Free parafermions: a challenge for non-Hermitian physics. This project aims to calculate and understand the physical properties of free parafermions. Parafermions have attracted interest in topological schemes for quantum computation because they are computationally more powerful than Majorana fermions. The core of this project is a fundamental model of free parafermions, which has been shown to exhibit unexplained puzzling properties. The project outcomes include an in-depth understanding of th ....Free parafermions: a challenge for non-Hermitian physics. This project aims to calculate and understand the physical properties of free parafermions. Parafermions have attracted interest in topological schemes for quantum computation because they are computationally more powerful than Majorana fermions. The core of this project is a fundamental model of free parafermions, which has been shown to exhibit unexplained puzzling properties. The project outcomes include an in-depth understanding of this model by taking the non-Hermitian features into account, establishing a connection with open quantum systems. Non-Hermitian systems are also of increasing relevance in physics, especially in quantum optics. The project also aims to contribute to training researchers in the mathematical sciences.
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The Ricci curvature of homogeneous spaces. The geometry of homogeneous spaces is an area of research with applications in numerous fields, including topology, harmonic analysis, relativity and quantum theory. This project aims to resolve a fundamental problem in this area, known as the prescribed Ricci curvature problem for homogeneous metrics, and to settle the important and closely related question of Ricci iteration existence and convergence. Moreover, the project aims to exploit the interpla ....The Ricci curvature of homogeneous spaces. The geometry of homogeneous spaces is an area of research with applications in numerous fields, including topology, harmonic analysis, relativity and quantum theory. This project aims to resolve a fundamental problem in this area, known as the prescribed Ricci curvature problem for homogeneous metrics, and to settle the important and closely related question of Ricci iteration existence and convergence. Moreover, the project aims to exploit the interplay between geometry and algebra to provide new insight into the physically significant problem of classifying unitary Lie algebra representations. This project is expected to facilitate interdisciplinary interaction leading to exciting developments across a range of fields.Read moreRead less
New approaches and applications of integrable quantum field theory. This project aims to develop new mathematical approaches to the theory of integrable systems to obtain exact solutions of various non-linear models of two-dimensional quantum field theory. The project is based on an unexpected correspondence between classical and quantum systems which provides a powerful method for describing physically interesting models of integrable quantum field theory. Expected outcomes include exact soluti ....New approaches and applications of integrable quantum field theory. This project aims to develop new mathematical approaches to the theory of integrable systems to obtain exact solutions of various non-linear models of two-dimensional quantum field theory. The project is based on an unexpected correspondence between classical and quantum systems which provides a powerful method for describing physically interesting models of integrable quantum field theory. Expected outcomes include exact solutions to non-linear sigma-models which have important applications in many areas, including condensed matter physics, string and field theories and Riemannian geometry. The project expects to provide significant benefit to the advancement of knowledge in physics and mathematics.Read moreRead less
Topological insulators and free fermions: from Hermitian to non-Hermitian. This project aims to develop and fully understand a class of mathematical models describing fundamental interacting systems of particles of central importance in the physics of topological insulators. This will include the extension of exact solutions to more complicated models and the development and application of topological data analysis for detecting topological phase transitions in these and more general materials. ....Topological insulators and free fermions: from Hermitian to non-Hermitian. This project aims to develop and fully understand a class of mathematical models describing fundamental interacting systems of particles of central importance in the physics of topological insulators. This will include the extension of exact solutions to more complicated models and the development and application of topological data analysis for detecting topological phase transitions in these and more general materials. The project will also apply diagrammatic methods to address a long-standing challenge in solving a particular model. The project aims to contribute to training researchers in an area of the mathematical sciences of benefit to the future development of new concepts for next-generation electronic devices and smart materials.Read moreRead less
Reaching new frontiers of quantum fields and gravity through deformations. This project aims to reach new frontiers in quantum field and gravity theories. These underpin systems ranging from semi-conductors to particle collisions and the quantum behavior of black holes. An obstacle is that these theories are notoriously hard to solve. This project proposes to tackle this longstanding problem by using new deformations, symmetries and dualities that have attracted widespread attention. Expected ou ....Reaching new frontiers of quantum fields and gravity through deformations. This project aims to reach new frontiers in quantum field and gravity theories. These underpin systems ranging from semi-conductors to particle collisions and the quantum behavior of black holes. An obstacle is that these theories are notoriously hard to solve. This project proposes to tackle this longstanding problem by using new deformations, symmetries and dualities that have attracted widespread attention. Expected outcomes will include innovative techniques that will greatly enhance and interconnect our knowledge of field theories and quantum gravity, together with new discoveries in quantum-corrected geometries. A new network of domestic and international experts will largely benefit the fields of theoretical and mathematical physics.Read moreRead less
Unravelling the neutron lifetime puzzle with lattice quantum chromodynamics. This project will perform supercomputer simulations to confront one of the outstanding puzzles of nuclear and particle physics, the neutron lifetime. New knowledge will be generated through the development of novel theoretical and numerical techniques to increase the precision of the leading theoretical inputs required to predict the neutron lifetime. The outcomes will provide crucial theoretical guidance into understan ....Unravelling the neutron lifetime puzzle with lattice quantum chromodynamics. This project will perform supercomputer simulations to confront one of the outstanding puzzles of nuclear and particle physics, the neutron lifetime. New knowledge will be generated through the development of novel theoretical and numerical techniques to increase the precision of the leading theoretical inputs required to predict the neutron lifetime. The outcomes will provide crucial theoretical guidance into understanding the neutron; helping to guide the next-generation neutron experiments, from particle physics to applications in advanced materials science. The results will have immediate benefit by resolving the neutron lifetime puzzle, while enabling Australian scientists to take a leadership role in this area of fundamental science.Read moreRead less
ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. The ARC Centre for the Mathematical Analysis of Cellular Systems aims to deliver the mathematics required to compute life. The Centre will deliver innovation in computational and mathematical biology and establish in silico biology alongside in vivo and in vitro biology. These models will allow us to understand the complexity of life at the cellu ....ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. The ARC Centre for the Mathematical Analysis of Cellular Systems aims to deliver the mathematics required to compute life. The Centre will deliver innovation in computational and mathematical biology and establish in silico biology alongside in vivo and in vitro biology. These models will allow us to understand the complexity of life at the cellular level and enable new ways of combining diverse and heterogenous data. This will allow us to understand the mechanisms underlying cellular behaviour, and to apply rational design engineering methods in order to control the dynamics of biological systems. Read moreRead less
Quantum tunnelling of composite systems. This project aims to investigate profound physics problem of quantum tunnelling of composite systems such as atoms, molecules and atomic nuclei. Using new theoretical concepts and tools to describe low-energy fusion between atomic nuclei, this project is expected to generate new knowledge and improve understanding of nuclear reactions, the formation of elements in the cosmos, and underpin future nuclear technologies. The project aims to leverage Australia ....Quantum tunnelling of composite systems. This project aims to investigate profound physics problem of quantum tunnelling of composite systems such as atoms, molecules and atomic nuclei. Using new theoretical concepts and tools to describe low-energy fusion between atomic nuclei, this project is expected to generate new knowledge and improve understanding of nuclear reactions, the formation of elements in the cosmos, and underpin future nuclear technologies. The project aims to leverage Australian capacity in quantum and nuclear theory to produce the first predictive model of quantum tunnelling with a modern microscopic treatment of nuclear dynamics. It will provide new theoretical guidance to experimental programs with exotic beams and focussing on nucleosynthesis.Read moreRead less