Fundamental mathematical structures in statistical and quantum systems. Mathematics is playing a key role in modern science and technology. This project will bring together world leading experts from Australia and the USA to unravel the most fundamental mathematical structures in of statistical and quantum systems arising in settings ranging from physics of tiny quantum dots to string theory in high energy physics. This research will ensure Australia's involvement in cutting-edge international d ....Fundamental mathematical structures in statistical and quantum systems. Mathematics is playing a key role in modern science and technology. This project will bring together world leading experts from Australia and the USA to unravel the most fundamental mathematical structures in of statistical and quantum systems arising in settings ranging from physics of tiny quantum dots to string theory in high energy physics. This research will ensure Australia's involvement in cutting-edge international developments in mathematical sciences poised to deliver new significant results in the fundamental quantum theory of matter. The project will also contribute to training young researchers to maintain Australia's international standing in fundamental science.Read moreRead less
Australian Laureate Fellowships - Grant ID: FL210100110
Funder
Australian Research Council
Funding Amount
$3,021,288.00
Summary
New Approaches to Understand How Form and Function Shape Complex Systems. As biology and medicine transform into quantitative sciences, existing mathematical methods are often inadequate to explain the data they generate. This project aims to unlock the potential of such biomedical data through the development of new mathematical approaches that combine concepts from pure and applied mathematics, statistics and data science, and then to investigate their ability to generate mechanistic insight i ....New Approaches to Understand How Form and Function Shape Complex Systems. As biology and medicine transform into quantitative sciences, existing mathematical methods are often inadequate to explain the data they generate. This project aims to unlock the potential of such biomedical data through the development of new mathematical approaches that combine concepts from pure and applied mathematics, statistics and data science, and then to investigate their ability to generate mechanistic insight into fundamental biomedical processes. In this way, the project expects to affect a paradigm shift in mathematical biology while strengthening Australia’s reputation as a world-leader in mathematical biology. An outcome from this project could be new mathematical models that guide decision making in the clinic.Read moreRead less
Security Applications of Combinatorial Puzzles. This project provides a basis for improving the implementation and maintenance of key management systems. The application of discrete mathematics to information security will help safeguard Australia, will provide opportunities for Australians to take a leading role in an important area and will develop a research network, bridging both theoretical and practical aspects of mathematics and computer science. The project will enhance Australia's inter ....Security Applications of Combinatorial Puzzles. This project provides a basis for improving the implementation and maintenance of key management systems. The application of discrete mathematics to information security will help safeguard Australia, will provide opportunities for Australians to take a leading role in an important area and will develop a research network, bridging both theoretical and practical aspects of mathematics and computer science. The project will enhance Australia's international reputation by establishing collaborations with well-respected international mathematicians and computer scientists. The proposal contains topics suitable for the training of new graduates, allowing them to make high quality original research contributions in a novel and important area. Read moreRead less
Timed Commitment Schemes to Smooth Internet Bottlenecks, Defend against Denial of Service Attacks, and Bypass Some Legal Problems of Enccryption. Bottlenecks on the Internet and Denial of Service attacks on a server are both caused by excessive demands made on a system. This proposal is to reduce the ill-effects of either by building on our previous theoretical work on strongboxes of combinatorial designs. In the case of bottlenecks, the demands are legitimate but badly timed, and our approach ....Timed Commitment Schemes to Smooth Internet Bottlenecks, Defend against Denial of Service Attacks, and Bypass Some Legal Problems of Enccryption. Bottlenecks on the Internet and Denial of Service attacks on a server are both caused by excessive demands made on a system. This proposal is to reduce the ill-effects of either by building on our previous theoretical work on strongboxes of combinatorial designs. In the case of bottlenecks, the demands are legitimate but badly timed, and our approach will redistribute the demands more evenly. In the case of Denial of Service attacks, the demands are malicious, and our approach will respond in such a way as to deplete the resources of the attacker.Read moreRead less
Quantization of polyhedral surfaces. Recent developments in the theory of discrete surfaces have revealed their fascinating links to many other areas of mathematics including integrable systems and quantum geometry. Rapid progress in this field is motivated by applications in pure mathematics, mathematical physics, computer graphics and engineering. Australian researchers are world recognized experts in integrable systems and this project will link them together with German experts in discrete d ....Quantization of polyhedral surfaces. Recent developments in the theory of discrete surfaces have revealed their fascinating links to many other areas of mathematics including integrable systems and quantum geometry. Rapid progress in this field is motivated by applications in pure mathematics, mathematical physics, computer graphics and engineering. Australian researchers are world recognized experts in integrable systems and this project will link them together with German experts in discrete differential geometry. The project will advance our knowledge base in fundamental and applied sciences and offer a unique research training opportunity for students in contemporary areas of pure and applied mathematics.Read moreRead less
Operations research without convexity. Operations Research (OR) is one of the most applicable areas of mathematics and of importance for the future of technologically advanced Australia. However, applications of OR often require convexity. This is a serious limitation. A new approach, monotonic analysis, which is applicable to a broad class of nonconvex problems, was given birth by the CI. Promising results have been obtained and leading researchers around the world (including the Presidents ....Operations research without convexity. Operations Research (OR) is one of the most applicable areas of mathematics and of importance for the future of technologically advanced Australia. However, applications of OR often require convexity. This is a serious limitation. A new approach, monotonic analysis, which is applicable to a broad class of nonconvex problems, was given birth by the CI. Promising results have been obtained and leading researchers around the world (including the Presidents of the Canadian Mathematical and French Applied Mathematics Societies) are keen to work with the CI developing this topic. This project both cements and extends world leadership in this field.Read moreRead less
Invariants of singular spaces from noncommutative geometry. The project addresses questions of significance at the international forefront in the mathematical sciences and the ARC funds will enable research training of students and postdoctoral fellows at this very high level. International collaboration and networking is a key feature that will enhance Australia's scientific standing and provide opportunities for early career researchers to engage internationally with world leaders. The mainten ....Invariants of singular spaces from noncommutative geometry. The project addresses questions of significance at the international forefront in the mathematical sciences and the ARC funds will enable research training of students and postdoctoral fellows at this very high level. International collaboration and networking is a key feature that will enhance Australia's scientific standing and provide opportunities for early career researchers to engage internationally with world leaders. The maintenance of a high quality research program at ANU enhances Australia's ability to attract international students and places the ANU in the top league of world universities. It brings with it recognition of Australia as a culturally advanced nation.Read moreRead less
Diffusion driven pattern formation and signal propagation in spatially complex excitable media. A basic understanding of the mechanisms for pattern formation, from the spots on leopards to electrical signalling of neurons, has been achieved through reaction-diffusion equations. However to obtain a complete understanding, which is vital for many applications, it is necessary to modify this mathematical model to incorporate spatial complexities in the underlying media. This project will develop ....Diffusion driven pattern formation and signal propagation in spatially complex excitable media. A basic understanding of the mechanisms for pattern formation, from the spots on leopards to electrical signalling of neurons, has been achieved through reaction-diffusion equations. However to obtain a complete understanding, which is vital for many applications, it is necessary to modify this mathematical model to incorporate spatial complexities in the underlying media. This project will develop a fractional calculus framework for pattern formation, including signal propagation, in spatially complex and excitable media. In a particular application we will model the way in which the signalling properties of neurons depend critically on their spatial complexity.Read moreRead less
Enhancing Privacy for Digital Communication. Protecting one's privacy in cyber world is a challenging task. Every contact to a Web server leaves a digital footprint that can be linked with other publicly available information to compile a profile of one's activities. Anonymous communication is a powerful tool for enhancing individuals' privacy and providing services such as electronic election where a person's vote must be unlinkable to him/her. However, anonymity may be misused by criminals to ....Enhancing Privacy for Digital Communication. Protecting one's privacy in cyber world is a challenging task. Every contact to a Web server leaves a digital footprint that can be linked with other publicly available information to compile a profile of one's activities. Anonymous communication is a powerful tool for enhancing individuals' privacy and providing services such as electronic election where a person's vote must be unlinkable to him/her. However, anonymity may be misused by criminals to hide their identities and engage in illegal activities. The aim of this project is to design and analyse privacy enhancing communication systems that balance individuals' privacy and accountability, and develop criteria and metrics to compare performance of these systems.Read moreRead less