Symmetries in real and complex geometry. This project concerns an important area of abstract modern geometry. The results and techniques of the project will lead to significant progress in this area. It will benefit the national scientific reputation, strengthen the research profile of the home institutions, and provide training to young researchers.
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
Organic Bioelectronics: Solving Key Barriers to Precision Neuromodulation. This project aims to combine the principles of molecular electronics and neurobiology to create organic conductors with enhanced biocompatibility that enable optical neuromodulation. This project expects to generate new knowledge regarding the properties of materials that promote connectivity with neurons and the ability of new microscopy tools to visualise this bio-interface. The expected outcome of this project includes ....Organic Bioelectronics: Solving Key Barriers to Precision Neuromodulation. This project aims to combine the principles of molecular electronics and neurobiology to create organic conductors with enhanced biocompatibility that enable optical neuromodulation. This project expects to generate new knowledge regarding the properties of materials that promote connectivity with neurons and the ability of new microscopy tools to visualise this bio-interface. The expected outcome of this project includes new high performing materials, measurement tools and fabrication approaches to overcome the key challenges to precision neuromodulation. A significant benefit of the new materials is their printability, providing the opportunity to establish a sovereign capability to manufacture low-cost bioelectronic systems in Australia.Read moreRead less