Advances in Conformal Field Theory with Extended Symmetry. This project aims to develop novel methods to formulate conformal field theories with extended symmetry that are important in variety of applications ranging from pure mathematics to phenomenology of elementary particles. The project expects to advance our knowledge in the most challenging areas of modern theoretical physics - Quantum Gravity and physics beyond the Standard Model of particle physics. Its expected outcomes will include co ....Advances in Conformal Field Theory with Extended Symmetry. This project aims to develop novel methods to formulate conformal field theories with extended symmetry that are important in variety of applications ranging from pure mathematics to phenomenology of elementary particles. The project expects to advance our knowledge in the most challenging areas of modern theoretical physics - Quantum Gravity and physics beyond the Standard Model of particle physics. Its expected outcomes will include conceptual results of major significance for modern theoretical and mathematical physics, thus placing Australia at the forefront of this research. A rich intellectual environment will be provided for training Australian PhD students by internationally recognised experts.
Read moreRead less
Conformal Field Theories with Higher Spin Symmetry and Duality Invariance. This project aims to develop novel methods to study conformal field theories with higher spin symmetry and duality invarianvce that are important in variety of applications ranging from cosmology to phenomenology of elementary particles. The project expects to advance our knowledge in one of the most challenging areas of modern theoretical physics - Quantum Gravity and physics beyond the Standard Model of particle physics ....Conformal Field Theories with Higher Spin Symmetry and Duality Invariance. This project aims to develop novel methods to study conformal field theories with higher spin symmetry and duality invarianvce that are important in variety of applications ranging from cosmology to phenomenology of elementary particles. The project expects to advance our knowledge in one of the most challenging areas of modern theoretical physics - Quantum Gravity and physics beyond the Standard Model of particle physics. Its expected outcomes will be new conceptual results of major significance for modern theoretical and mathematical physics, thus placing Australia at the forefront of this research. Benefits will include a rich intellectual environment for training Australian PhD students by internationally recognised experts.
Read moreRead less
Supersymmetry and supergravity: new approaches and applications. This project aims to advance our understanding of supersymmetric quantum field, gravity, and higher-spin theories. Supersymmetry and supergravity play crucial roles in modern developments in fundamental particle physics and cosmology. They also have rich connections with many branches of mathematical physics. Major conceptual questions in the description of general supergravity-matter couplings are still unsolved. By performing sta ....Supersymmetry and supergravity: new approaches and applications. This project aims to advance our understanding of supersymmetric quantum field, gravity, and higher-spin theories. Supersymmetry and supergravity play crucial roles in modern developments in fundamental particle physics and cosmology. They also have rich connections with many branches of mathematical physics. Major conceptual questions in the description of general supergravity-matter couplings are still unsolved. By performing state of the art analysis in supergravity and holographic dualities, the project will advance our understanding of quantum gravity, black holes, and cosmology placing Australia at the forefront of these important research fields.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE230100954
Funder
Australian Research Council
Funding Amount
$354,968.00
Summary
Partial Differential Equations, geometric aspects and applications. The study of Partial Differential Equations (PDEs) is a classical and prolific field of research having a fundamental role in the development of mathematical analysis and motivated by important applications in natural and applied sciences.
This project aims to obtain substantial progress in the field of PDEs. The area of mathematical research covered is extremely broad, at the confluence of analysis and geometry, and with many a ....Partial Differential Equations, geometric aspects and applications. The study of Partial Differential Equations (PDEs) is a classical and prolific field of research having a fundamental role in the development of mathematical analysis and motivated by important applications in natural and applied sciences.
This project aims to obtain substantial progress in the field of PDEs. The area of mathematical research covered is extremely broad, at the confluence of analysis and geometry, and with many applications to other areas of mathematics and natural and applied sciences. The results that will be obtained will produce a significant amount of new knowledge in this extremely difficult, but rapidly growing, field, by exploiting international scientific collaborations and interdisciplinary methods.Read moreRead less
Brain-skull interface: discovering the missing piece of head biomechanics. Overall objective of this project is to measure, mathematically describe and implement in software mechanical properties of brain-skull interface – a critical component of current large and sophisticated computational models of the brain and the last missing piece of brain biomechanics knowledge. This will allow increased reliability of comprehensive biomechanical models used to simulate realistic injury and surgery scena ....Brain-skull interface: discovering the missing piece of head biomechanics. Overall objective of this project is to measure, mathematically describe and implement in software mechanical properties of brain-skull interface – a critical component of current large and sophisticated computational models of the brain and the last missing piece of brain biomechanics knowledge. This will allow increased reliability of comprehensive biomechanical models used to simulate realistic injury and surgery scenarios.
The problem is significant and urgent. Every year in Australia, there are over 22,000 cases of traumatic brain injury, some of which could be prevented by better passive and active countermeasures; and over 12,000 neurosurgical procedures that surgical simulation could make more accurate and therefore safer.Read moreRead less
Mathematical and computational models for agrichemical retention on plants. Mathematical and computational models for agrichemical retention on plants. This project aims to build interactive software that simulates agrichemical spraying for multiple virtual plants reconstructed from scanned data. Mathematical modelling and computer simulation could offer an alternative to expensive experimental programs for agrichemical spraying of plants. This project will use contemporary fluid mechanics to bu ....Mathematical and computational models for agrichemical retention on plants. Mathematical and computational models for agrichemical retention on plants. This project aims to build interactive software that simulates agrichemical spraying for multiple virtual plants reconstructed from scanned data. Mathematical modelling and computer simulation could offer an alternative to expensive experimental programs for agrichemical spraying of plants. This project will use contemporary fluid mechanics to build practical mathematical models for droplet impaction, spreading and evaporation on leaf surfaces, and experimentally calibrate and validate the models. The software is expected to drive the development of agrichemical products that increase retention, minimise environmental impacts, and reduce costs for end-users.Read moreRead less
Complexity of group algorithms and statistical fingerprints of groups. This project aims to shape the next generation of efficient randomised algorithms in the field of group theory, the mathematics of symmetry. Fundamental mathematics underpins modern technological tasks such as web searches, sorting and data compression. This project aims to determine characteristic statistical fingerprints of key building-block groups. These group statistics lead to much faster procedures to essentially facto ....Complexity of group algorithms and statistical fingerprints of groups. This project aims to shape the next generation of efficient randomised algorithms in the field of group theory, the mathematics of symmetry. Fundamental mathematics underpins modern technological tasks such as web searches, sorting and data compression. This project aims to determine characteristic statistical fingerprints of key building-block groups. These group statistics lead to much faster procedures to essentially factor huge groups into smaller building-block groups in a manner akin to factoring an integer into its prime factors. The anticipated goal is to include the outcomes in publicly available symbolic algebra computer packages. As the theory of symmetry has broad applications in the mathematical and physical sciences, there is the potential for far reaching benefits.Read moreRead less
New perspectives on nonlocal equations. This project aims at tackling cutting-edge problems in the field of mathematical analysis, with specific focus on nonlocal equations, by introducing innovative approaches and a unified perspective. It focuses on the use of long-range interactions to deeply understand new effects arising in several mathematical problems of great impact.
The research will be performed through stimulating international collaborations, providing exchange opportunities and idea ....New perspectives on nonlocal equations. This project aims at tackling cutting-edge problems in the field of mathematical analysis, with specific focus on nonlocal equations, by introducing innovative approaches and a unified perspective. It focuses on the use of long-range interactions to deeply understand new effects arising in several mathematical problems of great impact.
The research will be performed through stimulating international collaborations, providing exchange opportunities and ideal conditions for students to complete their training.
The expected outcomes include new techniques to solve difficult problems, high impact international research collaborations, training of the next generation of mathematicians and top tier journal publications.Read moreRead less
Sewer corrosion reduction through model-supported ventilation control. Ventilation is one of the key technologies for sewer corrosion control. However, its design and operation are currently based on experience and empirical equations, often leading to unsatisfactory results. By integrating in-depth laboratory and pilot-sewer studies under defined conditions with extensive field investigations, this multidisciplinary project aims to develop critical models to predict the corrosion process in res ....Sewer corrosion reduction through model-supported ventilation control. Ventilation is one of the key technologies for sewer corrosion control. However, its design and operation are currently based on experience and empirical equations, often leading to unsatisfactory results. By integrating in-depth laboratory and pilot-sewer studies under defined conditions with extensive field investigations, this multidisciplinary project aims to develop critical models to predict the corrosion process in response to ventilation and dynamic wastewater and atmospheric conditions, enabling model-based sewer ventilation design and operation. The project also aims to deliver novel, field-demonstrated ventilation strategies. The project findings will be incorporated in the Australian ventilation design and operation guidelines.Read moreRead less