Coarse Geometry: a novel approach to the Callias index & topological matter. Coarse geometry is the study of the large-scale structure of metric spaces, in terms of operator algebras. This project aims to use coarse geometry to develop novel approaches to Callias index theory and its applications, and to topological phases of matter, where the Nobel Prize in physics in 2016 was awarded. This will yield new techniques in index theory and other areas, and solutions to several important problems. O ....Coarse Geometry: a novel approach to the Callias index & topological matter. Coarse geometry is the study of the large-scale structure of metric spaces, in terms of operator algebras. This project aims to use coarse geometry to develop novel approaches to Callias index theory and its applications, and to topological phases of matter, where the Nobel Prize in physics in 2016 was awarded. This will yield new techniques in index theory and other areas, and solutions to several important problems. Outcomes include a noncompact generalisation of the famous Guillemin-Sternberg conjecture that quantisation commutes with reduction, and new models of topological phases of matter in terms of K-theory of operator algebras. This project will benefit Australia by reinforcing its position in these highly active areas in science.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE150101647
Funder
Australian Research Council
Funding Amount
$330,000.00
Summary
Symplectic solvmanifolds and their friends. Symplectic geometry is the mathematical foundation of classical mechanics and quantum theory. The symmetry group of a physical system determines the conservation laws governing its behaviour. This project aims to advance the understanding of a large class of these symmetry groups and their associated symplectic geometries, which are called symplectic solvmanifolds. The project aims to: determine the topological properties of symplectic solvmanifolds as ....Symplectic solvmanifolds and their friends. Symplectic geometry is the mathematical foundation of classical mechanics and quantum theory. The symmetry group of a physical system determines the conservation laws governing its behaviour. This project aims to advance the understanding of a large class of these symmetry groups and their associated symplectic geometries, which are called symplectic solvmanifolds. The project aims to: determine the topological properties of symplectic solvmanifolds as encoded in their fundamental groups; their geometric properties in the form of holonomy groups; and the algebraic properties of their symplectic algebras. The project endeavours to classify the building blocks of symplectic geometry.Read moreRead less
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
Topological Optimisation of Fluid Mixing. The proposed research is aimed at improving the efficiency of fluid mixers,
which in the long term has potential to reduce vastly the economic and
environmental costs associated with large-scale mixing processes in Australian
chemical industries. The research will not only impact on practical mixer
design, but will also develop important results in the application of topology
to the the field of chaotic dynamical systems. This project will also prov ....Topological Optimisation of Fluid Mixing. The proposed research is aimed at improving the efficiency of fluid mixers,
which in the long term has potential to reduce vastly the economic and
environmental costs associated with large-scale mixing processes in Australian
chemical industries. The research will not only impact on practical mixer
design, but will also develop important results in the application of topology
to the the field of chaotic dynamical systems. This project will also provide a
graduate student and post-doctoral researcher with training to pursue a career
in fluid dynamics or general applied mathematics research.
Read moreRead less