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
Arithmetic hypergeometric series. Arithmetic, known nowadays as number theory, is the heart and one of the oldest parts of mathematics. The project is aimed at solving three difficult mathematical problems of contemporary mathematics by arithmetic means.
Discovery Early Career Researcher Award - Grant ID: DE200100056
Funder
Australian Research Council
Funding Amount
$403,019.00
Summary
Statistical shape analysis using persistent homology. Statistical shape analysis is the quantitative study of variation in geometric shape. An innovative approach applies concepts from algebraic topology in the form of the persistent homology transform. This project aims to prove mathematical theory relating to the persistent homology transform, to develop new statistical theory and methodology, and to apply this theory to a range of applications including the analysis of bird beaks, human skull ....Statistical shape analysis using persistent homology. Statistical shape analysis is the quantitative study of variation in geometric shape. An innovative approach applies concepts from algebraic topology in the form of the persistent homology transform. This project aims to prove mathematical theory relating to the persistent homology transform, to develop new statistical theory and methodology, and to apply this theory to a range of applications including the analysis of bird beaks, human skulls and boundary contours of stem cells. An anticipated goal is the generation of new and significant theoretical results in topological data analysis. Expected outcomes include a topologically motivated platform for shape analysis that is statistically rigorous and has firm mathematical foundations.
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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
Elliptic Schubert Calculus. We are well placed to become one of the world's leading centers in the emerging discipline of elliptic representation theory. This proposal describes our plan of establishing a cohesive research program spanning all the different aspects of this multi-disciplinary field, which applies elliptic cohomology to geometric representation theory, enumerative geometry, integrable systems and invariants of singular varieties.
Our mathematically diverse team all have played key ....Elliptic Schubert Calculus. We are well placed to become one of the world's leading centers in the emerging discipline of elliptic representation theory. This proposal describes our plan of establishing a cohesive research program spanning all the different aspects of this multi-disciplinary field, which applies elliptic cohomology to geometric representation theory, enumerative geometry, integrable systems and invariants of singular varieties.
Our mathematically diverse team all have played key roles in the recent developments surrounding the field, and in very different capacities. This is a unique moment, where we have the chance to transform our individual research programs into a cohesive and powerful collaboration with a strong
international presence.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.
Noncommutative analysis and geometry in interaction with quantum physics. Quantum theory has produced many advances in our understanding of the physical world for the last hundred years while mathematical breakthroughs have been made through exploiting innovative ideas from quantum physics. This project continues in this highly successful framework and will lead to advances in geometry both classical and noncommutative.