Decision theory in crisis. Decision theory's goals are to characterise and to guide rational decision-making—from the minor decisions of daily life, to the major decisions of industry and government— which, in its current state, it is unfit to do. This project will refine decision theory so that it may better achieve these goals.
Epistemically feasible choice: implications for sustainable risk management. The aim of this project is to examine procedural decision principles that will yield better choices in circumstances where, because of epistemic limitations, standard decision theory provides an inadequate guide. Individuals and policy-makers must make decisions even though they cannot be fully aware of all of the relevant possibilities or fully understand consequences they have not yet experienced. Examples include ind ....Epistemically feasible choice: implications for sustainable risk management. The aim of this project is to examine procedural decision principles that will yield better choices in circumstances where, because of epistemic limitations, standard decision theory provides an inadequate guide. Individuals and policy-makers must make decisions even though they cannot be fully aware of all of the relevant possibilities or fully understand consequences they have not yet experienced. Examples include individual decisions about marriage and childbearing, public policy decisions about complex environmental problems and decisions on funding scientific research. The expected outcome of the project will be a formal model of decision theory incorporating principles of resilience, sustainability and transformative experience.Read moreRead less
Defence and Security Risk Assessment using Agent Based Distillations. Today's society continues to be occupied with the idea of risk. The recent events of September 11th, the Bali bombing, SARS, the bush fires in Canberra, and the Tsunami are examples of human-made and natural disasters. These events had dramatic consequences on the social, economic, and political environment and numerous industries. This project offers an innovative methodological paradigm for assessing risk through the transfe ....Defence and Security Risk Assessment using Agent Based Distillations. Today's society continues to be occupied with the idea of risk. The recent events of September 11th, the Bali bombing, SARS, the bush fires in Canberra, and the Tsunami are examples of human-made and natural disasters. These events had dramatic consequences on the social, economic, and political environment and numerous industries. This project offers an innovative methodological paradigm for assessing risk through the transfer of technologies drawn from defence simulations to the safety and security areas. The success of this project will mark a paradigm shift in the area of risk assessment and management.Read moreRead less
Learning and choosing in a complex world. How do people make choices in a complex world? Making good choices requires expertise, but people must often forego rewards in order to acquire this knowledge. This is the essence of an "explore-exploit dilemma": to maximise rewards across a long time frame, people must take the time to explore and learn now. Empirically, this project aims to unify much of the existing psychological literature and extend it to cover richer, more complex problems. Theoret ....Learning and choosing in a complex world. How do people make choices in a complex world? Making good choices requires expertise, but people must often forego rewards in order to acquire this knowledge. This is the essence of an "explore-exploit dilemma": to maximise rewards across a long time frame, people must take the time to explore and learn now. Empirically, this project aims to unify much of the existing psychological literature and extend it to cover richer, more complex problems. Theoretically, the project aims to use tools from machine learning to compare human decision making to optimal planning models.Read moreRead less
A new approach to understanding decision making. Mathematical theories of decision-making have helped us understand many aspects of psychology (such as ageing, gambling, psychological disorders and consumer decisions). This project will extend these theories to a new level of finer-grained analysis, opening up new possibilities for understanding cognition and behaviour.
Algebraic K-theory and groups. This project will study the K-theory of division algebras, their generalisation to Azumaya algebras and the nonstable K-theory of rings. Expected outcomes would enhance our understanding on the structure of these K groups.
The goal is to settle some of the most significant conjectures in the subject: Bak's solvability of nonstable K groups over rings and the Merkurjev-Suslin conjectures on reduced K theory of division rings.
The study of these problems contribu ....Algebraic K-theory and groups. This project will study the K-theory of division algebras, their generalisation to Azumaya algebras and the nonstable K-theory of rings. Expected outcomes would enhance our understanding on the structure of these K groups.
The goal is to settle some of the most significant conjectures in the subject: Bak's solvability of nonstable K groups over rings and the Merkurjev-Suslin conjectures on reduced K theory of division rings.
The study of these problems contributes to and draws from such topics as group theory, commutative ring theory, algebraic number theory and algebraic geometry.
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Homotopy theory: interactions with representation theory and moduli spaces. This proposal will involve young researchers and train them for problem solving in many fields, including management, the sciences, the financial industries, and the development of technologies. Furthermore, many of the projects in this proposal are collaborative and interdisciplinary. It is the CI's sincere hope that this proposal can help bolster communication amongst the wealth of topology, number theory, and mathe ....Homotopy theory: interactions with representation theory and moduli spaces. This proposal will involve young researchers and train them for problem solving in many fields, including management, the sciences, the financial industries, and the development of technologies. Furthermore, many of the projects in this proposal are collaborative and interdisciplinary. It is the CI's sincere hope that this proposal can help bolster communication amongst the wealth of topology, number theory, and mathematical physics experts in Australia. The research in these exciting areas of mathematics will contribute to maintaining Australia's position as a research leader in pure mathematics.
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Games and decisions with bounded rationality: theory and economic implications. This project will develop concepts and tools for decision making in complex environments, where it is impossible to fully characterise the possible outcomes and factors that may affect them. A central goal will be to integrate heuristic rules such as the precautionary principle with the more formal approach adopted in benefit-cost analysis.
Explicit Construction of Global Function Fields with Many Rational Places. The use of error-correcting codes and cryptosystems is fundamental to the secure and reliable operation of many technological devices that we depend upon in our everyday lives. Essentially invisible, both coding theory and cryptography are essential for banking (ATM machines, e-banking), commerce (e-commerce), defense (cryptography) and entertainment (digital TV and radio, music CDs, DVDs). While certain families of "goo ....Explicit Construction of Global Function Fields with Many Rational Places. The use of error-correcting codes and cryptosystems is fundamental to the secure and reliable operation of many technological devices that we depend upon in our everyday lives. Essentially invisible, both coding theory and cryptography are essential for banking (ATM machines, e-banking), commerce (e-commerce), defense (cryptography) and entertainment (digital TV and radio, music CDs, DVDs). While certain families of "good" codes and cryptosystems can be constructed from specific function fields whose existence is guaranteed by abstract theory, often no actual construction for the function field is currently known. We aim to close this gap, making a greater range of "good" codes and cryptosystems available for practical applications.
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New dualities in modular representation theory. This project aims to introduce new geometric techniques in the modular representation theory of the general linear group, and resolve fundamental questions about modular representations of orthogonal and symplectic groups. Representation theory, the mathematical study of symmetry, has applications in many areas ranging from physics to computer science. The modular setting, where the characteristic of the field is positive, is a source of the deepes ....New dualities in modular representation theory. This project aims to introduce new geometric techniques in the modular representation theory of the general linear group, and resolve fundamental questions about modular representations of orthogonal and symplectic groups. Representation theory, the mathematical study of symmetry, has applications in many areas ranging from physics to computer science. The modular setting, where the characteristic of the field is positive, is a source of the deepest conjectures in this subject. Recent breakthroughs have provided approaches to some problems in modular representation theory that were previously inaccessible. This project will promote research at the forefront of the field, and help maintain Australia's international standing. It will train Australian postgraduates, who will be able to apply their research skills in industry, and strengthen the country's ties to a vibrant international community.Read moreRead less