Discovery Early Career Researcher Award - Grant ID: DE200101802
Funder
Australian Research Council
Funding Amount
$354,016.00
Summary
Combinatorial and Representation Theoretic Methods in Number Theory. This Project aims to explore connections of Number Theory and Representation Theory by utilising tools of Algebraic Combinatorics. Symmetries and constructions of crucial number theoretic objects such as Whittaker functions are underpinned by models for Lie algebras and root systems. The Project expects to advance the algebraic framework of the constructions. Expected outcomes include a unified combinatorial model of these obje ....Combinatorial and Representation Theoretic Methods in Number Theory. This Project aims to explore connections of Number Theory and Representation Theory by utilising tools of Algebraic Combinatorics. Symmetries and constructions of crucial number theoretic objects such as Whittaker functions are underpinned by models for Lie algebras and root systems. The Project expects to advance the algebraic framework of the constructions. Expected outcomes include a unified combinatorial model of these objects, and an extension of the costructions to the infinite dimensional setting. This will benefit the applications in Number Theory and strengthen nascent connections with Mathematical Physics. Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE190101063
Funder
Australian Research Council
Funding Amount
$319,474.00
Summary
Geometric flows and distinguished geometric structures with symmetry. This project aims to carry out analysis for the Ricci flow and a number of recent flows in complex geometry. Geometric evolution equations are a trending topic in modern mathematics, with successful applications such as the celebrated proof of the century-old Poincaré Conjecture in 2002-03 by means of the Ricci flow. An analysis of the behaviour of solutions with symmetry is an essential component in any mature theory on the s ....Geometric flows and distinguished geometric structures with symmetry. This project aims to carry out analysis for the Ricci flow and a number of recent flows in complex geometry. Geometric evolution equations are a trending topic in modern mathematics, with successful applications such as the celebrated proof of the century-old Poincaré Conjecture in 2002-03 by means of the Ricci flow. An analysis of the behaviour of solutions with symmetry is an essential component in any mature theory on the subject. The project will use the novel tools and ideas resulting from this analysis to address the Alekseevskii Conjecture, a 40-year old fundamental open question in the field with major ramifications in mathematics and beyond. This project will further reinforce Australia's leading role in geometric analysis.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE220100919
Funder
Australian Research Council
Funding Amount
$345,000.00
Summary
Distinguished Geometric Structures with Symmetry in Four Dimensions. The Ricci flow is a geometric evolution equation having significant applications in geometry, topology, as well as in physics, biology and image processing. This project aims to provide a complete description and classification of highly symmetric, self-similar solutions to the Ricci Flow in four dimensions. Such a classification is essential to understanding the behaviour of the flow, but has so far evaded discovery. This proj ....Distinguished Geometric Structures with Symmetry in Four Dimensions. The Ricci flow is a geometric evolution equation having significant applications in geometry, topology, as well as in physics, biology and image processing. This project aims to provide a complete description and classification of highly symmetric, self-similar solutions to the Ricci Flow in four dimensions. Such a classification is essential to understanding the behaviour of the flow, but has so far evaded discovery. This project intends to combine techniques from pure mathematics with computational techniques to complete this classification. Such an outcome would greatly improve the understanding of the geometry of four-dimensional manifolds, potentially leading to applications in several areas of science as well as image processing.Read moreRead less
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
Lie superalgebra representations: a geometric approach. The concept of a Lie group provides a mathematical underpinning for the idea of symmetry in mathematics, physics and chemistry. The project aims to advance two fundamental problems related to this concept: classification of unitary representations of Lie superalgebras, and the prescribed Ricci curvature problem on Lie groups. The research builds on newly-discovered connections between these problems to achieve exciting progress in their res ....Lie superalgebra representations: a geometric approach. The concept of a Lie group provides a mathematical underpinning for the idea of symmetry in mathematics, physics and chemistry. The project aims to advance two fundamental problems related to this concept: classification of unitary representations of Lie superalgebras, and the prescribed Ricci curvature problem on Lie groups. The research builds on newly-discovered connections between these problems to achieve exciting progress in their resolution. Outcomes are expected to find applications across a range of fields, such as condensed matter physics, particle physics, quantum field theory and knot theory. Anticipated benefits include stronger links between different areas of science achieved through a deeper understanding of symmetry.Read moreRead less
Industrial Transformation Training Centres - Grant ID: IC190100017
Funder
Australian Research Council
Funding Amount
$3,703,664.00
Summary
ARC Training Centre for Integrated Operations for Complex Resources. This Training Centre aims to increase value in mining through clever applications of ‘lean processing’ and train the next generation of scientists and engineers in advanced sensors and data analytics in complex resources; knowledge priorities for the mining industry. Sensor information will be linked to the resource’s in-place knowledge to enable data analytics of all embedded knowledge. Processing can then be tuned to resource ....ARC Training Centre for Integrated Operations for Complex Resources. This Training Centre aims to increase value in mining through clever applications of ‘lean processing’ and train the next generation of scientists and engineers in advanced sensors and data analytics in complex resources; knowledge priorities for the mining industry. Sensor information will be linked to the resource’s in-place knowledge to enable data analytics of all embedded knowledge. Processing can then be tuned to resource attributes, maximising value ‘on the fly’. Benefits will include increasing certainty on product quality and maximising throughput and recovery. Outcomes will include new tools to rapidly model geological and geometallurgical uncertainty with sensor inputs, to track the resource to product and enhance interpretation.Read moreRead less
Examining multi-level Information Technology (IT) project alignment in government services: the case of contracted employment services. Improved Information Technology (IT) alignment is essential for the delivery of government services within a complex public-private, inter-organisational environment. This project will investigate the extent to which well-aligned IT support systems contribute positively to the efficient and effective delivery of contracted employment services.
The Intended and Unintended Impact of Policy for Adaptive Policy Management. The project aims to advance knowledge about the intended and unintended consequences of policy on health and well-being. It expects to innovate through new methods and novel data to integrate policy evaluation into the policy cycle in a timely fashion to prevent harm from occurring. It also leverages technology to track policy effects in real time. Expected outcomes of this project include new knowledge and enhanced pol ....The Intended and Unintended Impact of Policy for Adaptive Policy Management. The project aims to advance knowledge about the intended and unintended consequences of policy on health and well-being. It expects to innovate through new methods and novel data to integrate policy evaluation into the policy cycle in a timely fashion to prevent harm from occurring. It also leverages technology to track policy effects in real time. Expected outcomes of this project include new knowledge and enhanced policy infrastructure using new methods and interdisciplinary approaches. Significant benefits include improvements to: (1) policy management by government departments; (2) the health and wellbeing of the Australians they serve; (3) our Partners' capacity to consult governments on how technology can assist policy management. Read moreRead less
Settling well in regional Australia: Experiences of people from refugee backgrounds. Regional humanitarian settlement is a key priority across all levels of government in Australia. This study aims to provide the first longitudinal assessment of the impacts of regional settlement for humanitarian migrants and destination communities. Its innovative, mixed-method and multi-sited approach will generate new knowledge of the opportunities and challenges for sustainable regional settlement. Expected ....Settling well in regional Australia: Experiences of people from refugee backgrounds. Regional humanitarian settlement is a key priority across all levels of government in Australia. This study aims to provide the first longitudinal assessment of the impacts of regional settlement for humanitarian migrants and destination communities. Its innovative, mixed-method and multi-sited approach will generate new knowledge of the opportunities and challenges for sustainable regional settlement. Expected outcomes include enhanced community, organisational and government decision-making capacity. By guiding end-users’ current and future actions, the study has strong potential to support the wellbeing of humanitarian migrants and to contribute to healthy and resilient regional communities.Read moreRead less
How parents manage climate anxiety: coping and hoping for the whole family. This project studies how Australian parents manage climate anxiety for themselves and their families. Using mixed-methods/mixed-media approaches, it examines whether an increase in climate disasters is accelerating the spread of collective anxiety amongst families, how parents manage this anxiety for their children and partners, and if there are associated mental health burdens and gendered inequities in this management. ....How parents manage climate anxiety: coping and hoping for the whole family. This project studies how Australian parents manage climate anxiety for themselves and their families. Using mixed-methods/mixed-media approaches, it examines whether an increase in climate disasters is accelerating the spread of collective anxiety amongst families, how parents manage this anxiety for their children and partners, and if there are associated mental health burdens and gendered inequities in this management. It also looks at climate anxiety management across generations and climate histories, drawing out pessimistic/optimistic narratives about the future to enable action, resilience, and hope. It will produce an evidence base and photo-voice/documentary resources to help parents and support organisations combat climate anxiety.Read moreRead less