Hypergraph models for complex discrete systems. This project aims to better understand the structure and properties of very large hypergraphs of various kinds. Hypergraphs are very general mathematical objects which can be used to model complex discrete systems. They arise naturally in many areas such as ecology, chemistry and computer science. Despite this, our theoretical understanding of very large, or random, hypergraphs lags far behind the intensely-studied special case of graphs. This proj ....Hypergraph models for complex discrete systems. This project aims to better understand the structure and properties of very large hypergraphs of various kinds. Hypergraphs are very general mathematical objects which can be used to model complex discrete systems. They arise naturally in many areas such as ecology, chemistry and computer science. Despite this, our theoretical understanding of very large, or random, hypergraphs lags far behind the intensely-studied special case of graphs. This project will answer many fundamental questions about large, random hypergraphs. The expected outcomes of the project also include new tools for working with hypergraphs, such as efficient algorithms for sampling hypergraphs. These outcomes will benefit researchers who use hypergraphs in their work and will enhance Australia's reputation for research in this area.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
Industrial Transformation Training Centres - Grant ID: IC200100009
Funder
Australian Research Council
Funding Amount
$4,861,236.00
Summary
ARC Training Centre in Optimisation Technologies, Integrated Methodologies, and Applications (OPTIMA). OPTIMA addresses industry’s urgent need for decision-making tools for global competitiveness: reducing lead times, and financial and environmental costs, while improving efficiency, quality, and agility. Despite strong expertise in academia, industry is yet to fully benefit from optimisation technology due to its high barrier to entry. Connecting industry partners with world-leading interdiscip ....ARC Training Centre in Optimisation Technologies, Integrated Methodologies, and Applications (OPTIMA). OPTIMA addresses industry’s urgent need for decision-making tools for global competitiveness: reducing lead times, and financial and environmental costs, while improving efficiency, quality, and agility. Despite strong expertise in academia, industry is yet to fully benefit from optimisation technology due to its high barrier to entry. Connecting industry partners with world-leading interdisciplinary researchers and talented students, OPTIMA will advance an industry-ready optimisation toolkit, while training a new generation of industry practitioners and over 120 young researchers, vanguarding a highly skilled workforce of change agents for transformation of the advanced manufacturing, energy resources, and critical infrastructure sectors.Read moreRead less
Intelligence and national security: ethics, efficacy and accountability. This project aims to generate an ethically informed set of practice and policy guidelines for viable security intelligence collection and analysis of electronic data by liberal democracies. In the context of global terrorism and the resurgence of technologically sophisticated authoritarian states, effective intelligence collection and analysis of electronic data is crucial for the national security of liberal democratic sta ....Intelligence and national security: ethics, efficacy and accountability. This project aims to generate an ethically informed set of practice and policy guidelines for viable security intelligence collection and analysis of electronic data by liberal democracies. In the context of global terrorism and the resurgence of technologically sophisticated authoritarian states, effective intelligence collection and analysis of electronic data is crucial for the national security of liberal democratic states. Yet intelligence agencies in Australia, United States, European Union and so on, are not only under pressure to perform, but must also meet a variety of ethical challenges, notably privacy constraints and democratic accountability. This project will contribute to Australia's national security policy making environment, and to privacy and broader human rights debates, by providing an evidenced based, ethically informed set of practice and policy guidelines for viable national security intelligence practice in liberal democracies.Read moreRead less
Policy Modelling for Ageing in Emerging Economies: The Case of Indonesia. This project, in collaboration with the World Bank and the Indonesian Planning Authority, will support major social and economic policy development in a rapidly ageing region. It will break new ground by developing a cutting-edge economic policy model reflecting salient features of ageing in emerging economies, taking into account the wider implications for education, employment, formalisation, growth, and retirement. It w ....Policy Modelling for Ageing in Emerging Economies: The Case of Indonesia. This project, in collaboration with the World Bank and the Indonesian Planning Authority, will support major social and economic policy development in a rapidly ageing region. It will break new ground by developing a cutting-edge economic policy model reflecting salient features of ageing in emerging economies, taking into account the wider implications for education, employment, formalisation, growth, and retirement. It will bring the armoury of policy analysis instruments available to these countries up to the standard now enjoyed by the developed world. Indonesia, on the brink of major pension reform, will be used as a test bed. Data sets will be developed to allow the model structure to be applied to other emerging economies in Asia. Read moreRead less
Singularity and regularity for Monge-Ampere type equations. The Monge-Ampere equation, as a premier nonlinear partial differential equation, arises in several areas including geometry, physics, and optimal transportation. Many important problems and applications are related to the regularity of solutions, which are obstructed by singularities. This project aims to classify the geometry of the singular sets, and to establish a comprehensive regularity theory for general Monge-Ampere type equation ....Singularity and regularity for Monge-Ampere type equations. The Monge-Ampere equation, as a premier nonlinear partial differential equation, arises in several areas including geometry, physics, and optimal transportation. Many important problems and applications are related to the regularity of solutions, which are obstructed by singularities. This project aims to classify the geometry of the singular sets, and to establish a comprehensive regularity theory for general Monge-Ampere type equations by using innovative approaches and developing cutting-edge technologies in partial differential equations. Expected outcomes include the resolution of outstanding open problems. This project will significantly enhance Australia’s leadership and expertise in a major area of mathematics and applications.Read moreRead less
Industrial Transformation Training Centres - Grant ID: IC210100008
Funder
Australian Research Council
Funding Amount
$4,282,859.00
Summary
ARC Training Centre for Behavioural Insights for Technology Adoption (BITA). Australia needs accelerated adoption of innovation technologies to improve outcomes in health, agriculture and cybersecurity. Despite technically viable solutions, innovations fail to be adopted due to behavioural barriers. Behavioural approaches can promote significant gains by bridging the barriers to technology adoption. The Centre for Behavioural Insights for Technology Adoption will boost national productivity by i ....ARC Training Centre for Behavioural Insights for Technology Adoption (BITA). Australia needs accelerated adoption of innovation technologies to improve outcomes in health, agriculture and cybersecurity. Despite technically viable solutions, innovations fail to be adopted due to behavioural barriers. Behavioural approaches can promote significant gains by bridging the barriers to technology adoption. The Centre for Behavioural Insights for Technology Adoption will boost national productivity by identifying, designing and evaluating solutions that address these barriers. By uniting industry and government with world-leading interdisciplinary researchers, the Centre will build transformative capability in people, data and solutions and support Australian organisations to achieve higher returns on technology investment.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE200101834
Funder
Australian Research Council
Funding Amount
$418,410.00
Summary
The structure of singularities in geometric flows. The proposed research aims to develop our understanding of the structure of singularities in mean curvature and related flows, with certain applications in mind.
Discovery Early Career Researcher Award - Grant ID: DE180100110
Funder
Australian Research Council
Funding Amount
$343,450.00
Summary
Analysis of fully non-linear geometric problems and differential equations. This project aims to investigate non-linear geometric evolution equations that have received considerable attention in the past decades through their use in solving outstanding problems in mathematics, such as the Poincare conjecture. By developing innovative new techniques intertwining geometry and analysis, the project endeavours to make advances in non-linear problems modelling complex phenomena. The project addresses ....Analysis of fully non-linear geometric problems and differential equations. This project aims to investigate non-linear geometric evolution equations that have received considerable attention in the past decades through their use in solving outstanding problems in mathematics, such as the Poincare conjecture. By developing innovative new techniques intertwining geometry and analysis, the project endeavours to make advances in non-linear problems modelling complex phenomena. The project addresses topics as varied as hyperbolic geometry, and a geometric approach to irregularities forming in crystal growth in materials science, focusing on developing cutting-edge mathematical tools and connections to geometry.Read moreRead less
Parabolic methods for elliptic boundary value problems. This project aims to uncover new results for second order nonlinear elliptic partial differential equations via the use of uniqueness properties of solutions for related nonlinear parabolic partial differential equations. This will build on theory for fully nonlinear equations developed over the last 30 years. The project expects to generate new knowledge in the theory that will guide future research and have direct impact to applications ....Parabolic methods for elliptic boundary value problems. This project aims to uncover new results for second order nonlinear elliptic partial differential equations via the use of uniqueness properties of solutions for related nonlinear parabolic partial differential equations. This will build on theory for fully nonlinear equations developed over the last 30 years. The project expects to generate new knowledge in the theory that will guide future research and have direct impact to applications in optimal transport, geometric problems and more applied areas including image analysis and mathematical finance. The project will enhance Australia's international reputation for research in the field and train some of the next generation of mathematical analysts.Read moreRead less