Stability conditions on triangulated categories and related aspects of homological mirror symmetry. The proposed research studies one of the deepest questions in nature through superstring theory and mathematics with leading experts around the world. So, the proposed project maintains the Australia's profile in science. Also, the proposed project fits within the the Research Priority: Frontier Technologies for Building and Transforming Australian Industries. We will have exciting mathematical di ....Stability conditions on triangulated categories and related aspects of homological mirror symmetry. The proposed research studies one of the deepest questions in nature through superstring theory and mathematics with leading experts around the world. So, the proposed project maintains the Australia's profile in science. Also, the proposed project fits within the the Research Priority: Frontier Technologies for Building and Transforming Australian Industries. We will have exciting mathematical discussions which stimulate Australian students. They will be able to take advantage of such experience, especially when they need innovation. Thus, it is an investment for future of Australian industries.Read moreRead less
Generalized Geometries and their Applications. Geometry is one of the pillars of both ancient and modern mathematics. It also plays a vital role in many scientific applications, in particular in physics. Progress on the mathematical aspects and the applications have often gone hand in hand, as for example with differential geometry and general relativity. Geometry is a very fruitful area for interdisciplinary research.
Australia has a long tradition and a recognized research strength in Mat ....Generalized Geometries and their Applications. Geometry is one of the pillars of both ancient and modern mathematics. It also plays a vital role in many scientific applications, in particular in physics. Progress on the mathematical aspects and the applications have often gone hand in hand, as for example with differential geometry and general relativity. Geometry is a very fruitful area for interdisciplinary research.
Australia has a long tradition and a recognized research strength in Mathematical Physics, and this project will contribute to maintaining that status. An integral part of this proposal is student involvement and postgraduate research training, for which the topic lends itself particularly well.Read moreRead less
Noncommutative geometry: new frontiers. This project is at the leading edge of fundamental mathematics and will result in important scientific advances. As a result Australian science will be seen to be at the forefront internationally. This area of mathematics is having a high impact at the moment so that research training is an important aspect. There will be PhD students trained as part of the project and honours students exposed to the latest advances. Australians would normally need to go ....Noncommutative geometry: new frontiers. This project is at the leading edge of fundamental mathematics and will result in important scientific advances. As a result Australian science will be seen to be at the forefront internationally. This area of mathematics is having a high impact at the moment so that research training is an important aspect. There will be PhD students trained as part of the project and honours students exposed to the latest advances. Australians would normally need to go to leading international centres such as Paris to partake in projects of this nature. That high profile research of this kind can be done in Australia will enhance our capacity to retain scientific talent.Read moreRead less
Energy, Cosmic Censorship and Black Hole Stability. Human progress is achieved by confronting fundamental questions, at the leading edge of knowledge. This project will lead to better understanding of space-time physics, and of the properties of singular solutions of non-linear hyperbolic equations. Such equations govern a wide range of physical phenomena, including fluid flow, weather and electromagnetic fields.
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
Noncommutative geometry and applications. Noncommutative geometry is a new field of mathematical research having its origins in quantum mechanics. The main feature of this theory is that it deals with geoemtric and topological aspects of objects for which the order in which we make measurements or perform operations or observations is relevant to the outcome. This happens with microscopic systems especially those at the atomic or subatomic length scale. The methods have been motivated by and fou ....Noncommutative geometry and applications. Noncommutative geometry is a new field of mathematical research having its origins in quantum mechanics. The main feature of this theory is that it deals with geoemtric and topological aspects of objects for which the order in which we make measurements or perform operations or observations is relevant to the outcome. This happens with microscopic systems especially those at the atomic or subatomic length scale. The methods have been motivated by and found application in condensed matter physics, string theory, random media, algebraic structures and the geometry and topology of manifoldsRead moreRead less