Estimation of non-additive genetic variance for complex traits using genome-wide single nucleotide polymorphyisms and sequence data. Finding genes for traits of importance in agriculture, ecology and human health depends on understanding the genetic basis of these traits. This project will investigate whether variation in traits in humans, cattle and wild sheep are influenced by gene-gene interactions.
The genetic architecture and evolution of quantitative traits. Most important traits are controlled by many genes and by the environment, however there is little knowledge of how many genes are involved in these complex traits and what their effects are. This project will describe the number of genes and their effects for complex traits in humans and livestock and explain how these genes evolve.
Rapid mapping of genes for complex traits. This project will develop a new resource that will allow rapid identification of genes controlling complex traits. This world-leading resource will improve knowledge of diseases like diabetes and neurological diseases.
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
Mutational genetic variance and the fitness optimum. Mutation and selection are ubiquitous forces in nature, but we do not understand how genetic variation produced by mutation is maintained in the presence of selection that depletes it. The recent discovery of apparent stabilising selection on traits with high levels of genetic variation provides a new approach to understanding this paradox.
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