Novel geometric invariants. Quantum theory is the language of fundamental physics, it describes the small scale structure of matter and possibly space-time. Sophisticated models in condensed matter physics and string theory have exposed geometric and topological structure as basic building blocks of the theory. Issues thrown up by quantum theory are very similar to, and have provided techniques to solve, problems in the geometry of three and four dimensional manifolds. Exciting two way exchanges ....Novel geometric invariants. Quantum theory is the language of fundamental physics, it describes the small scale structure of matter and possibly space-time. Sophisticated models in condensed matter physics and string theory have exposed geometric and topological structure as basic building blocks of the theory. Issues thrown up by quantum theory are very similar to, and have provided techniques to solve, problems in the geometry of three and four dimensional manifolds. Exciting two way exchanges of methods, problems and solutions have emerged. This project aims to settle fundamental questions in the interaction between these two fields.Read moreRead less
Asymptotic Geometric Analysis and Learning Theory. Learning Theory is used in various real-world applications in diverse research areas, ranging from Biology (e.g. DNA sequencing) to Information Sciences. Therefore, having a deep understanding of fundamental questions in Learning Theory, and in particular, pin-pointing the parameters that make a learning problem hard would have a significant practical impact. This projects aims to achieve this goal, and in addition, we expect it would have a hig ....Asymptotic Geometric Analysis and Learning Theory. Learning Theory is used in various real-world applications in diverse research areas, ranging from Biology (e.g. DNA sequencing) to Information Sciences. Therefore, having a deep understanding of fundamental questions in Learning Theory, and in particular, pin-pointing the parameters that make a learning problem hard would have a significant practical impact. This projects aims to achieve this goal, and in addition, we expect it would have a high theoretical value, as the questions we shall address are of independent interest to pure mathematicians.Read moreRead less
Asymptotic Geometric Analysis and Learning Theory. Learning Theory is used in various real-world applications in diverse research areas, ranging from Biology (e.g. DNA sequencing) to Information Sciences. Therefore, having a deep understanding of fundamental questions in Learning Theory, and in particular, pin-pointing the parameters that make a learning problem hard would have a significant practical impact. This projects aims to achieve this goal, and in addition, we expect it would have a hig ....Asymptotic Geometric Analysis and Learning Theory. Learning Theory is used in various real-world applications in diverse research areas, ranging from Biology (e.g. DNA sequencing) to Information Sciences. Therefore, having a deep understanding of fundamental questions in Learning Theory, and in particular, pin-pointing the parameters that make a learning problem hard would have a significant practical impact. This projects aims to achieve this goal, and in addition, we expect it would have a high theoretical value, as the questions we shall address are of independent interest to pure mathematicians.
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Development of nanoporous materials for capture and release of oxygen. This project aims to develop new materials to make lighter, more efficient oxygen concentrators. The project will combine materials that can capture oxygen with particles that can be magnetically heated, making it possible to release the oxygen rapidly and efficiently when needed. Expected outcomes from this project include new composite materials and better understanding of how gases are trapped and released within composite ....Development of nanoporous materials for capture and release of oxygen. This project aims to develop new materials to make lighter, more efficient oxygen concentrators. The project will combine materials that can capture oxygen with particles that can be magnetically heated, making it possible to release the oxygen rapidly and efficiently when needed. Expected outcomes from this project include new composite materials and better understanding of how gases are trapped and released within composite materials. Benefits from this project may include oxygen concentrators that are more portable and have longer battery life, both with industrial and medical applications.Read moreRead less
Global properties of evolution on manifolds. The aim is to analyze global properties of solutions of parabolic equations on manifolds and in particular the equations associated with a family of Hormander fields.
Exploiting shear to form new structures of carbon. This project aims to create new, technologically-interesting, materials by combining shear (sliding forces) with high pressure. The work will use both modelling and experiments to understand the pathways to form new materials such as a different form of diamond that is predicted to be harder than regular diamond. Such a material could be used in coatings for cutting tools or ultra-low-scratch surfaces. Expected outcomes include both an understan ....Exploiting shear to form new structures of carbon. This project aims to create new, technologically-interesting, materials by combining shear (sliding forces) with high pressure. The work will use both modelling and experiments to understand the pathways to form new materials such as a different form of diamond that is predicted to be harder than regular diamond. Such a material could be used in coatings for cutting tools or ultra-low-scratch surfaces. Expected outcomes include both an understanding of the importance of shear in the study of high-pressure science, and as a tool to manufacture new functional materials.Read moreRead less
HARMONIC ANALYSIS AND BOUNDARY VALUE PROBLEMS FOR ELLIPTIC SYSTEMS. It is of the utmost necessity for Australia to develop the theoretical
expertise needed in the current era. The type of mathematics under
investigation here is closely allied to that needed in much of the
current boom in communication technology and medical research. The
training which would be provided to the research associates is
considerable, and would flow on to produce the expertise needed to
keep the coming gen ....HARMONIC ANALYSIS AND BOUNDARY VALUE PROBLEMS FOR ELLIPTIC SYSTEMS. It is of the utmost necessity for Australia to develop the theoretical
expertise needed in the current era. The type of mathematics under
investigation here is closely allied to that needed in much of the
current boom in communication technology and medical research. The
training which would be provided to the research associates is
considerable, and would flow on to produce the expertise needed to
keep the coming generation involved in modern technological development. I will maintain my large collaborative effort with
leading mathematicians from the US, France and other countries, thus
helping to keep Australia at the forefront of a significant field of
research.Read moreRead less
HARMONIC ANALYSIS OF ELLIPTIC SYSTEMS ON RIEMANNIAN MANIFOLDS. It is of the utmost necessity for Australia to develop the theoretical expertise needed in the current era. The type of mathematics under investigation here is closely allied to that needed in much of the current boom in communication technology and medical research. The training which would be provided to the research associates is considerable, and would flow on to produce the expertise needed to keep the coming generation invol ....HARMONIC ANALYSIS OF ELLIPTIC SYSTEMS ON RIEMANNIAN MANIFOLDS. It is of the utmost necessity for Australia to develop the theoretical expertise needed in the current era. The type of mathematics under investigation here is closely allied to that needed in much of the current boom in communication technology and medical research. The training which would be provided to the research associates is considerable, and would flow on to produce the expertise needed to keep the coming generation involved in modern technological development. I will maintain my active collaborative effort with leading mathematicians from the US, France and other countries, thus helping to keep Australia at the forefront of a significant field of research.Read moreRead less
Core-scale geodynamic rock-typing of reservoir rock. This project aims to develop a robust classification method for reservoir rock incorporating static, dynamic and mechanical attributes via multiscale digital core analysis using the concept of regional measures. Rock-types are used to populate reservoir models in a sophisticated routine of geological classification, spatial modelling and uncertainty analysis. Introducing high-resolution rock-types incorporating hydraulic properties and compact ....Core-scale geodynamic rock-typing of reservoir rock. This project aims to develop a robust classification method for reservoir rock incorporating static, dynamic and mechanical attributes via multiscale digital core analysis using the concept of regional measures. Rock-types are used to populate reservoir models in a sophisticated routine of geological classification, spatial modelling and uncertainty analysis. Introducing high-resolution rock-types incorporating hydraulic properties and compaction allows the development of a new generation of reservoir simulators. The project aims to derive a consistent high-resolution definition of rock-types incorporating compaction for petrophysical, geological and reservoir engineering purposes. This would greatly enhance our capacity to develop thinly layered reservoirs with direct applications in 4-D seismic reservoir characterisation and the development of unconventional reservoirs.Read moreRead less
HARMONIC ANALYSIS, BOUNDARY VALUE PROBLEMS, AND MAXWELL'S EQUATIONS IN LIPSCHITZ DOMAINS. Boundary value problems for partial differential equations arise naturally when physical problems are expressed in mathematical terms. This project concerns the systematic development of the harmonic analysis of partial differential operators, and of the corresponding boundary integrals in order to solve such problems on irregular regions. Particular emphasis is given to studying the behaviour of electrom ....HARMONIC ANALYSIS, BOUNDARY VALUE PROBLEMS, AND MAXWELL'S EQUATIONS IN LIPSCHITZ DOMAINS. Boundary value problems for partial differential equations arise naturally when physical problems are expressed in mathematical terms. This project concerns the systematic development of the harmonic analysis of partial differential operators, and of the corresponding boundary integrals in order to solve such problems on irregular regions. Particular emphasis is given to studying the behaviour of electromagnetic waves both inside and outside irregularly shaped surfaces, and their propagation through it.Read moreRead less