Forecasting and management using imperfect models, with a focus on weather and climate. Research into complex systems is predicted to be the focus of twenty-first century science, since most of the problems of simple systems are solved. Examples include the weather and climate, economies, argriculture, ecologies, the mind and brain, genetics, biochemistry. Confidence in the reliability and usefulness of models will have significant bearing on how these models are used by decision making and how ....Forecasting and management using imperfect models, with a focus on weather and climate. Research into complex systems is predicted to be the focus of twenty-first century science, since most of the problems of simple systems are solved. Examples include the weather and climate, economies, argriculture, ecologies, the mind and brain, genetics, biochemistry. Confidence in the reliability and usefulness of models will have significant bearing on how these models are used by decision making and how the community perceives the value of this science. Specific immediate benefits of the project include better policy and management responses to climate change and servere weather events.Read moreRead less
Synthesis of dynamics, stochastics and information in forecasting and management of complex systems. Research into complex systems is predicted to be the focus of twenty-first century science, since most of the problems of simple systems are solved. Examples include the weather and climate, economies, agriculture, ecologies, the mind and brain, genetics, biochemistry. Confidence in the reliability and usefulness of models will have significant bearing on how these models are used by decision ma ....Synthesis of dynamics, stochastics and information in forecasting and management of complex systems. Research into complex systems is predicted to be the focus of twenty-first century science, since most of the problems of simple systems are solved. Examples include the weather and climate, economies, agriculture, ecologies, the mind and brain, genetics, biochemistry. Confidence in the reliability and usefulness of models will have significant bearing on how these models are used by decision making and how the community perceives the value of this science. Specific immediate benefits of the project include better policy and management responses to climate change and severe weather events.Read moreRead less
The fundamental structure of combinatorial configurations. Combinatorial configurations are fundamental mathematical tools used to model physical problems in the information sciences. Combinatorial trades arise from the differences between combinatorial configurations. They uniquely determine the underlying structure of the configuration and are central to the determination of defining sets. With this proposal we shall study the existence, properties and applications of combinatorial trades and ....The fundamental structure of combinatorial configurations. Combinatorial configurations are fundamental mathematical tools used to model physical problems in the information sciences. Combinatorial trades arise from the differences between combinatorial configurations. They uniquely determine the underlying structure of the configuration and are central to the determination of defining sets. With this proposal we shall study the existence, properties and applications of combinatorial trades and the associated defining sets. Our results will have applications in the areas of biotechnology, information systems, information security and experimental design.Read moreRead less
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
Polynomial representations of the Hecke algebra. This project will offer a great opportunity for talented students to engage in internationally competitive research in mathematics. In addition, through international collaboration, this project will be able to deliver an online database with software libraries which will be a world benchmark for computation with multivariate polynomials.
Statistical Topology and its Application to Deriving New Geometric Invariants. This project will offer a great opportunity for talented students to engage in internationally competitive research. Statistical topology, which combines ideas in topology, geometry and statistical mechanics is becoming a rapidly increasing branch of mathematics, with many emerging applications in bio-informatics, computer science and theoretical physics.
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
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
The mathematical analysis of ultracold quantum gases. Ongoing developments in the experimental realisation of ultracold quantum
gases play a leading role in the international effort towards the
eventual realisation of quantum technology. This project brings together Australian
researchers with complementary strengths to develop a sophisticated range of innovative
mathematical tools for understanding these fundamental quantum systems. The expected
outcomes will thus include potentially far r ....The mathematical analysis of ultracold quantum gases. Ongoing developments in the experimental realisation of ultracold quantum
gases play a leading role in the international effort towards the
eventual realisation of quantum technology. This project brings together Australian
researchers with complementary strengths to develop a sophisticated range of innovative
mathematical tools for understanding these fundamental quantum systems. The expected
outcomes will thus include potentially far reaching impacts on downstream quantum technology.
The project will contribute to training mathematically talented students and thus take essential
steps to establish the long term future of mathematical physics in Australia. It will also establish enduring key international research links.Read moreRead less
Problems of duality for semigroups and other algebras. The theory of natural dualities has emerged as a powerful tool in algebra and its applications, including logic, computer science and theoretical physics. The project aims to apply recently developed techniques to a particular class of mathematical objects of established application in areas such as automata and language theory; namely the class of semigroups. As well as the contribution to the theory of semigroups, the work will provide a ....Problems of duality for semigroups and other algebras. The theory of natural dualities has emerged as a powerful tool in algebra and its applications, including logic, computer science and theoretical physics. The project aims to apply recently developed techniques to a particular class of mathematical objects of established application in areas such as automata and language theory; namely the class of semigroups. As well as the contribution to the theory of semigroups, the work will provide an understanding of the limits and full potential of application of the general theory of natural dualities.Read moreRead less