The canonical stratification of jet spaces. Singularities occur everywhere in nature, from the formation and collapse of stars to the morphology of living embryos. They appear whenever the geometry of surfaces or spaces undergoes a process of twisting, folding, or collapsing on itself. Singularity Theory is the study of such phenomena, an important branch of modern mathematics which has close connections with many other branches of mathematics and applied sciences. Singularity Theory lies at the ....The canonical stratification of jet spaces. Singularities occur everywhere in nature, from the formation and collapse of stars to the morphology of living embryos. They appear whenever the geometry of surfaces or spaces undergoes a process of twisting, folding, or collapsing on itself. Singularity Theory is the study of such phenomena, an important branch of modern mathematics which has close connections with many other branches of mathematics and applied sciences. Singularity Theory lies at the crossroads of the paths connecting the most important areas of applications of mathematics with its most abstract parts. Analytic Singularity Theory is a central part of Singularity Theory. This project would lead to substantially new advancements in Analytic Singularity Theory.Read moreRead less
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
Integrable Functional and Delay Differential Equations. Major challenges such as predicting epidemics or modelling the dynamics of human movement, rely on our understanding of functional and delay differential equations. This research will provide new methods for prediction and analysis of such models.
Modelling and estimation techniques for the transmission and control of Tuberculosis with new and existing vaccines. Most Tuberculosis in Australia is seen in foreign-born people. Australia has an important role in providing leadership in the Asia-Pacific region in Tuberculosis control, which will have flow-on benefits to TB control in this country. Using mathematical models, this project will assess the use of vaccines for Tuberculosis in the developing world. Rising levels of extremely drug r ....Modelling and estimation techniques for the transmission and control of Tuberculosis with new and existing vaccines. Most Tuberculosis in Australia is seen in foreign-born people. Australia has an important role in providing leadership in the Asia-Pacific region in Tuberculosis control, which will have flow-on benefits to TB control in this country. Using mathematical models, this project will assess the use of vaccines for Tuberculosis in the developing world. Rising levels of extremely drug resistant infections make this a timely and important study with significant policy implications, both externally and in the Australian context. Read moreRead less