Indecomposable representation theory. The project aims to develop a systematic approach to the study and application of indecomposable representations in pure mathematics and mathematical physics. Indecomposability is a central concept in representation theory and is thus fundamental to a wide range of applications in science. Examples of important contexts considered are diagram algebras and finite and infinite-dimensional Lie algebras including the Virasoro algebra underlying conformal field t ....Indecomposable representation theory. The project aims to develop a systematic approach to the study and application of indecomposable representations in pure mathematics and mathematical physics. Indecomposability is a central concept in representation theory and is thus fundamental to a wide range of applications in science. Examples of important contexts considered are diagram algebras and finite and infinite-dimensional Lie algebras including the Virasoro algebra underlying conformal field theory. Linear algebra is a ubiquitous mathematical tool playing a pivotal role in representation theory, and the project aims to resolve outstanding fundamental issues concerning families of so-called non-diagonalisable matrices.Read moreRead less
Quantum Integrable Systems and Applications: From Condensed Matter to Quantum Information. Quantum integrable systems have produced exciting results and techniques vital in the efforts to achieve the ultimate goal of understanding quantum science beyond perturbation. The proposal gathers four world experts from Australia, Japan and Russia to work on highly interdisciplinary projects designed to resolve fundamental problems in the field, which will underpin the development of emerging technologie ....Quantum Integrable Systems and Applications: From Condensed Matter to Quantum Information. Quantum integrable systems have produced exciting results and techniques vital in the efforts to achieve the ultimate goal of understanding quantum science beyond perturbation. The proposal gathers four world experts from Australia, Japan and Russia to work on highly interdisciplinary projects designed to resolve fundamental problems in the field, which will underpin the development of emerging technologies. As a result, Australian science will be seen to be at the forefront internationally, and the leading status of Australia in the field will be greatly strengthened. Early career researchers and PhD students will be trained as part of the project, important in enhancing Australia's capability to develop and retain scientific talent. Read moreRead less
Integrable quantum systems: mathematical foundations for developing quantum science. Quantum science is an exciting and challenging area, one which will underpin the development of the next generation of computers and novel devices such as atom lasers. New mathematical techniques are being pursued, to formulate the frameworks that will provide deep insights into the complex nature of the physical principles governing this field, in order to fully realise the potential applications. This project ....Integrable quantum systems: mathematical foundations for developing quantum science. Quantum science is an exciting and challenging area, one which will underpin the development of the next generation of computers and novel devices such as atom lasers. New mathematical techniques are being pursued, to formulate the frameworks that will provide deep insights into the complex nature of the physical principles governing this field, in order to fully realise the potential applications. This project will enhance the scale of an established and internationally competitive program in mathematics research, producing new approaches to meet these demands. It will also provide opportunities for research training, important in ensuring that Australia is well equipped to play a leading role in future quantum science developments.
Read moreRead less
Algebraic Structures and Correlations in Quantum Many-Body Systems. Algebraic structures such as quantized superalgebras are among the most important discoveries in mathematics and have applications in a wide range of physics. Internationally there has been recent excitement about vertex operators and representations of these algebraic structures and their applications to integrable systems and quantum field theory. I have made significant contributions to this rapidly expanding field, and will ....Algebraic Structures and Correlations in Quantum Many-Body Systems. Algebraic structures such as quantized superalgebras are among the most important discoveries in mathematics and have applications in a wide range of physics. Internationally there has been recent excitement about vertex operators and representations of these algebraic structures and their applications to integrable systems and quantum field theory. I have made significant contributions to this rapidly expanding field, and will capitalize on this success. I will develop a comprehensive theory of these mathematical structures and their applications in the construction of correlation functions and form factors, and in so doing write a definitive monograph on the subject.Read moreRead less
Metallic nanograins: superconducting correlations, Josephson tunneling and conformal field theory. Experimental studies of aluminium grains which are a few nanometres in size have exposed unexpected physical characteristics, including pairing interactions which are responsible for bulk superconductivity. Our previous theoretical work has shown that precise information about these nanograins can be gained in the framework of the exact solution of the BCS model. This project will continue our work ....Metallic nanograins: superconducting correlations, Josephson tunneling and conformal field theory. Experimental studies of aluminium grains which are a few nanometres in size have exposed unexpected physical characteristics, including pairing interactions which are responsible for bulk superconductivity. Our previous theoretical work has shown that precise information about these nanograins can be gained in the framework of the exact solution of the BCS model. This project will continue our work in this area with an emphasis on investigating the nature of Josephson tunneling between coupled nanograins. The results of this project will have important applications in emerging technologies such as the implementation of Josephson junctions of nanoscale size.Read moreRead less
Quantum many-body systems with long-range interactions. Integrable many-body systems with long-range interactions are the subject of intense research activity worldwide, because they involve powerful mathematics and have various physical applications ranging from condensed matter physics to high energy physics. This project involves intensive collaboration between leading mathematical physics groups in Japan and Australia on exciting new developments in the theory of such systems and their appli ....Quantum many-body systems with long-range interactions. Integrable many-body systems with long-range interactions are the subject of intense research activity worldwide, because they involve powerful mathematics and have various physical applications ranging from condensed matter physics to high energy physics. This project involves intensive collaboration between leading mathematical physics groups in Japan and Australia on exciting new developments in the theory of such systems and their applications to physics. The expected outcomes are new progress in an area at the cutting edge of mathematical physics and the establishment of strong research links between Japan and Australia.Read moreRead less
Quantized Algebraic (Super) Structures and Applications. Algebraic structures such as quantized superalgebras and affine Lie (super)algebras provide a universal common algebraic framework underlying applications in a wide range of physical systems, leading to a high level of research activity worldwide. The project involves intensive collaborations between leading mathematical physics groups in China and Australia on exciting new developments in the theory of these algebraic structures and their ....Quantized Algebraic (Super) Structures and Applications. Algebraic structures such as quantized superalgebras and affine Lie (super)algebras provide a universal common algebraic framework underlying applications in a wide range of physical systems, leading to a high level of research activity worldwide. The project involves intensive collaborations between leading mathematical physics groups in China and Australia on exciting new developments in the theory of these algebraic structures and their applications to condensed matter physics and quantum field theories. The expected outcomes are significant new progress in an area at the forefront of mathematical physics and the establishment of strong research links between China and Australia.Read moreRead less
Quantum integrable models in nano and mesoscopic physics. The current advances in nanoscale and mesoscopic physics are
generating a wealth of activity with many exciting applications. This
project aims to study several theoretical aspects in three key areas;
the theory of ultrasmall metallic grains of dimensions of a few nanometres,
which through experimental work have shown characteristics which
are similar to macroscopic superconductors, the Nobel Prize
winning phenomenon of Bose-Einstei ....Quantum integrable models in nano and mesoscopic physics. The current advances in nanoscale and mesoscopic physics are
generating a wealth of activity with many exciting applications. This
project aims to study several theoretical aspects in three key areas;
the theory of ultrasmall metallic grains of dimensions of a few nanometres,
which through experimental work have shown characteristics which
are similar to macroscopic superconductors, the Nobel Prize
winning phenomenon of Bose-Einstein condensation in dilute alkali gases and the effects of magnetic impurities in strongly interacting electron systems. The approach of the project is to use the mathematical theory of exactly solvable systems to study these important areas in contemporary physics.
Read moreRead less
Yield strength and plastic flow of heterogeneous materials: Designing optimal composites and porous materials. A major goal of materials science is to design materials with improved functionality at lower weight, cost and size. It is important to guide this expensive and time-consuming process with sophisticated computer modelling. In this project we aim to model how and why composite and porous materials fail when they are placed under stress. Our results will make materials design more efficie ....Yield strength and plastic flow of heterogeneous materials: Designing optimal composites and porous materials. A major goal of materials science is to design materials with improved functionality at lower weight, cost and size. It is important to guide this expensive and time-consuming process with sophisticated computer modelling. In this project we aim to model how and why composite and porous materials fail when they are placed under stress. Our results will make materials design more efficient by providing a valuable experimental interpretive tool and a theoretical map for material optimization. Our models will also provide crucial information needed for modelling the behavior of composites in applications.Read moreRead less
Special Research Initiatives - Grant ID: SR0354741
Funder
Australian Research Council
Funding Amount
$10,000.00
Summary
Quantum Many-Body Systems Network: Breakthrough Science and Frontier Technologies. This Initiative will bring together leading researchers with complementary expertise in mathematics and the enabling sciences to form a Network fostering world leading fundamental research and innovation in quantum many-body systems. The collaborative effort between mathematicians with powerful and sophisticated new techniques and physicists and chemists with deep insight into the challenges and opportunities of t ....Quantum Many-Body Systems Network: Breakthrough Science and Frontier Technologies. This Initiative will bring together leading researchers with complementary expertise in mathematics and the enabling sciences to form a Network fostering world leading fundamental research and innovation in quantum many-body systems. The collaborative effort between mathematicians with powerful and sophisticated new techniques and physicists and chemists with deep insight into the challenges and opportunities of the quantum realm will lead to breakthrough science of vital importance to the development of frontier technologies in Australia. This Network will also place a strong emphasis on research training, the mentoring of early career researchers and establishing collaborations with leading international research groups and networks.
Read moreRead less