Normal forms and Chern-Moser connection in the study of Cauchy-Riemann Manifolds. This research project is aimed at a systematic study of Cauchy-Riemann manifolds, their holomorphic mappings and automorphisms, by means of a unifying approach based on
Chern-Moser type normal forms. The importance of Cauchy-Riemann manifolds stems from the fact that they bridge complex structure and holomorphy with the Riemannian nature of real manifolds. Construction of an analogue of the Chern-Moser normal form ....Normal forms and Chern-Moser connection in the study of Cauchy-Riemann Manifolds. This research project is aimed at a systematic study of Cauchy-Riemann manifolds, their holomorphic mappings and automorphisms, by means of a unifying approach based on
Chern-Moser type normal forms. The importance of Cauchy-Riemann manifolds stems from the fact that they bridge complex structure and holomorphy with the Riemannian nature of real manifolds. Construction of an analogue of the Chern-Moser normal form for multicodimensional Levi-nondegenerate CR-manifolds and extension of CR-mappings between them are major goals in complex analysis. Identification of Chern-Moser chains and equivariant linearisation of isotropy automorphisms are major goals in 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
Linkage Infrastructure, Equipment And Facilities - Grant ID: LE0346888
Funder
Australian Research Council
Funding Amount
$288,000.00
Summary
3-D Optical Surface Profiler. Establishing a state-of-the-science 3-D optical surface profiler will enable macroscopic, microscopic and nanoscopic profiling of surfaces over a very broad range of research programs including, laser cleaning and surface modification, laser precision microfabrication, surface, materials and device characterisation and optical physics applications. The importance and significance of these projects has already been established by the projects having competitive fundi ....3-D Optical Surface Profiler. Establishing a state-of-the-science 3-D optical surface profiler will enable macroscopic, microscopic and nanoscopic profiling of surfaces over a very broad range of research programs including, laser cleaning and surface modification, laser precision microfabrication, surface, materials and device characterisation and optical physics applications. The importance and significance of these projects has already been established by the projects having competitive funding. The instrument will undoubtedly support many additional research programs. It is similar to an Atomic-Force-Microscope or stylus profilometer but has significant additional capabilites. These include profiling much larger areas at sub-nanometre resolution and the non-contact nature of the technique. These features will enable surface characterisation that can not be achieved by other means.Read moreRead less