The Sakai scheme-Askey table correspondence, analogues of isomonodromy and determinantal point processes. The Australian mathematical sciences enjoys two research groups with active interests on Painleve equations in applied mathematics which are able to address difficult problems. Such a problem is to give a formulation of Sakai's 2001 classification of the Painleve equations in a form most suitable for applications. For this links will be made with a seemingly distinct area of mathematics - t ....The Sakai scheme-Askey table correspondence, analogues of isomonodromy and determinantal point processes. The Australian mathematical sciences enjoys two research groups with active interests on Painleve equations in applied mathematics which are able to address difficult problems. Such a problem is to give a formulation of Sakai's 2001 classification of the Painleve equations in a form most suitable for applications. For this links will be made with a seemingly distinct area of mathematics - the Askey table from the theory of hypergeometric orthogonal polynomials. A number of tractable PhD projects are suggested by this proposal.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE140100620
Funder
Australian Research Council
Funding Amount
$395,220.00
Summary
Inference, control and protection of interdependent spatial networked structures. Networked structures are everywhere and modern societies largely depend on their proper functioning. Some of these networks are spatial with each node having a geographical tag. Examples include power grids, the internet and transportation networks. These networks are often interdependent where their functioning depends on each other. This project will establish a mathematical framework to efficiently observe and c ....Inference, control and protection of interdependent spatial networked structures. Networked structures are everywhere and modern societies largely depend on their proper functioning. Some of these networks are spatial with each node having a geographical tag. Examples include power grids, the internet and transportation networks. These networks are often interdependent where their functioning depends on each other. This project will establish a mathematical framework to efficiently observe and control interdependent spatial networks and develop design strategies in order to maximise residency of spatial networks against catastrophic failures in their components. The outcomes of the project will protect the Australian power grid and transportation networks against random and intentional failures. Read moreRead less
Engineering evolving complex network systems through structure intervention. This project aims to create a theory and technology for engineering complex network systems (CSS) through structural intervention. Complex network systems with evolving components are ubiquitous in nature and society. The science of biological networks, the Internet and large-scale power networks demand tools to understand and influence their evolving dynamics. This project could result in a breakthrough theory in netwo ....Engineering evolving complex network systems through structure intervention. This project aims to create a theory and technology for engineering complex network systems (CSS) through structural intervention. Complex network systems with evolving components are ubiquitous in nature and society. The science of biological networks, the Internet and large-scale power networks demand tools to understand and influence their evolving dynamics. This project could result in a breakthrough theory in network science and technology to augment biological systems and power grids. Expected benefits include cost-effective augmentation of power networks injected with renewable energy sources, and advancing basic biology research.Read moreRead less