Stochastic methods in mathematical geophysical fluid dynamics. We will develop analytical and numerical methods for long-term weather forecasting and climate modelling. The project deals with the mathematical aspects and fundamental mechanisms underpinning numerical
climate forecasting. We will develop new methodology for accurate modelling of the important and dominant slow global processes without explicitly resolving the precise detail of the weather of each day at all scales. Using sophisti ....Stochastic methods in mathematical geophysical fluid dynamics. We will develop analytical and numerical methods for long-term weather forecasting and climate modelling. The project deals with the mathematical aspects and fundamental mechanisms underpinning numerical
climate forecasting. We will develop new methodology for accurate modelling of the important and dominant slow global processes without explicitly resolving the precise detail of the weather of each day at all scales. Using sophisticated mathematics, this project investigates how to parameterize the fast and small processes by using stochastic processes in a controllable and adaptive way.Read moreRead less
Stochastic Methods in Mathematical Geophysical Fluid Dynamics. The project will develop analytical and numerical methods for long-term weather forecasting and climate modelling. The project deals with the mathematical aspects and fundamental mechanisms underpinning numerical climate forecasting. The project will develop new methodology for accurate modelling of the important and dominant slow global processes without explicitly resolving the precise detail of the weather of each day at all scale ....Stochastic Methods in Mathematical Geophysical Fluid Dynamics. The project will develop analytical and numerical methods for long-term weather forecasting and climate modelling. The project deals with the mathematical aspects and fundamental mechanisms underpinning numerical climate forecasting. The project will develop new methodology for accurate modelling of the important and dominant slow global processes without explicitly resolving the precise detail of the weather of each day at all scales. Using sophisticated mathematics, this project investigates how to parameterize the fast and small processes by using stochastic processes in a controllable and adaptive way.Read moreRead less
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
A Dynamical Systems Approach to Mapping Southern Ocean Circulation Pathways. Climate change can be expected to have complex, long-term consequences for Australia's biodiversity, for our agricultural and marine production systems, and for regional communities. The Southern Ocean is a critical driver of global climate, connecting the three major oceanic basins. Using sophisticated mathematics to analyse state-of-the-art global ocean models, this project will create a detailed picture of hitherto i ....A Dynamical Systems Approach to Mapping Southern Ocean Circulation Pathways. Climate change can be expected to have complex, long-term consequences for Australia's biodiversity, for our agricultural and marine production systems, and for regional communities. The Southern Ocean is a critical driver of global climate, connecting the three major oceanic basins. Using sophisticated mathematics to analyse state-of-the-art global ocean models, this project will create a detailed picture of hitherto invisible Southern Ocean circulation 'pathways'. The newly discovered pathways will greatly enhance our understanding of the Southern Ocean circulation, lead to improved coupled climate models, and increase our ability to predict future climate change and threats to marine populations. Read moreRead less
Geometric structures in representation theory. Mathematics underpins every aspect of people's interactions with nature (e.g. physics) and with each other (e.g. finance). Its uses range from formulating physical laws in order to understand and predict nature, to analysis of financial concepts and transactions. This project will formulate and develop three new fundamental mathematical concepts: cellular algebras, eigenspace geometries, and diagram algebras. Benefits include enhancement of Australi ....Geometric structures in representation theory. Mathematics underpins every aspect of people's interactions with nature (e.g. physics) and with each other (e.g. finance). Its uses range from formulating physical laws in order to understand and predict nature, to analysis of financial concepts and transactions. This project will formulate and develop three new fundamental mathematical concepts: cellular algebras, eigenspace geometries, and diagram algebras. Benefits include enhancement of Australia's position at the very frontier of world class mathematical research, and a myriad of potential applications to physics, coding theory, information technology, electronic security and experimental design.Read moreRead less
The geometry of exotic nilpotent cones. This research will describe the geometry of some important objects which sit at the boundary of algebra, geometry, and combinatorics. It has intrinsic value as a significant addition to the heritage of mathematical thought, and will strengthen Australian traditions in these areas of mathematics.
Pyramids and decomposition numbers for the symmetric and general linear groups. This project takes a novel approach to the decomposition number problem for the symmetric and general linear groups by setting up a new framework for computing them using the combinatorics of pyramids. The decomposition numbers of an algebra are an important statistic which gives detailed structural information about its representations. These numbers can be used to compute the dimensions of the irreducible represen ....Pyramids and decomposition numbers for the symmetric and general linear groups. This project takes a novel approach to the decomposition number problem for the symmetric and general linear groups by setting up a new framework for computing them using the combinatorics of pyramids. The decomposition numbers of an algebra are an important statistic which gives detailed structural information about its representations. These numbers can be used to compute the dimensions of the irreducible representations of the algebra and they play an important role in the applications of representation theory to other fields such as knot theory and statistical mechanics.Read moreRead less
Algebras with Frobenius morphisms and quantum groups. In this digitalized world, our life relies on mathematics more than ever. Counting and numbers are just one example of this. Another is the public key codes for online payments and transactions. Mathematics is of enormous importance in this technology dominated age. This proposal is to carry out high level mathematical research in Australia. Basic research on quantum groups underpins applied research and certain areas such as quantum mechanic ....Algebras with Frobenius morphisms and quantum groups. In this digitalized world, our life relies on mathematics more than ever. Counting and numbers are just one example of this. Another is the public key codes for online payments and transactions. Mathematics is of enormous importance in this technology dominated age. This proposal is to carry out high level mathematical research in Australia. Basic research on quantum groups underpins applied research and certain areas such as quantum mechanics and string theory. Some structure of quantum groups is too complicated to be seen by even a professional mathematician. A possible interpretation by using representations over a finite field would make it more usable and accessible by computer.Read moreRead less
New Geometric and Entropy Techniques for Differential Equations. The three main practical outcomes of this mathematical research will be better predictability of salt movement responsible for land degradation, better predictability of surface evolution of microelectronic components in nanoscale technology and an open source computer package that harnesses new and powerful geometrical techniques to solve differential equations. The project will train the next generation of researchers in the math ....New Geometric and Entropy Techniques for Differential Equations. The three main practical outcomes of this mathematical research will be better predictability of salt movement responsible for land degradation, better predictability of surface evolution of microelectronic components in nanoscale technology and an open source computer package that harnesses new and powerful geometrical techniques to solve differential equations. The project will train the next generation of researchers in the mathematical modelling of critical physical processes and it will bring international experts to Australia to work on these vital problems.Read moreRead less