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.
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
Noncommutative geometry in representation theory and quantum physics. One of the most important problems in natural science is to understand the structure of spacetime at the Planck scale. Mathematical investigations in recent years have predicted that at this scale, spacetime becomes noncommutative. Taking this noncommutativity into account, the project brings together geometry, algebra and quantum mechanics to develop new mathematical theories required for addressing the problem. It promises ....Noncommutative geometry in representation theory and quantum physics. One of the most important problems in natural science is to understand the structure of spacetime at the Planck scale. Mathematical investigations in recent years have predicted that at this scale, spacetime becomes noncommutative. Taking this noncommutativity into account, the project brings together geometry, algebra and quantum mechanics to develop new mathematical theories required for addressing the problem. It promises to make fundamental contributions to both mathematics and theoretical physics. 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