Symmetry: Groups, Graphs, Number Fields and Loops. Exploiting symmetry can greatly simplify complex mathematical problems. This project aims to apply the powerful Classification of Finite Simple Groups to advance our understanding of the internal structure of number fields, highly symmetric graphs, and algebraic structures associated with Latin squares. The project expects to generate new constructions and classifications utilising group theory. Expected outcomes include resolutions of major ope ....Symmetry: Groups, Graphs, Number Fields and Loops. Exploiting symmetry can greatly simplify complex mathematical problems. This project aims to apply the powerful Classification of Finite Simple Groups to advance our understanding of the internal structure of number fields, highly symmetric graphs, and algebraic structures associated with Latin squares. The project expects to generate new constructions and classifications utilising group theory. Expected outcomes include resolutions of major open problems in each area as well as innovative methods for studying algebraic and combinatorial structures based on group actions. Expected benefits include enhanced international collaboration, and highly trained mathematicians to strengthen Australia’s research standing in fundamental science.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
Non-local equations at work. This project aims to study non-local fractional equations. These problems arise naturally in many fields of pure and applied mathematics. This project will consider symmetry and rigidity results; problems from atom dislocation theory; nonlocal minimal surfaces; symbolic dynamics for nonlocal equations; and free boundary problems. This project aims to obtain substantial progress in this field, both from the point of view of the mathematical theory and in view of concr ....Non-local equations at work. This project aims to study non-local fractional equations. These problems arise naturally in many fields of pure and applied mathematics. This project will consider symmetry and rigidity results; problems from atom dislocation theory; nonlocal minimal surfaces; symbolic dynamics for nonlocal equations; and free boundary problems. This project aims to obtain substantial progress in this field, both from the point of view of the mathematical theory and in view of concrete applications. This project should contribute to the development of the mathematical theory and give insight for concrete applications in physics and biology.Read moreRead less
Cooperative control of networked systems with constraints. This project aims to address the challenge of networked systems in deploying teams of robotic agents. Control of the networked system is extremely difficult due to real world constraints imposed on each agent. This project will focus on motion constraints, equipment/capability constraints, and spatial constraints. In addition to theoretical advances, the wider scientific community will benefit directly, because the control algorithms dev ....Cooperative control of networked systems with constraints. This project aims to address the challenge of networked systems in deploying teams of robotic agents. Control of the networked system is extremely difficult due to real world constraints imposed on each agent. This project will focus on motion constraints, equipment/capability constraints, and spatial constraints. In addition to theoretical advances, the wider scientific community will benefit directly, because the control algorithms developed are expected to allow straightforward deployment of robotic teams. There are myriad applications for cooperative robotic agents, ranging from surveillance, to environmental monitoring using underwater and aerial drone formations – with an array of benefits and impacts including economic, commercial and societal. The results are intended to ensure and cement Australia’s front-line position in the current technological revolution known as “Industry 4.0”.Read moreRead less
Modelling, Design and Development of a Novel Wave-Energy Converter. Australia has an abundant source of wave-energy commercially untapped due to technical limitations of current wave-energy devices. This project aims to develop a novel wave-energy converter (WEC) that integrates energy capture and electricity generation through a single mechanism. This novel WEC can overcome or significantly reduce the drawbacks of existing WECs, is compact and light-weight (about 30 times less), ensures surviva ....Modelling, Design and Development of a Novel Wave-Energy Converter. Australia has an abundant source of wave-energy commercially untapped due to technical limitations of current wave-energy devices. This project aims to develop a novel wave-energy converter (WEC) that integrates energy capture and electricity generation through a single mechanism. This novel WEC can overcome or significantly reduce the drawbacks of existing WECs, is compact and light-weight (about 30 times less), ensures survivability, and has low-cost installation and maintenance. The project expects to deliver novel theoretical results in fluid-structure interaction, control systems and electrical conversion for WECs and other applications. The WEC will be demonstrated via a tested proof-of-concept physical model.Read moreRead less
Australian Laureate Fellowships - Grant ID: FL190100081
Funder
Australian Research Council
Funding Amount
$3,532,919.00
Summary
Minimal surfaces, free boundaries and partial differential equations. This project enhances Australia as a world leader in the field of mathematical analysis, focusing on regularity and qualitative properties of solutions of partial differential equations and nonlocal problems, and solving very challenging research questions in a key strategic area of international science.
The broad applicability of the results constitutes a very fertile ground for cross-disciplinary interactions with scientist ....Minimal surfaces, free boundaries and partial differential equations. This project enhances Australia as a world leader in the field of mathematical analysis, focusing on regularity and qualitative properties of solutions of partial differential equations and nonlocal problems, and solving very challenging research questions in a key strategic area of international science.
The broad applicability of the results constitutes a very fertile ground for cross-disciplinary interactions with scientists of other disciplines.
A new research team based in Western Australia will be founded, connecting world leaders and talented early career researchers, providing an ideal training environment for students and PostDocs, offering an excellent image of the scientific community and developing strategic fields of knowledge.Read moreRead less