Special Research Initiatives - Grant ID: SR0354716
Funder
Australian Research Council
Funding Amount
$10,000.00
Summary
Energetically Open Systems Research Network Study. Conceptual frameworks arising in the physical sciences, such as non-equilibrium statistical mechanics and thermodynamics, synergetics, chaos and dynamical systems theory, are seminal in the emerging science of complexity. This study will lay the groundwork for a network to link Australian and overseas research on these fundamental concepts, and their application within the context of entropy-producing systems vital to the long-term sustainabilit ....Energetically Open Systems Research Network Study. Conceptual frameworks arising in the physical sciences, such as non-equilibrium statistical mechanics and thermodynamics, synergetics, chaos and dynamical systems theory, are seminal in the emerging science of complexity. This study will lay the groundwork for a network to link Australian and overseas research on these fundamental concepts, and their application within the context of entropy-producing systems vital to the long-term sustainability of the earth - oceans, atmosphere, biosphere, CO2-free energy production, space and solar environment. The network would facilitate the development of young investigators and be linked into wider complex systems networks such as the CSIRO Centre for Complex Systems Science.Read moreRead less
Special Research Initiatives - Grant ID: SR0354466
Funder
Australian Research Council
Funding Amount
$20,000.00
Summary
Mathematics in Contemporary Science. The Mathematics in Contemporary Science Research Network brings contemporary methods of non-linear analysis and differential equations, geometric reasoning and relevant algebraic and topological ideas to enrich six application areas in modern science: Complex Systems, Computer Vision, Optimal Transportation, Nanotechnology, Physics and Shortest Networks. MiCS will develop both the mathematics and the application areas in parallel. It will focus on postgradu ....Mathematics in Contemporary Science. The Mathematics in Contemporary Science Research Network brings contemporary methods of non-linear analysis and differential equations, geometric reasoning and relevant algebraic and topological ideas to enrich six application areas in modern science: Complex Systems, Computer Vision, Optimal Transportation, Nanotechnology, Physics and Shortest Networks. MiCS will develop both the mathematics and the application areas in parallel. It will focus on postgraduate training through workshops, summer schools and web based resources and build long-term international collaborations with EU networks and NSERC, NSF and EPSRC institutes as well as bringing together academic and industry leaders.Read moreRead less
Mathematics for breaking limits of speed and density in magnetic memories. The aim of this project is to develop a mathematical theory and numerical models of stochastic partial differential equations for magnetic nano-structures. Such materials will yield next-generation magnetic memories with up to three orders of magnitude faster switching speeds and dramatically increased data storage density. New mathematical theories will help understand their sensitivity to small random fluctuations that ....Mathematics for breaking limits of speed and density in magnetic memories. The aim of this project is to develop a mathematical theory and numerical models of stochastic partial differential equations for magnetic nano-structures. Such materials will yield next-generation magnetic memories with up to three orders of magnitude faster switching speeds and dramatically increased data storage density. New mathematical theories will help understand their sensitivity to small random fluctuations that can destroy stored information. This project aims to revolutionise mathematical modelling of magnetic memories and put Australia at the forefront of international research. Technological advances to create much smaller and faster memory devices are expected to enable groundbreaking ways of managing and mining big data.Read moreRead less
Invariants, geometric and discrete structures on manifolds. This project aims to develop practical methods for finding geometric and discrete structures on manifolds in both low and high dimensions and advancing our understanding of the information that physics is providing about these spaces. Recently there have been spectacular advances in understanding 3-D spaces and the interaction between ideas in mathematical physics (quantum invariants, string theory) and such spaces. In this project, the ....Invariants, geometric and discrete structures on manifolds. This project aims to develop practical methods for finding geometric and discrete structures on manifolds in both low and high dimensions and advancing our understanding of the information that physics is providing about these spaces. Recently there have been spectacular advances in understanding 3-D spaces and the interaction between ideas in mathematical physics (quantum invariants, string theory) and such spaces. In this project, the first aim is to construct structures with good geometric properties on 3- and 4-manifolds, using triangulations. The second aim is to study combinatorial decompositions of n-manifolds, using our new technique of multisections and also searching for polyhedral metrics of non-positive curvature. The third aim is to connect quantum invariants and geometric structures, again using triangulations.Read moreRead less
Higher dimensional methods for algebras and dynamical systems. Australian researchers have pioneered recent research in combinatorial C*-algebras. We are now uniquely placed to capitalise on this situation to make significant connections with research in dynamical systems. This project will thus position Australian mathematics at the nexus of two important research areas.
Triangulations in dimensions 3 and 4: discrete and geometric structures. Recently there have been spectacular advances in understanding 3-dimensional spaces and the interaction between ideas in mathematical physics (quantum invariants) and such spaces. This project aims at practical methods for finding geometric structures and advancing our understanding of the information that physics is providing about these spaces.
Optimal shapes in geometry and physics: Isoperimetry in modern analysis. This project will find the best isoperimetric shapes in curved spaces: shapes that optimise geometric or analytic quantities, such as the volume enclosed by a surface of a given area, or the resonant frequency of a drum of given area. The optimal shapes lead to tools that are widely used in differential equations, geometric analysis, statistical physics, probability theory, and quantum computing. Through this work, we ....Optimal shapes in geometry and physics: Isoperimetry in modern analysis. This project will find the best isoperimetric shapes in curved spaces: shapes that optimise geometric or analytic quantities, such as the volume enclosed by a surface of a given area, or the resonant frequency of a drum of given area. The optimal shapes lead to tools that are widely used in differential equations, geometric analysis, statistical physics, probability theory, and quantum computing. Through this work, we will forge connections between the geometry of curved spaces, and the physics of operators therein. The significant benefits of this project include increasing fundamental mathematical knowledge, building capacity in Australia’s world-class geometric analysis community, and strong links with international partners.Read moreRead less
Extremal problems in hypergraph matchings. Matchings in hypergraphs are a way of understanding complex relationships between objects in any set. This project will develop a mathematical theory that covers both extreme and typical cases. This theory will have applications wherever hypergraphs are used as models, for example in machine learning, game theory, databases, data mining and optimisation.
Enumeration and properties of large discrete structures. This project aims to study a fundamental property of random graphs, by further developing a recently introduced approach to the problem of enumerating graphs with given degrees. Using this new method, the project expects to generate new knowledge on the number of connections that each node has with other nodes in a random graph, and to develop new strategies for counting the graphs or networks with a given property. The project expects to ....Enumeration and properties of large discrete structures. This project aims to study a fundamental property of random graphs, by further developing a recently introduced approach to the problem of enumerating graphs with given degrees. Using this new method, the project expects to generate new knowledge on the number of connections that each node has with other nodes in a random graph, and to develop new strategies for counting the graphs or networks with a given property. The project expects to produce new theoretical results as well as enhanced capabilities of mathematical research. Potential benefits arise through the uses of these theoretical combinatorial objects to study naturally occurring networks such as social networks, the network of the world wide web, and chemical compounds.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE170100789
Funder
Australian Research Council
Funding Amount
$324,499.00
Summary
Advances in graph Ramsey theory. This project aims to solve significant questions at the forefront of graph Ramsey theory, which provides the theoretical background for understanding networks that are omnipresent in the modern world. Major progress is anticipated on the recently introduced concept of Ramsey equivalence, including the development of deep new tools that combine probabilistic methods, extremal graph theory and graph decomposition techniques. The project will use these new tools to ....Advances in graph Ramsey theory. This project aims to solve significant questions at the forefront of graph Ramsey theory, which provides the theoretical background for understanding networks that are omnipresent in the modern world. Major progress is anticipated on the recently introduced concept of Ramsey equivalence, including the development of deep new tools that combine probabilistic methods, extremal graph theory and graph decomposition techniques. The project will use these new tools to solve old questions on the structure of minimal Ramsey graphs, thus fostering the international competitiveness of Australian research and enhancing Australia's reputation as a knowledge nation.Read moreRead less