New frontiers in statistical mechanics. The chiral Potts model has been introduced in 1981 as a model for commensurate-incommensurate phase transitions in a layer of atoms or molecules adsorbed to a solid surface. If the adsorbed atoms all fit to holes between the surface atoms, the added layer is frozen, commensurate with the surface. If the added atoms are unable to fit holes, the added layer is no longer commensurate with the surface and could be in a floating state. A deeper understanding of ....New frontiers in statistical mechanics. The chiral Potts model has been introduced in 1981 as a model for commensurate-incommensurate phase transitions in a layer of atoms or molecules adsorbed to a solid surface. If the adsorbed atoms all fit to holes between the surface atoms, the added layer is frozen, commensurate with the surface. If the added atoms are unable to fit holes, the added layer is no longer commensurate with the surface and could be in a floating state. A deeper understanding of this and similar phenomena in layered systems has nanotechnological implications. This may affect the design of new small electronic devices or could apply to small biological systems and the development of new medicines. The project will surely lead to new applicable mathematics.Read moreRead less
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
Expressive power and complexity of temporal logics for model-checking. Hardware verification based upon mathematical logic is now routinely
used in industry to verify the correctness of large digital circuits
using a technique called model-checking. Such discrete systems move
from one state to another according to the regular ticks of a clock.
The challenge now is to find tractable methods for reasoning about
real-time systems and hybrid systems that move in a continuous manner
with respec ....Expressive power and complexity of temporal logics for model-checking. Hardware verification based upon mathematical logic is now routinely
used in industry to verify the correctness of large digital circuits
using a technique called model-checking. Such discrete systems move
from one state to another according to the regular ticks of a clock.
The challenge now is to find tractable methods for reasoning about
real-time systems and hybrid systems that move in a continuous manner
with respect to time: examples include aeroplanes flying according to
the laws of physics and a moving robot arm. We shall invent new logics
which are specifically tailored for tractable reasoning about
real-time and hybrid systems.Read moreRead less
Testimonial narratives in the post-colonial era. This project aims to benefit the Australian public by analysing some of the ways testimony has been used as a means of coming to terms with the past in Australia. It aims to amplify the significance of Australian collections, such as the Bringing Them Home Oral History archive at the National Library, both within Australia and internationally, and thereby bring Australian materials and experiences into transnational discussions of testimony and co ....Testimonial narratives in the post-colonial era. This project aims to benefit the Australian public by analysing some of the ways testimony has been used as a means of coming to terms with the past in Australia. It aims to amplify the significance of Australian collections, such as the Bringing Them Home Oral History archive at the National Library, both within Australia and internationally, and thereby bring Australian materials and experiences into transnational discussions of testimony and contested histories. It aims to benefit the research communities in Canada and Australia by providing an interpretative framework for researching and teaching testimonial materials, and by strengthening links between the two countries.Read moreRead less