The Sakai scheme-Askey table correspondence, analogues of isomonodromy and determinantal point processes. The Australian mathematical sciences enjoys two research groups with active interests on Painleve equations in applied mathematics which are able to address difficult problems. Such a problem is to give a formulation of Sakai's 2001 classification of the Painleve equations in a form most suitable for applications. For this links will be made with a seemingly distinct area of mathematics - t ....The Sakai scheme-Askey table correspondence, analogues of isomonodromy and determinantal point processes. The Australian mathematical sciences enjoys two research groups with active interests on Painleve equations in applied mathematics which are able to address difficult problems. Such a problem is to give a formulation of Sakai's 2001 classification of the Painleve equations in a form most suitable for applications. For this links will be made with a seemingly distinct area of mathematics - the Askey table from the theory of hypergeometric orthogonal polynomials. A number of tractable PhD projects are suggested by this proposal.Read moreRead less
The implications for greying Australia of international property market interlinkages. Recent events in global financial markets have had a major effect on the retirement plans of Australians and the living standards of retirees. This research will permit pension fund managers to better gauge the fundamental links that exist across international property markets, as well as provide a better understanding for both academics and practitioners on the driving forces that link international real est ....The implications for greying Australia of international property market interlinkages. Recent events in global financial markets have had a major effect on the retirement plans of Australians and the living standards of retirees. This research will permit pension fund managers to better gauge the fundamental links that exist across international property markets, as well as provide a better understanding for both academics and practitioners on the driving forces that link international real estate markets together. The research will benefit all Australians as the outcomes will result in improved risk and return performance for superannuation funds, leading to a better standard of living for all retirees.Read moreRead less
Measuring uncertainty in global housing markets and its risk to Australia. This project aims to develop and construct a measure of systemic risk for the national real-estate markets in Australia, and its main trading partners, namely China, Japan, New Zealand, United Kingdom and United States of America. Recently developed methodology will be used to investigate how real estate risks migrate across these countries over time, and during periods of financial turbulence. This methodology is intende ....Measuring uncertainty in global housing markets and its risk to Australia. This project aims to develop and construct a measure of systemic risk for the national real-estate markets in Australia, and its main trading partners, namely China, Japan, New Zealand, United Kingdom and United States of America. Recently developed methodology will be used to investigate how real estate risks migrate across these countries over time, and during periods of financial turbulence. This methodology is intended to be employed as part of a market stability surveillance program and for assessing the impact of real-estate risk on the overall economy. Early detection of the onset of future housing bubble collapses would be of significant benefit to policy makers, Australia’s trading partners, the real estate industry and ultimately home buyers.Read moreRead less
Symmetries in CR-geometry. This project aims at investigating symmetries of geometric objects called CR-manifolds. It is expected to open new avenues for understanding such symmetries at the infinitesimal level and lead to ground-breaking results in CR-geometry. Expected outcomes include new methodology, solving long-standing problems, and establishing international research collaborations. The benefits are in enhancing the strength of the research in analysis and geometry performed in Australia ....Symmetries in CR-geometry. This project aims at investigating symmetries of geometric objects called CR-manifolds. It is expected to open new avenues for understanding such symmetries at the infinitesimal level and lead to ground-breaking results in CR-geometry. Expected outcomes include new methodology, solving long-standing problems, and establishing international research collaborations. The benefits are in enhancing the strength of the research in analysis and geometry performed in Australia, in fostering the international competitiveness of Australian research and in high-quality research training.Read moreRead less
Nilpotent associative algebras and spherical hypersurfaces. This project concerns pure basic research in mathematics and is based on an important recently discovered relationship between certain geometric and algebraic objects. In the project, this relationship will be applied in a novel way to solve several significant long-standing problems in the research area of complex geometry.
The Reconstruction and Recognition Problems for Hypersurface Singularities. This project concerns pure basic research in mathematics. It is centred around a surprising relationship between geometric objects called quasi-homogeneous isolated hypersurface singularities, and algebraic structures described as Artinian Gorenstein algebras. This relationship has not been fully understood despite numerous attempts by internationally based experts to shed light on it. Armed with a novel approach to Arti ....The Reconstruction and Recognition Problems for Hypersurface Singularities. This project concerns pure basic research in mathematics. It is centred around a surprising relationship between geometric objects called quasi-homogeneous isolated hypersurface singularities, and algebraic structures described as Artinian Gorenstein algebras. This relationship has not been fully understood despite numerous attempts by internationally based experts to shed light on it. Armed with a novel approach to Artinian Gorenstein algebras, this project proposes to clarify the nature of this relationship and utilise it for solving related geometric and algebraic problems. In particular, it aims at obtaining a groundbreaking result in the area of classical invariant theory.Read moreRead less
Homotopical structures in algebraic, analytic, and equivariant geometry. This is a project for fundamental research in pure mathematics. It is focused on an emerging subfield of complex geometry concerned with spaces and maps that exhibit exceptional flexibility properties, which often go hand-in-hand with a high degree of symmetry. The project aims to develop the foundations of this new area, solve several open problems, and pursue interconnections with and applications to algebraic geometry, c ....Homotopical structures in algebraic, analytic, and equivariant geometry. This is a project for fundamental research in pure mathematics. It is focused on an emerging subfield of complex geometry concerned with spaces and maps that exhibit exceptional flexibility properties, which often go hand-in-hand with a high degree of symmetry. The project aims to develop the foundations of this new area, solve several open problems, and pursue interconnections with and applications to algebraic geometry, complex analysis, geometric invariant theory, and topology.Read moreRead less
A new class of statistical methods for analysing long memory time series models with heteroskedasticity. This project will result in a class of statistical methods that will aid policy makers and financial analysts when examining and predicting key international and Australian macroeconomic and financial variables that exhibit long memory. Leading applications of long memory modelling in the literature include GDP, CPI, asset pricing models, stock returns, exchange rates and interest rates. It w ....A new class of statistical methods for analysing long memory time series models with heteroskedasticity. This project will result in a class of statistical methods that will aid policy makers and financial analysts when examining and predicting key international and Australian macroeconomic and financial variables that exhibit long memory. Leading applications of long memory modelling in the literature include GDP, CPI, asset pricing models, stock returns, exchange rates and interest rates. It will be possible to robustly and efficiently analyse such series in the presence of changes in variability, such as the overall reduction in variability that has occurred since the 1970's, called the "Great Moderation". The utility of the new methods will be demonstrated by a robust and efficient analysis of the Purchasing Power Parity hypothesis.Read moreRead less
Why is most of the genetic variance for complex traits undetected by large powerful screens of common variants? The genomics revolution has made it possible to measure thousands of DNA variants in individuals. These variants have been associated with phenotypic outcomes in a range of species. Paradoxically, even very large studies have only accounted for a fraction of the resemblance between relatives that we know exist. Our study will test three specific hypotheses to explain this paradox. A be ....Why is most of the genetic variance for complex traits undetected by large powerful screens of common variants? The genomics revolution has made it possible to measure thousands of DNA variants in individuals. These variants have been associated with phenotypic outcomes in a range of species. Paradoxically, even very large studies have only accounted for a fraction of the resemblance between relatives that we know exist. Our study will test three specific hypotheses to explain this paradox. A better understanding about the genetic architecture for complex traits will improve the efficiency of gene mapping methods, including applications in humans for traits related to productive ageing and a healthy start to life, will lead to more efficient selection programs in agricultural populations and will inform us with respect to past evolutionary events.Read moreRead less
Australian Real Time Data: Construction, Analysis and Implications for Real Time Policy Making. This first comprehensive macroeconomic real time database for Australia recording the actual data available to policy makers at the time of making decisions will serve as a standard reference for accurate ex post macroeconomic policy evaluation and for accurate forecasts and decision making which are robust to data revisions. The free database will be of interest to Australian researchers, economists, ....Australian Real Time Data: Construction, Analysis and Implications for Real Time Policy Making. This first comprehensive macroeconomic real time database for Australia recording the actual data available to policy makers at the time of making decisions will serve as a standard reference for accurate ex post macroeconomic policy evaluation and for accurate forecasts and decision making which are robust to data revisions. The free database will be of interest to Australian researchers, economists, forecasters and policy makers. Readily applicable and interpretable forecasts of the business cycle and the current state of the Australian (and US) economy (e.g. likelihood of recessions or inflation) will be of direct relevance to Australian policy-makers in Government, the Reserve Bank of Australia, and to the Australian decision-makers. Read moreRead less