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
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
Modular Index Theory. This project capitilises on Australian advances in mathematics, particularly noncommutative geometry. It will maintain and extend Australia's prominence in this subject, providing excellent opportunities for young researchers via the research networks this project will establish. Being at the interface of ideas in mathematics and physics, there is potential for future technological spin offs for Australia.
Linear Dynamical Quantum Networks: Synthesis and Control. Australia is recognized as a leader in the international race to develop quantum technologies of the future. This project will strengthen Australia's profile in quantum technology engineering by developing a new theory for building arbitrary complex linear quantum mechanical control systems for control tasks in quantum technology, and presenting new control system design tools to support high performance quantum communication systems. The ....Linear Dynamical Quantum Networks: Synthesis and Control. Australia is recognized as a leader in the international race to develop quantum technologies of the future. This project will strengthen Australia's profile in quantum technology engineering by developing a new theory for building arbitrary complex linear quantum mechanical control systems for control tasks in quantum technology, and presenting new control system design tools to support high performance quantum communication systems. The project outcomes together with advances in experimental physics are anticipated to play an important role in the long term as enablers of viable quantum technologies that can provide new commercial opportunities for Australian hi-tech industries to benefit Australia's economy in the future.Read moreRead less
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
Quantum Networks: Dynamics, Design and Control. The outcomes of this project have the potential to enhance the ability of researchers in Australia to invent significant new quantum technologies. The outcomes will provide researchers with new ways to consider architecture design for quantum technologies, new concepts and tools to help them model devices and systems, to interconnect them, to control them, to build them, and to understand how they behave. This will help place Australia in a leadi ....Quantum Networks: Dynamics, Design and Control. The outcomes of this project have the potential to enhance the ability of researchers in Australia to invent significant new quantum technologies. The outcomes will provide researchers with new ways to consider architecture design for quantum technologies, new concepts and tools to help them model devices and systems, to interconnect them, to control them, to build them, and to understand how they behave. This will help place Australia in a leading position internationally to engineer new quantum technologies.Read moreRead less
New quantum and robust control theory with applications to quantum optics. The application of quantum mechanics to the creation of quantum technology promises to be one of the most exciting technological developments of this century. Possible applications of quantum technologies include vastly improved sensors to search for minerals or gravity waves, secure quantum cryptography, and quantum computing. Quantum feedback control is a key tool in quantum technology. This project will lay the fou ....New quantum and robust control theory with applications to quantum optics. The application of quantum mechanics to the creation of quantum technology promises to be one of the most exciting technological developments of this century. Possible applications of quantum technologies include vastly improved sensors to search for minerals or gravity waves, secure quantum cryptography, and quantum computing. Quantum feedback control is a key tool in quantum technology. This project will lay the foundations of systematic theories of robust, coherent and nonlinear quantum feedback control and lead to advances in the control of highly resonant systems which underlie experimental quantum and nano technology. This will enable Australia to reap great benefits as this new technological area emerges.Read moreRead less
Self-assembly and complexity: networks and patterns from materials to markets. Self-assembly leads the formation of patterns without external directing agents. It is responsible for the growth of complex multiscale structures found in biology and materials science and is a crucial concept for development of viable nanotechnologies. Complex systems, from biological ecosystems to financial markets and the Internet, are also characterized by spontaneous clustering and linkages that determine their ....Self-assembly and complexity: networks and patterns from materials to markets. Self-assembly leads the formation of patterns without external directing agents. It is responsible for the growth of complex multiscale structures found in biology and materials science and is a crucial concept for development of viable nanotechnologies. Complex systems, from biological ecosystems to financial markets and the Internet, are also characterized by spontaneous clustering and linkages that determine their collective behaviour. The project will investigate in detail the geometry, topology, materials science and statistical physics of networks, leading to design and characterization of robust self-assembled materials and complex systems.Read moreRead less
The mathematics and physics of interacting systems. Much of the world around us involves the networked interaction between a large number of components. For example, such complex networks may be physical, biological, social or technical in nature and represent connections between magnetic spins, species, people or computers. This Project will provide a firm theoretical foundation for such complex interacting systems through an investigation of the fascinating mathematics and physics behind them. ....The mathematics and physics of interacting systems. Much of the world around us involves the networked interaction between a large number of components. For example, such complex networks may be physical, biological, social or technical in nature and represent connections between magnetic spins, species, people or computers. This Project will provide a firm theoretical foundation for such complex interacting systems through an investigation of the fascinating mathematics and physics behind them. This perspective from mathematical physics, in particular using the tools of statistical mechanics, will lead to a better understanding of many real-world complex systems.Read moreRead less