Propagation of singularities for the Schrodinger equation. The time-dependent Schrodinger equation governs the evolution of quantum particles. In this project we aim to use new techniques from mathematical scattering theory to analyse solutions of the Schrodinger equation and obtain sharp bounds on their singularities. Controlling such singularities will allow us to deduce quantitative bounds on the number of eigenvalues in certain situations, and provide new techniques for studying nonlinear Sc ....Propagation of singularities for the Schrodinger equation. The time-dependent Schrodinger equation governs the evolution of quantum particles. In this project we aim to use new techniques from mathematical scattering theory to analyse solutions of the Schrodinger equation and obtain sharp bounds on their singularities. Controlling such singularities will allow us to deduce quantitative bounds on the number of eigenvalues in certain situations, and provide new techniques for studying nonlinear Schrodinger equations. Read moreRead less
Three-dimensional flow, temperature and melting distributions in mantle subduction zones. We will predict spatial distributions and time evolution of temperature and magma production in subduction zones, where cold oceanic plates sink into the Earth's mantle, recycle crust and sediments, and generate volcanic arcs. Three-dimensional laboratory experiments, including 3-D flow visualization and high-resolution temperature measurements, will model slab segments, different rates and modes of subduct ....Three-dimensional flow, temperature and melting distributions in mantle subduction zones. We will predict spatial distributions and time evolution of temperature and magma production in subduction zones, where cold oceanic plates sink into the Earth's mantle, recycle crust and sediments, and generate volcanic arcs. Three-dimensional laboratory experiments, including 3-D flow visualization and high-resolution temperature measurements, will model slab segments, different rates and modes of subduction and upward transport of melt. Ocean trench migration (?rollback? subduction) is of special interest because it gives patterns of temperature and vertical motion most conducive to melting. Results will be used to interpret geochemical and seismic data from the Tonga subduction zone in the South Pacific.Read moreRead less
Crafting Authoritarian Politics. Although Russia is nominally a democracy, strong elements of authoritarianism remain dominant. This project examines how Russia has accommodated these authoritarian themes within a representative democracy and, more generally, seeks to shed new light on the process of democratization in postcommunist societies. Russia is the 8th largest country in the world by population and the 11th largest economy based on GDP; it also remains nuclear-armed. Understanding th ....Crafting Authoritarian Politics. Although Russia is nominally a democracy, strong elements of authoritarianism remain dominant. This project examines how Russia has accommodated these authoritarian themes within a representative democracy and, more generally, seeks to shed new light on the process of democratization in postcommunist societies. Russia is the 8th largest country in the world by population and the 11th largest economy based on GDP; it also remains nuclear-armed. Understanding the dynamics of democratization in Russia has implications for political stability across a large section of the world which is currently in transition from authoritarianism to democracy.Read moreRead less
The impact of crime on the mental wellbeing of communities. Considering not only the direct impact of crime on the victims but also the indirect consequences of living in a community with a higher crime rate may in fact lead to a more accurate analysis of the size of the consequences of criminal activities on the society. Further, it may also be the case that the negative externality of crime on non-victims is much larger for some crimes than for others. If this were the case, it could have impl ....The impact of crime on the mental wellbeing of communities. Considering not only the direct impact of crime on the victims but also the indirect consequences of living in a community with a higher crime rate may in fact lead to a more accurate analysis of the size of the consequences of criminal activities on the society. Further, it may also be the case that the negative externality of crime on non-victims is much larger for some crimes than for others. If this were the case, it could have implications for the way in which police resources are presently distributed across different crimes. Better understanding the total societal cost of crime - to both victims and non-victims - could therefore help improve public policy. Read moreRead less
Hardy spaces of differential forms and applications. Hardy spaces on Euclidean spaces were developed in the 1970's following the fundamental work of Stein, Weiss and Fefferman. These spaces play an important role in harmonic analysis, as they are the natural spaces on which to consider singular integral operators. They arise in many contexts, such as when using Jacobians in non-linear partial differential equations. Recently the French participants and the Australian participants have have obt ....Hardy spaces of differential forms and applications. Hardy spaces on Euclidean spaces were developed in the 1970's following the fundamental work of Stein, Weiss and Fefferman. These spaces play an important role in harmonic analysis, as they are the natural spaces on which to consider singular integral operators. They arise in many contexts, such as when using Jacobians in non-linear partial differential equations. Recently the French participants and the Australian participants have have obtained different but related results concerning Hardy spaces of exact differential forms. The time is now ripe to construct a unified theory.
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Asymptotic Geometric Analysis and Machine Learning. Phenomena in large dimensions appear in a number of domains of Mathematics and adjacent domains of science (e.g. Computer Science), dealing with functions of infinitely growing number of parameters. Here, we focus on several questions naturally linked to Asymptotic Geometric Analysis which have natural applications to Statistical Learning Theory. We intend to use geometric, probabilistic and combinatorial methods to investigate these problems, ....Asymptotic Geometric Analysis and Machine Learning. Phenomena in large dimensions appear in a number of domains of Mathematics and adjacent domains of science (e.g. Computer Science), dealing with functions of infinitely growing number of parameters. Here, we focus on several questions naturally linked to Asymptotic Geometric Analysis which have natural applications to Statistical Learning Theory. We intend to use geometric, probabilistic and combinatorial methods to investigate these problems, with an emphasis on modern tools in Empirical Processes Theory and the theory of Random Matrices.Read moreRead less
International linkages between financial and real economy cycles. This project will develop empirical multivariate models of business cycles for different countries, and will study how they are linked via international financial markets. The significance of the project is that the models will integrate previous work done on financial-real economy links in single country settings, and it will explicitly study the effects of disequilibrium in international financial markets (such as overvaluation ....International linkages between financial and real economy cycles. This project will develop empirical multivariate models of business cycles for different countries, and will study how they are linked via international financial markets. The significance of the project is that the models will integrate previous work done on financial-real economy links in single country settings, and it will explicitly study the effects of disequilibrium in international financial markets (such as overvaluation of foreign currency) on individual economies. The project will determine the appropriate domestic monetary policy response to such shocks, and the potential for forecasting both the advent of such shocks and their impact on individual economies.Read moreRead less
What are the determinants and effects of school choice? An international comparison between Australia and the UK. The project will provide a clearer picture of the determinants of school choice, most notably the impact of economic phenomena on that choice. For Australia, this will mean we have a better understanding of the competing explanations of the growth of students at private schools over the past three decades: the role of government subsidies; the role of demographic changes; the effec ....What are the determinants and effects of school choice? An international comparison between Australia and the UK. The project will provide a clearer picture of the determinants of school choice, most notably the impact of economic phenomena on that choice. For Australia, this will mean we have a better understanding of the competing explanations of the growth of students at private schools over the past three decades: the role of government subsidies; the role of demographic changes; the effects of increased income inequality; and the role of changes in preferences towards private schools. This information will provide a better evidence base for future policy development in this area.Read moreRead less
Low-order dynamical models for non-linear fluid behaviour in quasi two-dimensional plasmas. Two complex systems in which a magnetic field imposes two-dimensional fluid motions are turbulent fusion plasmas and magnetospheric plasmas. A distinctive property of 2D flows is the inverse energy cascade, whereby energy streaming into large-scale vortices, coherent structures, or sheared flows gives a remarkable propensity for self-organizing behaviour. This can be exploited to govern or guide our respo ....Low-order dynamical models for non-linear fluid behaviour in quasi two-dimensional plasmas. Two complex systems in which a magnetic field imposes two-dimensional fluid motions are turbulent fusion plasmas and magnetospheric plasmas. A distinctive property of 2D flows is the inverse energy cascade, whereby energy streaming into large-scale vortices, coherent structures, or sheared flows gives a remarkable propensity for self-organizing behaviour. This can be exploited to govern or guide our response to such systems. We propose to investigate the dynamics of momentum and energy exchange in these plasmas, using reduced dynamical models and bifurcation and stability mathematics. Expected outcomes are improved prediction of magnetospheric substorms and confinement of fusion plasmas.
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Complex Motion Processing in Primate Visual Cortex. As we move through the world, a dynamic visual image is projected onto our retinas. The pattern of movement in the retinal image contains information about three-dimensional structure in the environment and the time of impending collisions. Our visual systems are expert at exploiting this information, enabling us to navigate through complex visual environments at a level far beyond the most sophisticated artificial systems. We plan to investiga ....Complex Motion Processing in Primate Visual Cortex. As we move through the world, a dynamic visual image is projected onto our retinas. The pattern of movement in the retinal image contains information about three-dimensional structure in the environment and the time of impending collisions. Our visual systems are expert at exploiting this information, enabling us to navigate through complex visual environments at a level far beyond the most sophisticated artificial systems. We plan to investigate complex motion processing in the primate brain by recording the responses of neurons in identified regions of the visual cortex of macaque monkeys to a range of behaviourally relevant motion stimuli.Read moreRead less