Relative quantum information theory. Quantum information encoded in relative degrees of freedom of multiple quantum systems offers striking advantages in communication and cryptography: it is immune to common types of noise and does not require reference systems shared between parties. This project aims to formulate a theory of relative quantum information, to develop practical information processing protocols that take advantage of relative encodings, and to propose proof-of-principle experim ....Relative quantum information theory. Quantum information encoded in relative degrees of freedom of multiple quantum systems offers striking advantages in communication and cryptography: it is immune to common types of noise and does not require reference systems shared between parties. This project aims to formulate a theory of relative quantum information, to develop practical information processing protocols that take advantage of relative encodings, and to propose proof-of-principle experiments in quantum optics that reveal these advantages. Expected outcomes include powerful communication and cryptographic protocols, a design for programmable quantum computation, and a fundamentally relative theory of quantum information connecting with other foundational fields of physics.Read moreRead less
Indecomposable Structure in Representation Theory and Logarithmic Conformal Field Theory. Logarithmic conformal field theory describes non-local observables in statistical models of important physical systems (eg. polymers, percolation). This realisation has led to a recent explosion of activity among physicists and mathematicians. Mathematical physics in Australia is well-placed to capitalise on this activity, having several experts working in the area, and this project will significantly aug ....Indecomposable Structure in Representation Theory and Logarithmic Conformal Field Theory. Logarithmic conformal field theory describes non-local observables in statistical models of important physical systems (eg. polymers, percolation). This realisation has led to a recent explosion of activity among physicists and mathematicians. Mathematical physics in Australia is well-placed to capitalise on this activity, having several experts working in the area, and this project will significantly augment Australia's reputation within the international community by bringing (and developing) mathematical tools and insights which complement current research strengths. Such augmentations are vital to the well-being of mathematics and physics in Australia.Read moreRead less
Geometry and representations of classical and quantum Lie supergroups. The physical notion of supersymmetry is a unifying principle which ensures that bosonic and fermionic particles in quantum physics obey the same fundamental laws. It has permeated the forefront of mathematical research since 1980s, leading to the creation of some of the deepest theories in diverse areas. The mathematical foundation of supersymmetry lies in the theory of Lie supergroups. This project addresses major outstandin ....Geometry and representations of classical and quantum Lie supergroups. The physical notion of supersymmetry is a unifying principle which ensures that bosonic and fermionic particles in quantum physics obey the same fundamental laws. It has permeated the forefront of mathematical research since 1980s, leading to the creation of some of the deepest theories in diverse areas. The mathematical foundation of supersymmetry lies in the theory of Lie supergroups. This project addresses major outstanding problems in the geometry and representations of Lie supergroups and their quantum analogues. Results will be important to the quest for a consistent quantum theory of all the four interactions in nature.Read moreRead less
Infinite Dimensional Unitarizable Representations of Lie Superalgebras. The project addresses major outstanding mathematical problems, which are of fundamental importance to the development of a unified theory of all four interactions in quantum physics. Mathematics is essential for the understanding of our own rationality. Advances in the field promised by this project are of intrinsic value. Physics is the foundation of modern technology. Success of the project will help to create a scientif ....Infinite Dimensional Unitarizable Representations of Lie Superalgebras. The project addresses major outstanding mathematical problems, which are of fundamental importance to the development of a unified theory of all four interactions in quantum physics. Mathematics is essential for the understanding of our own rationality. Advances in the field promised by this project are of intrinsic value. Physics is the foundation of modern technology. Success of the project will help to create a scientific environment in Australia that fosters technological creativity and innovation. Results of the project will greatly enhance the scientific reputation of Australia internationally, attracting foreign researchers and Ph.D students to Australian shores. Read moreRead less
Quantum algebras: their symmetries, invariants and representations. The project addresses major outstanding mathematical problems, which are of fundamental importance to theoretical physics. The algebraic structures originated from statistical mechanics will be investigated by methods of modern mathematics. Successful completion of the project will provide physicists with important new tools for investigating the symmetry of phenomena such as quantum gravity and spinor reflections. Success of th ....Quantum algebras: their symmetries, invariants and representations. The project addresses major outstanding mathematical problems, which are of fundamental importance to theoretical physics. The algebraic structures originated from statistical mechanics will be investigated by methods of modern mathematics. Successful completion of the project will provide physicists with important new tools for investigating the symmetry of phenomena such as quantum gravity and spinor reflections. Success of the project will help to create a scientific environment in Australia that fosters technological creativity and innovation. Results of the project will greatly enhance the scientific reputation of Australia internationally, attracting foreign researchers and PhD students to Australia.Read moreRead less
Algebraic Structures in Mathematical Physics and Their Applications. Algebraic structures such as affine (super)algebras, quantised algebras and vertex operator algebras are among the most important discoveries in mathematics. They provide a universal common algebraic framework underlying applications in a wide range of physics (eg. statistical mechanics, string theory, condensed matter physics etc.) leading to a high level of research activity worldwide. The project harnessess the high level ....Algebraic Structures in Mathematical Physics and Their Applications. Algebraic structures such as affine (super)algebras, quantised algebras and vertex operator algebras are among the most important discoveries in mathematics. They provide a universal common algebraic framework underlying applications in a wide range of physics (eg. statistical mechanics, string theory, condensed matter physics etc.) leading to a high level of research activity worldwide. The project harnessess the high level of expertise in mathematical physics across Australia to focus on exciting new developments in the theory of these algebraic structures and their application to physics, thus ensuring Australia plays a leading role in this rapidly expanding field.Read moreRead less
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