Novel geometric invariants. Quantum theory is the language of fundamental physics, it describes the small scale structure of matter and possibly space-time. Sophisticated models in condensed matter physics and string theory have exposed geometric and topological structure as basic building blocks of the theory. Issues thrown up by quantum theory are very similar to, and have provided techniques to solve, problems in the geometry of three and four dimensional manifolds. Exciting two way exchanges ....Novel geometric invariants. Quantum theory is the language of fundamental physics, it describes the small scale structure of matter and possibly space-time. Sophisticated models in condensed matter physics and string theory have exposed geometric and topological structure as basic building blocks of the theory. Issues thrown up by quantum theory are very similar to, and have provided techniques to solve, problems in the geometry of three and four dimensional manifolds. Exciting two way exchanges of methods, problems and solutions have emerged. This project aims to settle fundamental questions in the interaction between these two fields.Read moreRead less
New approaches to index theory. The laws of nature are often expressed by differential equations, involving their rates of change. If 'elliptic,' they have an 'index,' which is the number of solutions minus the number of constraints imposed. The Atiyah-Singer index theorem gives a striking calculation of this "index'. An extension is Fractional Index Theory, which has received international attention, having solved a fundamental open problem. A central aim is to investigate this further. I will ....New approaches to index theory. The laws of nature are often expressed by differential equations, involving their rates of change. If 'elliptic,' they have an 'index,' which is the number of solutions minus the number of constraints imposed. The Atiyah-Singer index theorem gives a striking calculation of this "index'. An extension is Fractional Index Theory, which has received international attention, having solved a fundamental open problem. A central aim is to investigate this further. I will assist beginners to navigate to the cutting edge of research through workshops, spring-schools and supervision. Benefits include the enhancement of Australia's position in the forefront of international research.Read moreRead less
Operator Integrals and Derivatives. The project is a contribution to the study of non-commutative differential and integral calculus. The novelty of the present project lies in the study of smoothness properties of functions whose domains and ranges are spaces of unbounded, non-commuting operators on some Hilbert space. Our general approach will be based on a detailed investigation of properties of double operator integrals, which permit smoothness estimates of operator-functions. It can be expe ....Operator Integrals and Derivatives. The project is a contribution to the study of non-commutative differential and integral calculus. The novelty of the present project lies in the study of smoothness properties of functions whose domains and ranges are spaces of unbounded, non-commuting operators on some Hilbert space. Our general approach will be based on a detailed investigation of properties of double operator integrals, which permit smoothness estimates of operator-functions. It can be expected that the new techniques generated will find further application in areas of mathematical physics and non-commutative geometry related to quantized calculus.
Read moreRead less
Non-commutative analysis and differential calculus. This project is in an area of central mathematical importance and will lead to important scientific advances that will keep Australia at the forefront internationally in this field of research. There is an emphasis on international networking and we will collaborate with leading researchers in USA and France.
Preventing biological growth – a new generation anti-biofouling coatings. The project aims to improve anti-biofouling technology by developing a ‘smart and green’ coating that requires no toxic biocides and makes use of copper already present in the water. Biofouling is the unwanted attachment and growth on surfaces in water; it causes significant problems on ships and in drinking water systems, and damages infrastructure and capital investment. Biofouling also carries a significant risk of spre ....Preventing biological growth – a new generation anti-biofouling coatings. The project aims to improve anti-biofouling technology by developing a ‘smart and green’ coating that requires no toxic biocides and makes use of copper already present in the water. Biofouling is the unwanted attachment and growth on surfaces in water; it causes significant problems on ships and in drinking water systems, and damages infrastructure and capital investment. Biofouling also carries a significant risk of spreading diseases and environmental damage through the introduction of invasive marine species. Existing coatings release highly toxic substances into the water, causing untold environmental damage. This project offers a single, comprehensive solution for all of the above problems.Read moreRead less
There and back again: operator algebras, algebras and dynamical systems. The aim of this project is to develop mathematics that enables us to transfer information back and forth between dynamical systems and algebras, including operator algebras. Dynamical systems - systems that change over time - are ubiquitous, and central to modern mathematics and its applications. In mathematics, dualities allow us to translate questions from one context to another in which they are easier to solve and then ....There and back again: operator algebras, algebras and dynamical systems. The aim of this project is to develop mathematics that enables us to transfer information back and forth between dynamical systems and algebras, including operator algebras. Dynamical systems - systems that change over time - are ubiquitous, and central to modern mathematics and its applications. In mathematics, dualities allow us to translate questions from one context to another in which they are easier to solve and then translate the answer back again. Expected outcomes include increased understanding of the relationship between operator algebras and the dynamical systems that they represent. Benefits include enhanced international collaboration, and increased Australian capacity in pure mathematics, particularly operator algebras.Read moreRead less
Left to right is front to back: attentional distortions in near and far space for healthy and clinical populations. We are investigating a perceptual bias that makes people think objects right in front of them are actually slightly to the right but objects far away are slightly to the left. This project will help understand why this happens, to help reduce traffic collisions and help people with brain damage that causes similar perceptual biases.
Attentional asymmetries for navigation in healthy and clinical groups. This project plans to investigate how differences in attentional capacity between the left and right sides of the brain affect the ability to walk or manoeuvre vehicles between obstacles. To navigate our environment and avoid obstacles, we need to attend to stimuli that are important and ignore those that are not. Unfortunately, the brain’s attentional capacity is limited, which can result in errors and collisions. Using the ....Attentional asymmetries for navigation in healthy and clinical groups. This project plans to investigate how differences in attentional capacity between the left and right sides of the brain affect the ability to walk or manoeuvre vehicles between obstacles. To navigate our environment and avoid obstacles, we need to attend to stimuli that are important and ignore those that are not. Unfortunately, the brain’s attentional capacity is limited, which can result in errors and collisions. Using the techniques of cognitive neuroscience, the project aims to provide a better understanding of the cognitive and neural mechanisms that govern attention in an applied setting. It expects to identify the factors that exacerbate lapses in attention and collisions. The effect of everyday impediments such as mobile phones, alcohol and fatigue will be investigated together with means of minimising these attentional lapses and improving safety.Read moreRead less
Close to me: the effect of distractors on spatial attention in healthy and clinical populations. To function well, we need to pay attention to what is important. This project investigates how the brain responds to distractors, such as a person or object that is close by. This knowledge will help with the treatment of people with attentional disorders and will assist the design of human/machine interfaces, such as cars and security screening.
Solar-thermal desalination system for parallel water-electricity generation. This project aims to develop a multi-functional solar-thermal desalination device to simultaneously produce clean water and electricity. Interfacial solar evaporation-based desalination technology has the unique advantage of using solar light as the sole energy source for affordable clean water production. However, its absolute evaporation rate is still too low for practical application and all of the latent heat releas ....Solar-thermal desalination system for parallel water-electricity generation. This project aims to develop a multi-functional solar-thermal desalination device to simultaneously produce clean water and electricity. Interfacial solar evaporation-based desalination technology has the unique advantage of using solar light as the sole energy source for affordable clean water production. However, its absolute evaporation rate is still too low for practical application and all of the latent heat released from vapor condensation during desalination is wasted. Solving these two critical issues by the study of energy nexus, design and fabrication of advanced photothermal materials and desalination devices could accelerate practical adoption of this technology and benefit millions of people who desperately need clean water. Read moreRead less