Asymptotics of the exponentially small. Asymptotic analysis plays a vital role in studying the complex interfacial dynamics that are fundamental for practical problems in fluid mechanics such as the withdrawal of oil and gas from underground reservoirs and the optimal design of ship hulls to minimise wave drag. These applications exhibit extremely small physical effects that may be crucially important but cannot be described using classical asymptotic analysis. This project will develop state of ....Asymptotics of the exponentially small. Asymptotic analysis plays a vital role in studying the complex interfacial dynamics that are fundamental for practical problems in fluid mechanics such as the withdrawal of oil and gas from underground reservoirs and the optimal design of ship hulls to minimise wave drag. These applications exhibit extremely small physical effects that may be crucially important but cannot be described using classical asymptotic analysis. This project will develop state of the art mathematical techniques in exponential asymptotics to address this deficiency in the classical theory, and provide a deeper understanding of pattern formation, instabilities and wave propagation on the interface between two fluids.Read moreRead less
Image-based Multiscale Modelling of Transport Phenomena in Porous Media. This project aims to develop an innovative general framework to build multiphase porous media transport models directly from electron microscope images of the underlying microstructure. Leading edge experimental, computational and applied mathematical techniques are proposed to drive this novel approach of multiscale modelling, employable across numerous fields of science and engineering. The central project theme of develo ....Image-based Multiscale Modelling of Transport Phenomena in Porous Media. This project aims to develop an innovative general framework to build multiphase porous media transport models directly from electron microscope images of the underlying microstructure. Leading edge experimental, computational and applied mathematical techniques are proposed to drive this novel approach of multiscale modelling, employable across numerous fields of science and engineering. The central project theme of developing an efficient and accurate multiscale model for simulating transport in heterogeneous porous media is expected to find application in the drying, timber and crop industries, and governmental agencies managing pollution in groundwater resources. This insight is likely to be invaluable for designing new industrial technologies and optimising current operations.Read moreRead less
Transforming Australian bio-based industries through multiscale modelling. Agricultural and forestry biomass can be converted into feedstocks for production of biofuels and biomaterials via synthetic biology. A key challenge is the complex biomass microstructure renders it highly resistant to conversion, and pretreatment is crucial for enhancing process efficiency. Micro-CT imaging will enable particle characterisation and identification of changes in the fibre composition during pretreatment. T ....Transforming Australian bio-based industries through multiscale modelling. Agricultural and forestry biomass can be converted into feedstocks for production of biofuels and biomaterials via synthetic biology. A key challenge is the complex biomass microstructure renders it highly resistant to conversion, and pretreatment is crucial for enhancing process efficiency. Micro-CT imaging will enable particle characterisation and identification of changes in the fibre composition during pretreatment. This information will be used to create a virtual biomass particle model for an in silico investigation to inform optimal process design. The framework will transform the way biomass is processed, contributing to the growth of the Australian bio-manufacturing industry by making it more productive, profitable and sustainable.Read moreRead less
Games and decisions with bounded rationality: theory and economic implications. This project will develop concepts and tools for decision making in complex environments, where it is impossible to fully characterise the possible outcomes and factors that may affect them. A central goal will be to integrate heuristic rules such as the precautionary principle with the more formal approach adopted in benefit-cost analysis.
Discovery Early Career Researcher Award - Grant ID: DE140100633
Funder
Australian Research Council
Funding Amount
$395,169.00
Summary
Problems in the Langlands Program. The Langlands program is an international research program sitting at the interface of number theory, representation theory, algebraic geometry, and mathematical physics. The aim of this project is to prove three conjectures in this program. Settling these conjectures would lead to significant advances in the Langlands program by strengthening connections between this program and the geometry of loop groups, representations of finite groups, and representations ....Problems in the Langlands Program. The Langlands program is an international research program sitting at the interface of number theory, representation theory, algebraic geometry, and mathematical physics. The aim of this project is to prove three conjectures in this program. Settling these conjectures would lead to significant advances in the Langlands program by strengthening connections between this program and the geometry of loop groups, representations of finite groups, and representations of affine Kac-Moody algebras at the critical level.Read moreRead less
The economics of (mis)information in the age of social media. New media technologies allow anyone to broadcast their views, leading to a “cacophony of voices” where misinformation flourishes. Tools from information economics are tailor-made for understanding information consumption in settings with many biased news sources. We develop economic models where many sources compete to attract and influence heterogenous listeners. We then study how misinformation spreads and amplifies when consumers ....The economics of (mis)information in the age of social media. New media technologies allow anyone to broadcast their views, leading to a “cacophony of voices” where misinformation flourishes. Tools from information economics are tailor-made for understanding information consumption in settings with many biased news sources. We develop economic models where many sources compete to attract and influence heterogenous listeners. We then study how misinformation spreads and amplifies when consumers of information communicate with many others through a social network. Finally, we study how to design simple and robust rules to foster informative discourse and filter misinformation. The results will shape economic policy recommendations for regulating misinformation in media platforms and social media.Read moreRead less
Heterogeneity, Wage Inequality, Unemployment, and Economic Growth. This project would provide the first internally consistent theory of wage inequality, unemployment and economic growth - and the roles that government policy variables play in determining them. It would use and extend frontier developments in theory, and identify the settings of policy variables (unemployment insurance, tax structures, education policies) that maximise social welfare, given that governments must satisfy their bud ....Heterogeneity, Wage Inequality, Unemployment, and Economic Growth. This project would provide the first internally consistent theory of wage inequality, unemployment and economic growth - and the roles that government policy variables play in determining them. It would use and extend frontier developments in theory, and identify the settings of policy variables (unemployment insurance, tax structures, education policies) that maximise social welfare, given that governments must satisfy their budget constraints. It also aims to uncover the relationship between the innate abilities of workers and their education choices - and the consequences for macro economies and public policy.Read moreRead less
Categorical symmetries in representation theory. This project aims to develop categorical symmetries of central objects in mathematics such as braid groups, the Hilbert scheme of points, and the Virasoro algebra. The concept of symmetry is an important organising principle in science. Representation theory is the field of mathematics concerned with studying symmetries. The problems proposed have connections to many different areas including algebra, geometry, topology, and mathematical physics. ....Categorical symmetries in representation theory. This project aims to develop categorical symmetries of central objects in mathematics such as braid groups, the Hilbert scheme of points, and the Virasoro algebra. The concept of symmetry is an important organising principle in science. Representation theory is the field of mathematics concerned with studying symmetries. The problems proposed have connections to many different areas including algebra, geometry, topology, and mathematical physics. This project expects to advance pure mathematics and provide potential benefit in many related fields.Read moreRead less
Productivity, growth and unemployment in economies with frictions. This project aims to examine decisions driving productivity, growth, and unemployment in macroeconomies with frictions. It examines how government (fiscal, monetary, and education) policies determine these decisions, and identifies the best configurations of these policies. It will construct dynamic general equilibrium models of economies to analyse the causal structure behind productivity changes, growth and unemployment. It wil ....Productivity, growth and unemployment in economies with frictions. This project aims to examine decisions driving productivity, growth, and unemployment in macroeconomies with frictions. It examines how government (fiscal, monetary, and education) policies determine these decisions, and identifies the best configurations of these policies. It will construct dynamic general equilibrium models of economies to analyse the causal structure behind productivity changes, growth and unemployment. It will conduct quantitative experiments using simulations, to estimate optimal government policy design settings. This project expects to identify policies that promote productivity, growth and employment.Read moreRead less