Loss-based Bayesian Prediction. This project proposes a new paradigm for prediction. Using state-of-the-art computational methods, the project aims to produce accurate, fit for purpose, predictions which, by design, reduce the loss incurred when the prediction is inaccurate. Theoretical validation of the new predictive method, without reliance on knowledge of the correct statistical model, is an expected outcome, as is an extensive numerical assessment of its performance in empirical settings. T ....Loss-based Bayesian Prediction. This project proposes a new paradigm for prediction. Using state-of-the-art computational methods, the project aims to produce accurate, fit for purpose, predictions which, by design, reduce the loss incurred when the prediction is inaccurate. Theoretical validation of the new predictive method, without reliance on knowledge of the correct statistical model, is an expected outcome, as is an extensive numerical assessment of its performance in empirical settings. The new paradigm should produce significant benefits for all fields in which the consequences of predictive inaccuracy are severe. Problems that lead to substantial economic, financial or environmental loss if predictions are incorrect will be given particular attention.Read moreRead less
New methods for modelling complex trends in climate and energy time series. The project aims to contribute to Australian and international efforts on emission control by advancing the methods for quantifying the relationships between energy production, emission and climate, and assessing the real and financial risks associated with changing the ways in which economies produce and use energy. The project is interdisciplinary and expects to develop new knowledge in the areas of energy and climate ....New methods for modelling complex trends in climate and energy time series. The project aims to contribute to Australian and international efforts on emission control by advancing the methods for quantifying the relationships between energy production, emission and climate, and assessing the real and financial risks associated with changing the ways in which economies produce and use energy. The project is interdisciplinary and expects to develop new knowledge in the areas of energy and climate econometrics. The anticipated outcomes of this project are new methods for modelling variables with complex trends, and an innovative data-driven approach for learning from policy experiences of other countries. This should provide significant benefits by enabling evidence-based policy making in the era of climate change. Read moreRead less
Linking wave–sea ice feedbacks to rapid ice retreat. Antarctic sea ice extent has been in sharp decline since 2016, which is stressing the fragile Southern Ocean and Antarctic environments so vital to the global climate. This project aims to investigate a crucial candidate mechanism of sea ice loss by predicting rapid ice retreat in response to large Southern Ocean waves. New theory and modelling capabilities that account for wave–ice feedbacks will underpin the predictions, leveraging on recent ....Linking wave–sea ice feedbacks to rapid ice retreat. Antarctic sea ice extent has been in sharp decline since 2016, which is stressing the fragile Southern Ocean and Antarctic environments so vital to the global climate. This project aims to investigate a crucial candidate mechanism of sea ice loss by predicting rapid ice retreat in response to large Southern Ocean waves. New theory and modelling capabilities that account for wave–ice feedbacks will underpin the predictions, leveraging on recent research breakthroughs, including novel datasets derived from satellite and field observations. The outcomes are expected to quantify sea ice retreat due to ocean waves for the first time, with potentially major implications for coupled wave–sea ice modelling in climate studies.Read moreRead less
Towards logarithmic representation theory of W-algebras. Aims: To construct and analyse indecomposable representations of significance in conformal field theory.
Significance: Conformal field theory plays a key role in many developments in mathematics and physics. Logarithmic conformal field theories govern important systems such as two-dimensional critical percolation. This proposal aims to develop the representation theory necessary for understanding salient features of critical systems des ....Towards logarithmic representation theory of W-algebras. Aims: To construct and analyse indecomposable representations of significance in conformal field theory.
Significance: Conformal field theory plays a key role in many developments in mathematics and physics. Logarithmic conformal field theories govern important systems such as two-dimensional critical percolation. This proposal aims to develop the representation theory necessary for understanding salient features of critical systems described by logarithmic conformal field theory.
Expected Outcomes: Novel representations of fundamental importance in logarithmic conformal field theory.
Benefit: Resolution of open problems in logarithmic conformal field theory, thus continuing the strong tradition in the field in Australia.
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Transformative simulation techniques for complex polymer networks. The study of long chain polymers like DNA using computer simulations has uncovered exciting insights over many years. Generally these have been limited to simple topologies, interactions, and environments. This project aims to develop the next generation of simulation techniques to tackle a new frontier of polymer models, including those with complex topologies like stars, knots, and links, which have hitherto been inaccessible. ....Transformative simulation techniques for complex polymer networks. The study of long chain polymers like DNA using computer simulations has uncovered exciting insights over many years. Generally these have been limited to simple topologies, interactions, and environments. This project aims to develop the next generation of simulation techniques to tackle a new frontier of polymer models, including those with complex topologies like stars, knots, and links, which have hitherto been inaccessible. Expected outcomes include new simulation methods which harness modern computational clusters, leading to greater understanding of polymers with complex topologies and in complicated environments. Important elements of biological processes may be discovered, such as how polymer structure affects DNA transcription.Read moreRead less
Shuffle algebras and vertex models. Shuffle algebras are important new mathematical structures that offer a new approaches and techniques to solve outstanding open problems in a variety of branches of mathematics, including mathematical physics, algebraic geometry and combinatorics. This project proposes to find solutions to key open problems using connections between shuffle algebras and integrable lattice models. The expected outcomes include (i) a new framework of shuffle algebra techniques t ....Shuffle algebras and vertex models. Shuffle algebras are important new mathematical structures that offer a new approaches and techniques to solve outstanding open problems in a variety of branches of mathematics, including mathematical physics, algebraic geometry and combinatorics. This project proposes to find solutions to key open problems using connections between shuffle algebras and integrable lattice models. The expected outcomes include (i) a new framework of shuffle algebra techniques to solve challenging research problems in mathematical physics and statistical mechanics, (ii) practical and computationally feasible constructions of shuffle algebras using vertex models, (iii) solutions to unresolved spectral problems of open quantum systems.Read moreRead less
Matrix product multi-variable polynomials from quantum algebras. This project aims to expand the theory of polynomials and develop generalised polynomial families using connections to affine and toroidal algebras. Many combinatorial and computational problems in pure and applied mathematics as well as mathematical physics can be solved using polynomials in many variables, such as Macdonald polynomials. This project is anticipated to address the current difficulty of implementing symmetric and no ....Matrix product multi-variable polynomials from quantum algebras. This project aims to expand the theory of polynomials and develop generalised polynomial families using connections to affine and toroidal algebras. Many combinatorial and computational problems in pure and applied mathematics as well as mathematical physics can be solved using polynomials in many variables, such as Macdonald polynomials. This project is anticipated to address the current difficulty of implementing symmetric and non-symmetric polynomials in symbolic algebra packages by developing completely new algorithms. New understanding from the project is expected to facilitate challenging computational problems of measurable quantities in quantum systems.Read moreRead less
From superintegrability to quasi-exact solvability: theory and application. This project aims to develop mathematical techniques to resolve longstanding problems in the area of integrability and exact solvability. Quantum integrable systems and exact solvable models are of central importance for understanding the correct behaviours of complex quantum problems without approximation. This project aims to construct sophisticated mathematical tools to settle key questions across a variety of models ....From superintegrability to quasi-exact solvability: theory and application. This project aims to develop mathematical techniques to resolve longstanding problems in the area of integrability and exact solvability. Quantum integrable systems and exact solvable models are of central importance for understanding the correct behaviours of complex quantum problems without approximation. This project aims to construct sophisticated mathematical tools to settle key questions across a variety of models such as superintegrable systems, quantum spin chains, and spin-boson models. Anticipated applications of the proposed research include the accurate prediction of physical phenomena, from energy spectra to quantum correlations. Such advances should have significant ramifications, and provide benefits, well beyond the mathematical discipline itself.Read moreRead less
Quantum control designed from broken integrability. This Project aims to open new avenues in quantum device engineering design. This will be achieved through the use of advanced mathematical methodologies developed around the notion of quantum integrability, and the breaking of that integrability. The expert team of Investigators will capitalise on their recent achievements in this field, which includes a first example of a quantum switch designed through broken integrability. The expected outco ....Quantum control designed from broken integrability. This Project aims to open new avenues in quantum device engineering design. This will be achieved through the use of advanced mathematical methodologies developed around the notion of quantum integrability, and the breaking of that integrability. The expert team of Investigators will capitalise on their recent achievements in this field, which includes a first example of a quantum switch designed through broken integrability. The expected outcomes will encompass novel applications of abstract mathematical physics towards the concrete control of quantum mechanical architectures. These outcomes will promote new opportunities for the construction of atomtronic devices, which are rising as a foundation for next-generation quantum technologies.
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Unraveling ocean mixing and air-sea forcing along the Indo-Pacific exchange. This project aims to collect unprecedented observations and develop high resolution model simulations to examine changes in the Indonesian Throughflow (ITF) north of Australia. This project expects to develop new knowledge of ocean-atmosphere interactions along the path of the ITF from the Pacific to the Indian Ocean, which are the powerhouse that drives changes in winds and rainfall around Australia and the entire Indo ....Unraveling ocean mixing and air-sea forcing along the Indo-Pacific exchange. This project aims to collect unprecedented observations and develop high resolution model simulations to examine changes in the Indonesian Throughflow (ITF) north of Australia. This project expects to develop new knowledge of ocean-atmosphere interactions along the path of the ITF from the Pacific to the Indian Ocean, which are the powerhouse that drives changes in winds and rainfall around Australia and the entire Indo-Pacific region. Expected outcomes include a 1000-fold increase in the observations of mixing in the Indonesian seas and new understanding of the ocean-atmosphere processes that control water property change along the ITF. This should lead to strong improvement in the skill of climate forecast models in the Australian region.Read moreRead less