Algorithms and computation in four-dimensional topology. This project will establish Australia as a world leader in computational topology, particularly in the all-important areas of topology in three and four dimensions. In four dimensions this work will be truly groundbreaking; until now the field has seen little development due to the complexity of the algorithms and computations required, and the applicant is in the unique position of having the necessary tools to make significant progress ....Algorithms and computation in four-dimensional topology. This project will establish Australia as a world leader in computational topology, particularly in the all-important areas of topology in three and four dimensions. In four dimensions this work will be truly groundbreaking; until now the field has seen little development due to the complexity of the algorithms and computations required, and the applicant is in the unique position of having the necessary tools to make significant progress in a feasible time frame. In three dimensions this project will strengthen the distinguished computational topology community in Melbourne, led by pioneers such as Rubinstein, Goodman, Hodgson as well as the applicant himself.Read moreRead less
Industrial Transformation Research Hubs - Grant ID: IH230100013
Funder
Australian Research Council
Funding Amount
$5,000,000.00
Summary
ARC Research Hub for Future Digital Manufacturing. This Hub aims to grow and accelerate Australian digital manufacturing (DM) transformation by devising novel DM technology and commercialisation/adoption pathways. The Hub expects to transform industry by developing novel AI and IoT-powered DM technology that provides for dramatic improvement in manufacturing productivity, resilience and competitiveness. Expected outcomes include novel DM technology for digitally representing, predicting, and imp ....ARC Research Hub for Future Digital Manufacturing. This Hub aims to grow and accelerate Australian digital manufacturing (DM) transformation by devising novel DM technology and commercialisation/adoption pathways. The Hub expects to transform industry by developing novel AI and IoT-powered DM technology that provides for dramatic improvement in manufacturing productivity, resilience and competitiveness. Expected outcomes include novel DM technology for digitally representing, predicting, and improving production and its outcomes via an open platform that supports reusing industry co-created DM solutions. Through supporting advanced manufacturing priorities and Industry 4.0, the Hub should provide significant benefits by increasing Australian manufacturing productivity and resilience by 30%.Read moreRead less
Unlocking the potential for linear and discrete optimisation in knot theory and computational topology. Computational topology is a young, energetic field that uses computers to solve complex geometric problems, such as whether a loop of string is tangled. Such computations are becoming increasingly important in mathematics, and applications span biology, physics and information sciences, however many core problems in the field remain intractable for all but the simplest cases. This project unit ....Unlocking the potential for linear and discrete optimisation in knot theory and computational topology. Computational topology is a young, energetic field that uses computers to solve complex geometric problems, such as whether a loop of string is tangled. Such computations are becoming increasingly important in mathematics, and applications span biology, physics and information sciences, however many core problems in the field remain intractable for all but the simplest cases. This project unites geometric techniques with powerful methods from operations research, such as linear and discrete optimisation, to build fast, powerful tools that can for the first time systematically solve large topological problems. Theoretically, this project has significant impact on the famous open problem of detecting knottedness in fast polynomial time.Read moreRead less