Non-commutative analysis and differential calculus. This project is in an area of central mathematical importance and will lead to important scientific advances that will keep Australia at the forefront internationally in this field of research. There is an emphasis on international networking and we will collaborate with leading researchers in USA and France.
There and back again: operator algebras, algebras and dynamical systems. The aim of this project is to develop mathematics that enables us to transfer information back and forth between dynamical systems and algebras, including operator algebras. Dynamical systems - systems that change over time - are ubiquitous, and central to modern mathematics and its applications. In mathematics, dualities allow us to translate questions from one context to another in which they are easier to solve and then ....There and back again: operator algebras, algebras and dynamical systems. The aim of this project is to develop mathematics that enables us to transfer information back and forth between dynamical systems and algebras, including operator algebras. Dynamical systems - systems that change over time - are ubiquitous, and central to modern mathematics and its applications. In mathematics, dualities allow us to translate questions from one context to another in which they are easier to solve and then translate the answer back again. Expected outcomes include increased understanding of the relationship between operator algebras and the dynamical systems that they represent. Benefits include enhanced international collaboration, and increased Australian capacity in pure mathematics, particularly operator algebras.Read moreRead less
Structured barrier and penalty functions in infinite dimensional optimisation and analysis. Very large scale tightly-constrained optimisation problems are ubiquitous and include water management, traffic flow, and imaging at telescopes and hospitals. Massively parallel computers can solve such problems and provide physically realisable solution only if subtle design issues are mastered. Resolving such issues is the goal of this project.
Batteries of the future-a new strategy for CO2 fixation and energy storage. This project aims to develop metal-carbon dioxide batteries with high specific energy densities for carbon dioxide capture as well as energy conversion and storage. Metal-carbon dioxide batteries are promising not only for conversion of waste carbon dioxide to value-added chemicals, but also for storage of electricity from renewable power and balancing of the carbon cycle. By combining experimental work and theoretical m ....Batteries of the future-a new strategy for CO2 fixation and energy storage. This project aims to develop metal-carbon dioxide batteries with high specific energy densities for carbon dioxide capture as well as energy conversion and storage. Metal-carbon dioxide batteries are promising not only for conversion of waste carbon dioxide to value-added chemicals, but also for storage of electricity from renewable power and balancing of the carbon cycle. By combining experimental work and theoretical modelling, this study will explore novel electrode materials via catalyst design and understanding of the underlying reaction mechanisms. The outcomes will revolutionize battery technology and position Australia as a global leader in the critical transition to a decarbonized economy.Read moreRead less
Multiparameter Harmonic Analysis: Weighted Estimates for Singular Integrals. This project aims to study advanced harmonic analysis concerning multiparameter theory and related topics. Harmonic analysis lies at the intersection of the frontiers of many branches of mathematics. It is fundamental to the study of operator theory and partial differential equations which has wide applications in many fields such as mathematical modelling, probability and number theory. This project aims to solve a num ....Multiparameter Harmonic Analysis: Weighted Estimates for Singular Integrals. This project aims to study advanced harmonic analysis concerning multiparameter theory and related topics. Harmonic analysis lies at the intersection of the frontiers of many branches of mathematics. It is fundamental to the study of operator theory and partial differential equations which has wide applications in many fields such as mathematical modelling, probability and number theory. This project aims to solve a number of open problems at the frontier of research in modern harmonic analysis including estimates on multilinear operators with nonsmooth kernels and advanced multiparameter theory on product spaces.Read moreRead less
Harmonic analysis: function spaces and singular integral operators. This project advances knowledge in harmonic analysis to new settings such as dyadic and multiparameter theories, Laplacian-like operators, and rough singular integrals. Outcomes will be solutions to long-standing problems, training of researchers, strong links with international researchers and enhancement of Australia's reputation in mathematics.
Engineered topological nanostructures – a new frontier in materials design. The aim of engineering and utilising topological defects such as domain walls and and skyrmions in functional materials is currently receiving tremendous attention. Their significance lies in a plethora of fascinating phenomena for fundamental research and future technological applications in nanoelectronics. One frontier area of research is negative capacitance nanoelectronics using such materials, carrying the prospect ....Engineered topological nanostructures – a new frontier in materials design. The aim of engineering and utilising topological defects such as domain walls and and skyrmions in functional materials is currently receiving tremendous attention. Their significance lies in a plethora of fascinating phenomena for fundamental research and future technological applications in nanoelectronics. One frontier area of research is negative capacitance nanoelectronics using such materials, carrying the prospect of revolutionizing ultralow energy electronics, which will be developed here. The project's expected outcomes are new concepts for the synthesis and design of topological nanostructures for such applications. The utilization of these materials will benefit efficient controllable functionality for future nanoelectronics.Read moreRead less
The paradox of choice: Unravelling complex superannuation decisions. Australia has been a world-leader in retirement savings policy, but there remains a pervasive lack of understanding about how best to communicate complex financial information to decision-makers, along with a push by government for clearer disclosure and greater financial literacy. This project will inform regulators and the superannuation industry on how choices are made and how to present clearer, better-designed information ....The paradox of choice: Unravelling complex superannuation decisions. Australia has been a world-leader in retirement savings policy, but there remains a pervasive lack of understanding about how best to communicate complex financial information to decision-makers, along with a push by government for clearer disclosure and greater financial literacy. This project will inform regulators and the superannuation industry on how choices are made and how to present clearer, better-designed information to be understood by ordinary participants, thus encouraging active, well-informed participation rather than passive 'default' decisions. More efficient investment and benefit choices will improve the economic welfare of retirees, reduce the burden on the working-age population and improve fiscal sustainability.Read moreRead less
Risk Measures and Management in Finance and Actuarial Science Under Regime-Switching Models. New models for assessing and managing risk of financial products will place Australia at the forefront of risk management. The work will also sustain the competitive edge of Australia as one of the major financial centres in the Asia-Pacific region through enhancing both the theory and practice of financial risk management. The project outcome will also benefit to the country in other areas of risk, for ....Risk Measures and Management in Finance and Actuarial Science Under Regime-Switching Models. New models for assessing and managing risk of financial products will place Australia at the forefront of risk management. The work will also sustain the competitive edge of Australia as one of the major financial centres in the Asia-Pacific region through enhancing both the theory and practice of financial risk management. The project outcome will also benefit to the country in other areas of risk, for example, environment risk, climate change, and energy and security problems.Read moreRead less
Targeted electrolyte design for high energy aqueous batteries. The Project aims to develop a new generation, high-energy aqueous battery. A range of new aqueous electrolytes with large working window at low concentration will be designed to replace traditional, flammable and toxic organic electrolytes, and; low-cost and multi-electron reaction materials will be developed as high-capacity electrodes to replace traditional intercalation-type materials. The Project will establish the structure-prop ....Targeted electrolyte design for high energy aqueous batteries. The Project aims to develop a new generation, high-energy aqueous battery. A range of new aqueous electrolytes with large working window at low concentration will be designed to replace traditional, flammable and toxic organic electrolytes, and; low-cost and multi-electron reaction materials will be developed as high-capacity electrodes to replace traditional intercalation-type materials. The Project will establish the structure-property relationship for electrolytes and interphases via advanced characterization(s) and computation. The new battery will be safe, energetic and sustainable for the billion-dollar energy storage market for electric vehicle, and smart-grid whilst addressing concurrently battery safety and boosted energy-density.Read moreRead less