field theory. The project will study quantum symmetry, and classify and construct new classes of conformal field theories, using novel tools from enriched category theory, modular forms, and lattice gauge theory.
The main goal is to understand the landscape of topological and conformal field theories, laying the foundation for new technologies based on topological order. This timely project capitalises on the recent arrival of subfactor experts in Australia, and builds capacity in mathematical research and international links in a cutting edge field.Read moreRead less