Fractional analytic index theory. Atiyah-Singer index theory, for which M.F. Atiyah and I.M. Singer received the 2004 Abel Prize, has stimulated considerable interaction between mathematicians and mathematical physicists. An extension of this theory is Fractional Index Theory, co-invented by R.B. Melrose, I.M. Singer and myself, which has received international attention, having solved a fundamental open problem. A central aim in my research project is to extend our theory to elliptic boundary ....Fractional analytic index theory. Atiyah-Singer index theory, for which M.F. Atiyah and I.M. Singer received the 2004 Abel Prize, has stimulated considerable interaction between mathematicians and mathematical physicists. An extension of this theory is Fractional Index Theory, co-invented by R.B. Melrose, I.M. Singer and myself, which has received international attention, having solved a fundamental open problem. A central aim in my research project is to extend our theory to elliptic boundary value problems. I will assist beginners to navigate to the cutting edge of research through workshops, spring-schools and supervision. Benefits include the enhancement of Australia's position in the forefront of international research.Read moreRead less
Global aspects of dualities in String Theory in the presence of background fluxes. String Theory, known to the general public as the "Theory of Everything', is currently an extremely active area of research internationally. It has not only stimulated considerable interaction between mathematical physicists and mathematicians, but also increased public interest in science through television programs and books. Unfortunately, the majority of the Australian scientific community has not yet caught ....Global aspects of dualities in String Theory in the presence of background fluxes. String Theory, known to the general public as the "Theory of Everything', is currently an extremely active area of research internationally. It has not only stimulated considerable interaction between mathematical physicists and mathematicians, but also increased public interest in science through television programs and books. Unfortunately, the majority of the Australian scientific community has not yet caught up with these developments. Our recent papers, all published in premier journals in this field, have not only received widespread international attention but have also increased the profile of String Theory amongst Australia's mathematicians and mathematical physicists. The proposed project is expected to continue this trend.Read moreRead less
Twisted K-theory and its application to String Theory and Conformal Field Theory. String Theory is, at present, the only consistent theory of quantum gravity. Recently, twisted K-theory was proposed as the algebraic structure underlying the classification of D-branes, i.e. solitonic extended objects, in certain closed string backgrounds. In this project we aim to advance our understanding of the properties of twisted K-theory in the context of String Theory and Conformal Field Theory. The ult ....Twisted K-theory and its application to String Theory and Conformal Field Theory. String Theory is, at present, the only consistent theory of quantum gravity. Recently, twisted K-theory was proposed as the algebraic structure underlying the classification of D-branes, i.e. solitonic extended objects, in certain closed string backgrounds. In this project we aim to advance our understanding of the properties of twisted K-theory in the context of String Theory and Conformal Field Theory. The ultimate goal is to find the appropriate K-theory classifying D-branes in arbitrary closed string backgrounds or, similarly, classifying boundary Conformal Field Theories. It has already emerged that the K-theory of C*-algebras will play an important role.Read moreRead less
Dualities in String Theory and Conformal Field Theory in the context of the Geometric Langlands Program. The Langlands program ties together seemingly unrelated areas of Mathematics. Recently, in the context of the Geometric Langlands correspondence, novel connections with Theoretical Physics have emerged, thus becoming one of the most active areas of research in both Mathematics and Theoretical Physics. Australia has a number of world-renowned experts, including the two CI's, in various aspect ....Dualities in String Theory and Conformal Field Theory in the context of the Geometric Langlands Program. The Langlands program ties together seemingly unrelated areas of Mathematics. Recently, in the context of the Geometric Langlands correspondence, novel connections with Theoretical Physics have emerged, thus becoming one of the most active areas of research in both Mathematics and Theoretical Physics. Australia has a number of world-renowned experts, including the two CI's, in various aspects of the Langlands program, and is therefore well-placed to make seminal contributions. Being involved in these new developments is of crucial importance to the health of Mathematics and Theoretical Physics in Australia. An integral part of this proposal is student involvement and postgraduate training.Read moreRead less
Study of mathematical models of evolution using the theory of quantum games - strengthening the theoretical foundation of quantum computation. The fields of nanotechnology, quantum technology and quantum information processing are rapidly converging. This project aims to provide a novel approach in the fundamental understanding of quantum computation/information by using methods inspired by mathematics of evolutionary competition. The project will contribute towards the theoretical foundations o ....Study of mathematical models of evolution using the theory of quantum games - strengthening the theoretical foundation of quantum computation. The fields of nanotechnology, quantum technology and quantum information processing are rapidly converging. This project aims to provide a novel approach in the fundamental understanding of quantum computation/information by using methods inspired by mathematics of evolutionary competition. The project will contribute towards the theoretical foundations of quantum computation by complementing efforts of several groups in Australia collaborating on the experimental design of quantum computers. The outcome of this project will contribute towards the successful operation of quantum computers and will help maintain Australia's position in the global forefront of quantum computation/information.
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Normal forms and Chern-Moser connection in the study of Cauchy-Riemann Manifolds. This research project is aimed at a systematic study of Cauchy-Riemann manifolds, their holomorphic mappings and automorphisms, by means of a unifying approach based on
Chern-Moser type normal forms. The importance of Cauchy-Riemann manifolds stems from the fact that they bridge complex structure and holomorphy with the Riemannian nature of real manifolds. Construction of an analogue of the Chern-Moser normal form ....Normal forms and Chern-Moser connection in the study of Cauchy-Riemann Manifolds. This research project is aimed at a systematic study of Cauchy-Riemann manifolds, their holomorphic mappings and automorphisms, by means of a unifying approach based on
Chern-Moser type normal forms. The importance of Cauchy-Riemann manifolds stems from the fact that they bridge complex structure and holomorphy with the Riemannian nature of real manifolds. Construction of an analogue of the Chern-Moser normal form for multicodimensional Levi-nondegenerate CR-manifolds and extension of CR-mappings between them are major goals in complex analysis. Identification of Chern-Moser chains and equivariant linearisation of isotropy automorphisms are major goals in geometry.Read moreRead less
Very high energy gamma-ray astronomy in Australia and the development of future gamma-ray detectors. Australia contributes to the burgeoning field of ground-based gamma-ray astronomy via its involvement in the CANGAROO-III project.
I will continue the development of CANGAROO-III and establish links with the other collaborations in this field, in particular H.E.S.S., also in the southern hemisphere. Studies with CANGAROO-III of high energy gamma-ray sources such as supernova remnants and active ....Very high energy gamma-ray astronomy in Australia and the development of future gamma-ray detectors. Australia contributes to the burgeoning field of ground-based gamma-ray astronomy via its involvement in the CANGAROO-III project.
I will continue the development of CANGAROO-III and establish links with the other collaborations in this field, in particular H.E.S.S., also in the southern hemisphere. Studies with CANGAROO-III of high energy gamma-ray sources such as supernova remnants and active galaxies will finally reveal the type of particles that are accelerated in such violent regions of our universe. The development of future ground-based gamma-ray detectors beyond CANGAROO-III is also a project aim, and will expand the energy coverage of gamma-ray detectors into uncharted territory.Read moreRead less
Collision data for lighting industry and plasma modeling. The project's primary aim is to progress the design of more efficient
and environmentally friendly light sources. Given the number of light
sources in use worldwide even a small improvement in the efficiency
could lead to enormous benefits to society via reduction of energy
consumption. Design of new mercury-free light sources will eliminate a
major neuro-toxin pollution source. Collaboration with research groups
at the OSRAM-SYLVA ....Collision data for lighting industry and plasma modeling. The project's primary aim is to progress the design of more efficient
and environmentally friendly light sources. Given the number of light
sources in use worldwide even a small improvement in the efficiency
could lead to enormous benefits to society via reduction of energy
consumption. Design of new mercury-free light sources will eliminate a
major neuro-toxin pollution source. Collaboration with research groups
at the OSRAM-SYLVANIA Corporation (USA) and Sheffield University (UK)
will herald the beginning of industrial application for our successful
atomic collisions research program. The previous substantial ARC
investment towards this fundamental science program has now enabled
practical application.Read moreRead less
The Quest for Ultimate Measurement Precision. Precision measurement is the foundation upon which modern technological society is built. The highest quality measurement devices rely on stable clocks for their operation. The group's existing research has been aimed at developing some of the world's most precise measurement tools based on clocks and lasers. In parallel with this, other scientists have developed the means for exquisite control of light on the microscopic scale. By combining these tw ....The Quest for Ultimate Measurement Precision. Precision measurement is the foundation upon which modern technological society is built. The highest quality measurement devices rely on stable clocks for their operation. The group's existing research has been aimed at developing some of the world's most precise measurement tools based on clocks and lasers. In parallel with this, other scientists have developed the means for exquisite control of light on the microscopic scale. By combining these two technologies, both of which lie at the extreme limit of precision, the group will develop a new generation of technology for fundamental science objectives as well as for industrial needs.Read moreRead less
Development and study of a new theory of gravity. Gravity is thought to be an understood physical phenomena. But recently dramatic discoveries have revealed that major aspects of this phenomenon have been completely missed. This research project will develop and explore implications of these discoveries. At one level this project is about major breakthroughs in fundamental science, but discoveries are revealing space to be a complex dynamic system, and new technologies to detect and exp ....Development and study of a new theory of gravity. Gravity is thought to be an understood physical phenomena. But recently dramatic discoveries have revealed that major aspects of this phenomenon have been completely missed. This research project will develop and explore implications of these discoveries. At one level this project is about major breakthroughs in fundamental science, but discoveries are revealing space to be a complex dynamic system, and new technologies to detect and exploit this are foreseen. There is some evidence that space is a self-organising information system of a totally new kind, and this will also have applications. At a scientific level these developments will attract considerable international attention and will enthuse younger researchersRead moreRead less