Lifting the curse of dimensionality - bringing together the quasi Monte Carlo and sparse grid methods. This project is expected to lead to improved methods for handling high-dimensional problems (i.e. problems with many variables) that arise in finance, statistics, commerce, physics, and many other fields. In turn this could lead to significant economic benefit, especially to high-value service industries such as the finance industry. By strengthening international collaboration, it will also ....Lifting the curse of dimensionality - bringing together the quasi Monte Carlo and sparse grid methods. This project is expected to lead to improved methods for handling high-dimensional problems (i.e. problems with many variables) that arise in finance, statistics, commerce, physics, and many other fields. In turn this could lead to significant economic benefit, especially to high-value service industries such as the finance industry. By strengthening international collaboration, it will also help to maintain Australia's strong position in international research in the mathematical sciences.Read moreRead less
Lie-type methods for totally disconnected groups. Groups are algebraic objects which convey symmetry, much as numbers convey size. For example, the rotations of a sphere form a group. This rotation group is one of a class known as the Lie groups that is well understood and has important applications. Totally disconnected groups arise as symmetries of network structures having nodes and a `neighbour' relation between nodes. The Australian investigator has discovered powerful methods for analysing ....Lie-type methods for totally disconnected groups. Groups are algebraic objects which convey symmetry, much as numbers convey size. For example, the rotations of a sphere form a group. This rotation group is one of a class known as the Lie groups that is well understood and has important applications. Totally disconnected groups arise as symmetries of network structures having nodes and a `neighbour' relation between nodes. The Australian investigator has discovered powerful methods for analysing totally disconnected groups which have parallels with Lie group techniques. This project will develop these parallels and establish links with international researchers on Lie groups.Read moreRead less
Totally disconnected groups, representations and discrete mathematics. This project involves participation in programs at the Institute of Advanced Studies in Princeton and the nearby Center for Discrete Mathematics and Theoretical Computer Science that are designed to initiate collaborations across distinct mathematical research areas. These programs will set future research directions and could lead to innovations in computer science. Discoveries I have made in one of the research areas mean ....Totally disconnected groups, representations and discrete mathematics. This project involves participation in programs at the Institute of Advanced Studies in Princeton and the nearby Center for Discrete Mathematics and Theoretical Computer Science that are designed to initiate collaborations across distinct mathematical research areas. These programs will set future research directions and could lead to innovations in computer science. Discoveries I have made in one of the research areas mean that I may be able to make substantial contributions to these programs. Early involvement in influential programs such as these means that Australia is well placed to take advantage of developments that result and also enhances the reputation of Australian mathematics.Read moreRead less
Hecke Algebras in Algebra and Analysis. The aim of this program is to adapt techniques from harmonic analysis and operator-algebraic representation theory to study Hecke algebras arising in algebraic and geometric settings. The relevant analytic structures are C*-algebras and the fundamental question is then "Which Hecke algebras have a faithful enveloping C*-algebra?" We investigate this question, first by developing an appropriate theory of crossed products by semigroups and, second, by using ....Hecke Algebras in Algebra and Analysis. The aim of this program is to adapt techniques from harmonic analysis and operator-algebraic representation theory to study Hecke algebras arising in algebraic and geometric settings. The relevant analytic structures are C*-algebras and the fundamental question is then "Which Hecke algebras have a faithful enveloping C*-algebra?" We investigate this question, first by developing an appropriate theory of crossed products by semigroups and, second, by using the notion of topologization which enables the Hecke algebra to be studied in the context of topological groups.Read moreRead less
Combinatorial structures for computer security and communication. Hadamard matrices in their various guises arise many times in the study of reliable communications and secure communications. The aim of this research project is to use the theory of cyclotomy in both fields and rings to find new number theoretic results which will then be used to obtain new with zero or small autocorrelation functions.
The significance of this research is to propose new construction of Hadamard matrices and bloc ....Combinatorial structures for computer security and communication. Hadamard matrices in their various guises arise many times in the study of reliable communications and secure communications. The aim of this research project is to use the theory of cyclotomy in both fields and rings to find new number theoretic results which will then be used to obtain new with zero or small autocorrelation functions.
The significance of this research is to propose new construction of Hadamard matrices and block designs for computer security and wireless network communication.
We expect some new classes of Hadamard matrices and block designs can be constructed for security and communication applications and several papers would be submitted or published.
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Relative quantum information theory. Quantum information encoded in relative degrees of freedom of multiple quantum systems offers striking advantages in communication and cryptography: it is immune to common types of noise and does not require reference systems shared between parties. This project aims to formulate a theory of relative quantum information, to develop practical information processing protocols that take advantage of relative encodings, and to propose proof-of-principle experim ....Relative quantum information theory. Quantum information encoded in relative degrees of freedom of multiple quantum systems offers striking advantages in communication and cryptography: it is immune to common types of noise and does not require reference systems shared between parties. This project aims to formulate a theory of relative quantum information, to develop practical information processing protocols that take advantage of relative encodings, and to propose proof-of-principle experiments in quantum optics that reveal these advantages. Expected outcomes include powerful communication and cryptographic protocols, a design for programmable quantum computation, and a fundamentally relative theory of quantum information connecting with other foundational fields of physics.Read moreRead less
Advances in Theoretical Methodologies in Surface and Materials Science. This collaborative project is concerned with the review, development, and advancement of modern theoretical methodologies and approaches for the study and description of phenomena in materials and surface science. The particular focus is on first-principles-based schemes which combine accurate electronic structure calculations with more phenomenological, analytical, or statistical mechanical schemes in order to describe long ....Advances in Theoretical Methodologies in Surface and Materials Science. This collaborative project is concerned with the review, development, and advancement of modern theoretical methodologies and approaches for the study and description of phenomena in materials and surface science. The particular focus is on first-principles-based schemes which combine accurate electronic structure calculations with more phenomenological, analytical, or statistical mechanical schemes in order to describe long time and length scales, and/or to include thermodynamic effects. The theories will be applied to a range of surface and interface phenomenon, e.g., chemical reactions, quantum dots, crystal growth, as well as defects in solids, to demonstrate the power of such methods.Read moreRead less
Cultures of Trade in the Indian Ocean. A decline in cultural understandings in the IO is threatening trade opportunities. 'Value', accordingly, must be understood both in economic and cultural terms. Another outcome of this collaboration will be an analysis of the ways in which current regional security issues are being posed, and it is essential to have an international network of scholars to provide an appropriate comparative perspective. By giving us a clearer understanding of the impact of c ....Cultures of Trade in the Indian Ocean. A decline in cultural understandings in the IO is threatening trade opportunities. 'Value', accordingly, must be understood both in economic and cultural terms. Another outcome of this collaboration will be an analysis of the ways in which current regional security issues are being posed, and it is essential to have an international network of scholars to provide an appropriate comparative perspective. By giving us a clearer understanding of the impact of culture on commercial relations and of Australia's place in the Indian Ocean Region, the project will help Australia to build strong, peaceful and mutually beneficial relations with its neighbours.Read moreRead less
Meta-Ontology based Protocols for the Cooperation in Heterogeneous Agent Systems. Cooperation and communication are two important research issues in the area of multi-agent systems and distributed artificial intelligence. The aim of this project is to study and develop meta-ontology based protocols for cooperation in multi-agent systems. The outcomes of the project include semantics of meta-ontology, a conceptual model to encompass the defined semantics, implementation of the model, and test res ....Meta-Ontology based Protocols for the Cooperation in Heterogeneous Agent Systems. Cooperation and communication are two important research issues in the area of multi-agent systems and distributed artificial intelligence. The aim of this project is to study and develop meta-ontology based protocols for cooperation in multi-agent systems. The outcomes of the project include semantics of meta-ontology, a conceptual model to encompass the defined semantics, implementation of the model, and test results in an open environment. The Key Laboratory of Intelligent Information Processing at Institute of Computing Technology, Chinese Academy of Sciences, is very active in the area of distributed artificial intelligence and agent technologies, and is an ideal partner for this project.Read moreRead less
Conceptual Knowledge Processing. The aim of this collaboration between Computer Science and Mathematics disciplines is to develop a theoretical, methodological and practical understanding of how to support a range of tasks concerning conceptual knowledge processing. The view of the project is that knowledge processing takes place primarily in the human mind and that human communication can only be effectively supported by appropriate design means and devices. Developing prototype software that d ....Conceptual Knowledge Processing. The aim of this collaboration between Computer Science and Mathematics disciplines is to develop a theoretical, methodological and practical understanding of how to support a range of tasks concerning conceptual knowledge processing. The view of the project is that knowledge processing takes place primarily in the human mind and that human communication can only be effectively supported by appropriate design means and devices. Developing prototype software that demonstrates these devices in practical domains continues to be a key feature of the collaboration that benefits from existing DFG (Deutsche Forschungsgemeinschaft) support and has been on going since 1999.Read moreRead less