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
Representations of dynamical systems, amenability, and proper actions. Mathematicians study abstract objects by representing them in terms of well-understood concrete models, and need to know when a representation is faithful, in the sense that the model contains complete information. Dynamical systems are an abstraction of physical systems suitable for studying time evolution and symmetries. The project aims to determine when important representations of dynamical systems are faithful, or, in ....Representations of dynamical systems, amenability, and proper actions. Mathematicians study abstract objects by representing them in terms of well-understood concrete models, and need to know when a representation is faithful, in the sense that the model contains complete information. Dynamical systems are an abstraction of physical systems suitable for studying time evolution and symmetries. The project aims to determine when important representations of dynamical systems are faithful, or, in mathematical language, when the dynamical system is amenable. The proposed strategy involves extending Rieffel's notion of proper actions; the construction should be of wide applicability apart from the intended applications to amenability.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
The structure of quantum groups. We propose to study the structure of mathematical objects used in describing symmetries of micro-scale phenomena. The project will significantly develop already well established Australian-Korean cooperation in this exciting and rapidly growing area of research. The results will be immediately applicable to related fields of mathematics, most notably to noncommutative geometry. In the long run, the outcomes will help in better understanding of fundamental problem ....The structure of quantum groups. We propose to study the structure of mathematical objects used in describing symmetries of micro-scale phenomena. The project will significantly develop already well established Australian-Korean cooperation in this exciting and rapidly growing area of research. The results will be immediately applicable to related fields of mathematics, most notably to noncommutative geometry. In the long run, the outcomes will help in better understanding of fundamental problems of modern quantum physics.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
The biology and epidemiology of the grapevine canker fungi, Botryosphaeria sp. Decline and dieback of grapevines is becoming an increasing problem for the viticulture industry in NSW. Recently, species of the fungus Botryosphaeria, were isolated from grapevines exhibiting these symptoms. In order to understand the biology and epidemiology of the causal organisms, we aim to; (i) determine species of Botryosphaeria present in NSW vineyards; (ii) determine which species are pathogenic on grapevines ....The biology and epidemiology of the grapevine canker fungi, Botryosphaeria sp. Decline and dieback of grapevines is becoming an increasing problem for the viticulture industry in NSW. Recently, species of the fungus Botryosphaeria, were isolated from grapevines exhibiting these symptoms. In order to understand the biology and epidemiology of the causal organisms, we aim to; (i) determine species of Botryosphaeria present in NSW vineyards; (ii) determine which species are pathogenic on grapevines; (iii) characterise the genetic diversity of strains and; (iv) screen fungicides for the control of these fungi. Information on the species, their biology and pathogenicity on grapevines, will enable the development of appropriate management strategies for its control and may lead to the development of molecular tools to identify species of Botryosphaeria.Read moreRead less
Methods to infer dense genomic information from sparsely genotyped populations. Prediction of phenotype based on DNA polymorphisms or sequence has important applications such as prediction of disease risk in human medicine and prediction of genetic value in plant or animal breeding. This project will enhance precision and lower the cost of association studies leading to substantial increase in accuracy of such predictions. This will allow more effective genetic improvement, particularly of diff ....Methods to infer dense genomic information from sparsely genotyped populations. Prediction of phenotype based on DNA polymorphisms or sequence has important applications such as prediction of disease risk in human medicine and prediction of genetic value in plant or animal breeding. This project will enhance precision and lower the cost of association studies leading to substantial increase in accuracy of such predictions. This will allow more effective genetic improvement, particularly of difficult but important traits such as disease resistance, reduced green-house gas emissions and product quality. The same methods can be extended to improve genetic improvement in plants and better prediction of human disease risk. Read moreRead less