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
Harmonic analysis of Laplacians in curved spaces. Harmonic Analysis is a branch of mathematics which is interrelated to other fields of mathematics like complex analysis, number theory and partial differential equations (pdes) with many applications in engineering and technology. This project aims to solve a number of difficult fundamental problems at the frontier of harmonic analysis in understanding Laplacians in curved spaces. Such Laplacians control the propagation of heat and waves on manif ....Harmonic analysis of Laplacians in curved spaces. Harmonic Analysis is a branch of mathematics which is interrelated to other fields of mathematics like complex analysis, number theory and partial differential equations (pdes) with many applications in engineering and technology. This project aims to solve a number of difficult fundamental problems at the frontier of harmonic analysis in understanding Laplacians in curved spaces. Such Laplacians control the propagation of heat and waves on manifolds and Lie groups, arising in mathematical physics and quantum mechanics. Expected outcomes are the solutions of dispersive equations and the framework of singular integrals in curved spaces; new ideas and techniques in harmonic analysis developed; and training of Australian future mathematicians.Read moreRead less
Generalised conformal mappings. A conformal mapping preserves shape, at least at very small scale, circles are mapped to circles. The more recently introduced quasi-conformal mappings nearly preserves shape, at least at a very small scale, circles are mapped to regions which are similar to circles. This project will allow different directions to be scaled differently, and will consider mappings that send circles to ellipses of arbitrary eccentricity. The theory to be developed is mathematical an ....Generalised conformal mappings. A conformal mapping preserves shape, at least at very small scale, circles are mapped to circles. The more recently introduced quasi-conformal mappings nearly preserves shape, at least at a very small scale, circles are mapped to regions which are similar to circles. This project will allow different directions to be scaled differently, and will consider mappings that send circles to ellipses of arbitrary eccentricity. The theory to be developed is mathematical and it will provide a unified approach to important results in several areas, including Lie groups and functions of several complex variables. Read moreRead less
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
A genetic analysis of the role of an atypical hexokinase in gene regulation. This project addresses a question which is relevant to all living things-how do changes in the environment of a cell bring about a change in gene expression? The aim of this project is to investigate the role of hexokinases in gene regulation by studying the Aspergillus nidulans xprF gene, which encodes an an unusual hexokinase. Hexokinases are thought to be the glucose sensors in plants, animals and fungi, and play a ....A genetic analysis of the role of an atypical hexokinase in gene regulation. This project addresses a question which is relevant to all living things-how do changes in the environment of a cell bring about a change in gene expression? The aim of this project is to investigate the role of hexokinases in gene regulation by studying the Aspergillus nidulans xprF gene, which encodes an an unusual hexokinase. Hexokinases are thought to be the glucose sensors in plants, animals and fungi, and play a role in the development of diabetes in humans. In plants, sugars affect many processes including growth, flowering, photosynthesis, nitrogen metabolism, starch synthesis, pigmentation and response to pathogens.Read moreRead less
The transcriptional co-repressor C-terminal Binding Protein (CtBP) in metabolic control. This project will provide insights into the genes that regulate the storage of fat. We will learn about basic biology but will also discover mechanisms that may be used to influence fat storage in human health. We will also consolidate Australia's expertise in the use of the genetic model organism, the worm C. elegans, and validate the findings in mammalian systems. Finally, the process of training young sci ....The transcriptional co-repressor C-terminal Binding Protein (CtBP) in metabolic control. This project will provide insights into the genes that regulate the storage of fat. We will learn about basic biology but will also discover mechanisms that may be used to influence fat storage in human health. We will also consolidate Australia's expertise in the use of the genetic model organism, the worm C. elegans, and validate the findings in mammalian systems. Finally, the process of training young scientists in these modern systems, will also equip future researchers to make additional contributions to Australia's research output.Read moreRead less
RNA splicing: factors and mechanisms. Most primary gene transcripts must have their noncoding intronic sequences spliced out before the mRNA can be translated. Moreover, alternative splicing enables cells to generate a far more proteins than there are genes in the nucleus. Based on our proven success with ZNF265 we will isolate novel RNA interactors and their partners, colocalize these in intranuclear compartments, and elucidate their effect on pre-mRNA splicing. This will provide timely spin-of ....RNA splicing: factors and mechanisms. Most primary gene transcripts must have their noncoding intronic sequences spliced out before the mRNA can be translated. Moreover, alternative splicing enables cells to generate a far more proteins than there are genes in the nucleus. Based on our proven success with ZNF265 we will isolate novel RNA interactors and their partners, colocalize these in intranuclear compartments, and elucidate their effect on pre-mRNA splicing. This will provide timely spin-offs to the Human genome Project and EST sequence information, where the finding of only approx. 30,000 genes in our genome highlights the important role of alternative splicing in generating the large proteome repertoire of cells. This will bring considerable benefits to science, society, and the biotech industry.Read moreRead less
A new mechanism of gene regulation. This project will advance our knowledge of how genes are switched on and off, by focusing on a very common class of gene regulatory proteins known as zinc finger proteins. The results of this study will improve our understanding of the fundamental molecular events that underpin gene regulation and how we might control it in fields such as biotechnology and gene therapy.
New mechanisms of DNA recognition by zinc-finger domains. The work described in this proposal carries long-term benefits to the health of Australians. Many debilitating diseases, including many varieties of cancer, arise as a result of a breakdown in the normal regulation of gene transcription. It is only once we have a thorough understanding of transcriptional regulation in normal organisms that we will be in a position to devise effective therapies to deal with the disorders that result from a ....New mechanisms of DNA recognition by zinc-finger domains. The work described in this proposal carries long-term benefits to the health of Australians. Many debilitating diseases, including many varieties of cancer, arise as a result of a breakdown in the normal regulation of gene transcription. It is only once we have a thorough understanding of transcriptional regulation in normal organisms that we will be in a position to devise effective therapies to deal with the disorders that result from aberrant gene expression. Our proposed research program also provides the opportunity to train younger scientists in state-of-the-art molecular and structural biology, thus representing a significant national benefit. Read moreRead less