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
Coarse Geometry: a novel approach to the Callias index & topological matter. Coarse geometry is the study of the large-scale structure of metric spaces, in terms of operator algebras. This project aims to use coarse geometry to develop novel approaches to Callias index theory and its applications, and to topological phases of matter, where the Nobel Prize in physics in 2016 was awarded. This will yield new techniques in index theory and other areas, and solutions to several important problems. O ....Coarse Geometry: a novel approach to the Callias index & topological matter. Coarse geometry is the study of the large-scale structure of metric spaces, in terms of operator algebras. This project aims to use coarse geometry to develop novel approaches to Callias index theory and its applications, and to topological phases of matter, where the Nobel Prize in physics in 2016 was awarded. This will yield new techniques in index theory and other areas, and solutions to several important problems. Outcomes include a noncompact generalisation of the famous Guillemin-Sternberg conjecture that quantisation commutes with reduction, and new models of topological phases of matter in terms of K-theory of operator algebras. This project will benefit Australia by reinforcing its position in these highly active areas in science.Read moreRead less
Identification Power and Instrument Strength in Discrete Outcome Models. This project aims to develop new econometric and statistical techniques to quantify causal effects in treatment models with discrete outcomes. Expected outcomes include a much-needed weak instrument test, a measure for identification strength in partial identification setting, and an instrument-covariate selection procedure for high dimensional discrete models based identification power. The benefits include advanced knowle ....Identification Power and Instrument Strength in Discrete Outcome Models. This project aims to develop new econometric and statistical techniques to quantify causal effects in treatment models with discrete outcomes. Expected outcomes include a much-needed weak instrument test, a measure for identification strength in partial identification setting, and an instrument-covariate selection procedure for high dimensional discrete models based identification power. The benefits include advanced knowledge in econometrics and statistics, and enhanced tools for program evaluation and policy assessment in empirical causal analysis using observational data. The project falls into the category of smarter information use and is relevant to any national priority areas where policy interventions require assessment.Read moreRead less
Selection of mixed strength moment restrictions and optimal inference . This project aims to develop consistent model selection criteria even if the target model only provides a weak signal about the parameter of interest. This project expects to generate new knowledge on model selection using new and innovative techniques. Expected outcomes include the quantification of the maximum information on parameter from weak-signal models; new entropy-based model selection criteria; and a robust investi ....Selection of mixed strength moment restrictions and optimal inference . This project aims to develop consistent model selection criteria even if the target model only provides a weak signal about the parameter of interest. This project expects to generate new knowledge on model selection using new and innovative techniques. Expected outcomes include the quantification of the maximum information on parameter from weak-signal models; new entropy-based model selection criteria; and a robust investigation of the still debated hypothesis in environmental economics that with open and liberalized trade, developing countries would become pollution havens for dirty industries of advanced countries. Success in this undertaking will dramatically enlarge the pool of applied work involving economic models with weak signals.Read moreRead less
Empowering next-generation sea-ice models with wave–ice mathematics. Sea ice is a crucial part of the Australian and global climate systems, and the most sensitive indicator of the alarming climate changes in motion. This project aims to deliver a vital component in next-generation sea-ice models, by modelling ocean waves in the ice-covered ocean, and implementing it in the leading large-scale sea-ice model. The waves-in-ice model will be accurate for the range of possible wave–ice conditions, u ....Empowering next-generation sea-ice models with wave–ice mathematics. Sea ice is a crucial part of the Australian and global climate systems, and the most sensitive indicator of the alarming climate changes in motion. This project aims to deliver a vital component in next-generation sea-ice models, by modelling ocean waves in the ice-covered ocean, and implementing it in the leading large-scale sea-ice model. The waves-in-ice model will be accurate for the range of possible wave–ice conditions, using understanding derived from state-of-the-art experimental measurements. Powerful mathematical approximation methods will be developed to generate model efficiency. The outcomes will create a new standard in sea-ice modelling, with significant benefits for sea-ice forecasting and climate studies.Read moreRead less
Symmetry and geometric partial differential equations. This project aims to develop tools to assist the study of partial differential equations, which are fundamental to our understanding of the physical world. Symmetries of the Laplace equation are fundamental in both finding and interpreting its solutions and can be traced to the conformal symmetries of the underlying space. Only for the most symmetric of spaces, Euclidean space and the sphere, is this correspondence well understood. Using pow ....Symmetry and geometric partial differential equations. This project aims to develop tools to assist the study of partial differential equations, which are fundamental to our understanding of the physical world. Symmetries of the Laplace equation are fundamental in both finding and interpreting its solutions and can be traced to the conformal symmetries of the underlying space. Only for the most symmetric of spaces, Euclidean space and the sphere, is this correspondence well understood. Using powerful geometric tools from conformal geometry, the project will extend this to less symmetric spaces. The knowledge generated from this project will extend to more general geometric contexts providing a concrete setting for the study of the associated natural equations in curved spaces.Read moreRead less
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
Prediction of inertial particle focusing in curved microfluidic ducts. This project aims to develop mathematical models to predict migration of particles suspended in flow through curved microfluidic ducts and their focusing by size to different regions in the cross-section of the duct. New knowledge in mathematics and engineering will be generated through models that capture the two-way force balance between fluid and particles and by a novel use of asymptotics for computational efficiency. Exp ....Prediction of inertial particle focusing in curved microfluidic ducts. This project aims to develop mathematical models to predict migration of particles suspended in flow through curved microfluidic ducts and their focusing by size to different regions in the cross-section of the duct. New knowledge in mathematics and engineering will be generated through models that capture the two-way force balance between fluid and particles and by a novel use of asymptotics for computational efficiency. Expected outcomes are understanding of the physics that drives particle migration and the parameters that may be used to control particle focusing. This will benefit design and operation of microfluidic devices for particle sorting as required for "liquid biopsy", the isolation of cancer cells in a routine blood sample.Read moreRead less
Mathematical modelling of information flow in social networks. This proposal aims to develop new mathematical and statistical methods to understand information flow in social networks. By using novel information theoretic techniques, it will create new methods to characterise social information flow in social networks. These tools will allow derivation of fundamental limits of predictability for AI methods applied to digital data. New mathematics of information flow will produce insights into so ....Mathematical modelling of information flow in social networks. This proposal aims to develop new mathematical and statistical methods to understand information flow in social networks. By using novel information theoretic techniques, it will create new methods to characterise social information flow in social networks. These tools will allow derivation of fundamental limits of predictability for AI methods applied to digital data. New mathematics of information flow will produce insights into social influence in online social networks. Benefits include: better understanding of how echo chambers may form in social networks, predictive models for how misinformation can spread online such as during an emergency, and a framework for intercomparison of AI methods applied to digital data on individuals. Read moreRead less
Early desert settlement of Arabia following out-of-Africa human dispersals. This project aims to improve our understanding of the nature, timing and climatic context of early human expansion into SW Asia, from a new extensive archaeological complex with associated palaeoenvironmental sequences on the Arabian Peninsula – a strategic out-of-Africa migratory corridor. It will combine innovative approaches in archaeology, geochronology and palaeoenvironmental research to evaluate the environmental a ....Early desert settlement of Arabia following out-of-Africa human dispersals. This project aims to improve our understanding of the nature, timing and climatic context of early human expansion into SW Asia, from a new extensive archaeological complex with associated palaeoenvironmental sequences on the Arabian Peninsula – a strategic out-of-Africa migratory corridor. It will combine innovative approaches in archaeology, geochronology and palaeoenvironmental research to evaluate the environmental and cultural adaptability of early desert settlement, providing critical new insights into globally significant human dispersal debates spanning multiple continents, including Australia. The aim is a fundamental new perspective on long-term human occupation dynamics of deserts and new understanding of regional dispersals.Read moreRead less