Structure and states of operator-algebraic dynamical systems. This project is in the general area of functional analysis, and more specifically operator theory, an area in which the University of Wollongong has an active research group and a strong international reputation. The investigators will study dynamical systems arising in combinatorial and number-theoretic situations, where the analogue of the "dynamics'' is provided by an action of the real line on an operator algebra. Thus the project ....Structure and states of operator-algebraic dynamical systems. This project is in the general area of functional analysis, and more specifically operator theory, an area in which the University of Wollongong has an active research group and a strong international reputation. The investigators will study dynamical systems arising in combinatorial and number-theoretic situations, where the analogue of the "dynamics'' is provided by an action of the real line on an operator algebra. Thus the project will involve ideas and techniques from a wide range of mathematical disciplines, and will help to broaden Australia's expertise across these disciplines.Read moreRead less
Endomorphisms, transfer operators and Hilbert modules. This project is in the general area of functional analysis, an area where both Newcastle University and the University of New South Wales have strong international reputations. The aim of the project is to study irreversible dynamics in the presence of transfer operators, as recently introduced by Professor Exel. The motivation comes from a variety of examples arising in different areas of mathematics, including number theory and graph theor ....Endomorphisms, transfer operators and Hilbert modules. This project is in the general area of functional analysis, an area where both Newcastle University and the University of New South Wales have strong international reputations. The aim of the project is to study irreversible dynamics in the presence of transfer operators, as recently introduced by Professor Exel. The motivation comes from a variety of examples arising in different areas of mathematics, including number theory and graph theory. It is hoped that the results will give new understanding of the algebraic and analytic structure underlying the multi-resolution analyses used in approximation theory and Fourier analysis. This project will help ensure that Australia has a strong foundation in mathematics which will foster innovation.Read moreRead less
Operator algebras associated to semigroups and graphs. This project aims to unify ideas from two highly topical areas of mathematics in which one studies discrete objects by representing them as families of linear transformations. In the first area, one represents the semigroups which model irreversible dynamics as isometries (that is, distance-preserving transformations); in the second, one represents networks by families of partially defined isometries in a way which reflects the behaviour of ....Operator algebras associated to semigroups and graphs. This project aims to unify ideas from two highly topical areas of mathematics in which one studies discrete objects by representing them as families of linear transformations. In the first area, one represents the semigroups which model irreversible dynamics as isometries (that is, distance-preserving transformations); in the second, one represents networks by families of partially defined isometries in a way which reflects the behaviour of paths in the network. The link will be achieved by viewing the operator algebras they generate as semidirect products which have been twisted by a noncommutative cocycle.Read moreRead less
Operator algebras associated to groupoids. Australian researchers have a strong reputation for excellence and innovation in the field of operator algebras. Operator algebras associated to groupoids have been immensely influential in recent decades, both within mathematics and via applications to theoretical physics. This project will develop an innovative approach to groupoid algebras, and will help to maintain the high standing of Australian researchers in this important field.
Co-universal operator algebras. Australian researchers have established themselves at the very forefront of research into operator algebras associated to graphs. The proposed research will make an important impact, at a fundamental level, on the way that researchers around the world view these operator algebras. This will help to further strengthen Australia's reputation in this field. The proposed program will also train two PhD students in a very active area of mathematics and put them in cont ....Co-universal operator algebras. Australian researchers have established themselves at the very forefront of research into operator algebras associated to graphs. The proposed research will make an important impact, at a fundamental level, on the way that researchers around the world view these operator algebras. This will help to further strengthen Australia's reputation in this field. The proposed program will also train two PhD students in a very active area of mathematics and put them in contact with a vibrant research community. This will help contribute to the strong future of pure mathematics in Australia.Read moreRead less
Molecular dissection of the functional regions of genes that encode actinins (ACTN2 and ACTN3) and their contribution to normal variation in skeletal muscle function. The project has discovered a common genetic variant that affects skeletal muscle structure, function and metabolism and influences athletic ability, and response to diet and exercise. The project will study how this gene influences muscle bulk and strength, the metabolic efficiency of muscle and the risk of obesity in the general ....Molecular dissection of the functional regions of genes that encode actinins (ACTN2 and ACTN3) and their contribution to normal variation in skeletal muscle function. The project has discovered a common genetic variant that affects skeletal muscle structure, function and metabolism and influences athletic ability, and response to diet and exercise. The project will study how this gene influences muscle bulk and strength, the metabolic efficiency of muscle and the risk of obesity in the general population.Read moreRead less
Sexual antagonism and the consequences of sex-specific selection. Males and females arise from essentially the same genome yet are selected in vastly different ways. This exposes gene pools to alternate episodes of feminising- and masculinising-selection, thereby promoting Sexually Antagonistic (SA) evolution. Sex chromosomes are predicted to play an important role in SA evolution because sex-linkage allows for gender-specific gene expression, but data on the role of sex-linked genes are limited ....Sexual antagonism and the consequences of sex-specific selection. Males and females arise from essentially the same genome yet are selected in vastly different ways. This exposes gene pools to alternate episodes of feminising- and masculinising-selection, thereby promoting Sexually Antagonistic (SA) evolution. Sex chromosomes are predicted to play an important role in SA evolution because sex-linkage allows for gender-specific gene expression, but data on the role of sex-linked genes are limited to Drosophila, a male heterogametic (XY) model. This project will determine the consequences of SA selection in the butterfly Eurema hecabe (a female ZW heterogamete) using experimental evolution and the feminising endosymbiont Wolbachia to force male genomes through bouts of feminising selection.Read moreRead less
New Directions in Noncommutative Geometry. A. Connes' noncommutative geometry has recently become important in topology, geometry and physics. The central geometric objects in noncommutative geometry are called spectral triples. Spectral triples also provide the framework for studying some important classes of equations. This project will extend the definitions of spectral triples to cover additional important examples. This extension will provide the tools to study a broad class of boundary val ....New Directions in Noncommutative Geometry. A. Connes' noncommutative geometry has recently become important in topology, geometry and physics. The central geometric objects in noncommutative geometry are called spectral triples. Spectral triples also provide the framework for studying some important classes of equations. This project will extend the definitions of spectral triples to cover additional important examples. This extension will provide the tools to study a broad class of boundary value problems in the theory of equations. Such problems occur in several areas of modern physics. In addition, results obtained will be useful for studying the structure of the most important spectral triples, called noncommutative manifolds.Read moreRead less
Refining the timescale of human evolution and dispersal using ancient DNA. Understanding the timescale of human evolution and migration is a key goal of genetic analysis. It provides the foundation for studying our evolutionary and demographic history, our relationships to other hominids and our impact on the natural world. This project aims to use ancient DNA data to improve estimates of our evolutionary timescale.
Cellular Gene Regulation Networks. The benefit to Australia will be scientific in terms of providing an understanding of how cells integrate transcriptional control systems and the networks that are involved. This will inform research on folate deficiency and aberrant human development and towards identifying genes that are important in improving efficiency of microbial fermentations. Additional and more practical major benefits will follow from the development of tools to analyse interaction ....Cellular Gene Regulation Networks. The benefit to Australia will be scientific in terms of providing an understanding of how cells integrate transcriptional control systems and the networks that are involved. This will inform research on folate deficiency and aberrant human development and towards identifying genes that are important in improving efficiency of microbial fermentations. Additional and more practical major benefits will follow from the development of tools to analyse interactions between control systems, including software of value to the research community. The work will provide postgraduate students with major training in up-to-date genomic technologies, and in the interface between application of bioinformatics and experimental science.
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