Research strengths

Bioinformatics

Modern biology is much more quantitative than the biology of the past, and is now critically dependent on the mathematical, physical and computer sciences. The School of Mathematical Sciences has a strong group of statistical bioinformaticians who conduct research in genomics, proteomics and systems biology in collaboration with biomedical researchers from government, universities and industry.

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Biostatistics

Biostatistics, also known as medical statistics, is central to the development and practice of modern medicine. Indeed, without biostatistical principles for the conduct of clinical trials and epidemiological studies, the pharmaceutical industry would not exist. Biostatistics has driven a great of novel statistical methodology over the past three decades, and top universities around the world have whole departments devoted to biostatistics. This is an area of critical skills shortage in Australia, and the School of Mathematical Sciences has one of the few strong biostatistical groups in this country.

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Geometry

Geometry lies at the core of modern mathematics with deep and wide implications in other mathematical disciplines, pure and applied. For example, geometry is used in cryptology, medical imaging, and physics. Geometry draws on methods from algebra, differential equations, and topology to investigate spaces ranging from our own 3-dimensional space to abstract spaces that can have infinitely many dimensions. The School of Mathematical Sciences has an active group of researchers in geometry with an international reputation.

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Mathematical Physics

Mathematics and physics have been closely linked since the earliest of times. Today's physics requires sophisticated mathematical ideas and, in turn, feeds back new ideas and physical intuition to long-standing mathematical problems. The School of Mathematical Sciences has an active group of researchers in mathematical physics with an international reputation. The Differential Geometry Seminar meets regularly with talks by local researchers and visitors. The Institute for Geometry and its Applications organises international conferences and workshops .

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Mathematics of Risk

From observing previous and current financial and other problems it is clear that risk is a pervasive component of existence for all organizations. What is perhaps less well known is how mathematics can model exposure and indicate appropriate steps to reduce loss. Financial risk is only one aspect of the subject, though at the moment probably the most highly developed mathematically. Risk arises when companies plan future operations; risk arises when governments decide policies at the national or international level; indeed, risk arises when individuals make plans for the future. The essence of risk, indeed of life, is that the future is unknown. Here mathematics, the study of patterns, can contribute. Mathematically the future can be modelled by considering, in simplified frameworks, possible scenarios or future states of the world. These outcomes can then be assessed using methods from probability and random processes. Objectives of the research include: (1) the development of new risk measures, particularly those related to nonlinear expectations and backward stochastic differential equations, (2) their implementation in both financial and non financial settings, (3) the calibration or tuning of the models, (4) the combining of information from different sources, and (5) the application of the results to problems provided by industry and government. While financial risk has, so far, motivated the most sophisticated modelling, mathematics can contribute to assessing and mitigating the effects of risk in many situations.

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Stochastic Modelling and Optimisation

Much of human intellectual endeavour is directed to predicting and modifying the future. Initially this is attempted by looking for patterns. Sophisticated methods for the study of patterns are provided by mathematics. Measurements and data are studied to suggest patterns, which are then modelled mathematically. The predictions of the models are tested against further observations and the models used to make decisions and modify future outcomes. The applications of stochastic, or random, processes in engineering, finance, biology and many other fields fit this paradigm. In all cases real world measurements and data provide the foundations for theoretical models. These models are then explored to make predictions and assist in improved decisions, whether they are investment strategies, management policies in telecommunications networks, or potential new avenues for cancer treatment. We are associated with two groups that specialise in performing contract research and consulting with the defence sector, CDCIN, and the telecommunications sector and general industry, TRC Mathematical Modelling.

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Nanomechanics

The power of nanotechnology is rooted in its potential to revolutionise technology and industry, including information technology, biotechnology, medicine, aerospace, defence, energy and the environment. In order to fully realise the promise of nanotechnology, all the scientific disciplines must be brought to bear, including mathematics and mathematical modelling which can provide insights into the many novel results that are being reported in the experimental literature every week. In the Nanomechanics Group, we employ mathematical modelling using integral calculus, geometry, the calculus of variations, classical mechanics and many other mathematical techniques in order to understand and explain the unique behaviour of nanoscale systems.

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Theoretical and Applied Mechanics

Theoretical and Applied Mechanics (TAM) is the study of fluid and solid mechanics, from both a theoretical and applied perspective. Research in TAM at Adelaide dates back to the founding of the University through the work of the Foundation Chair of Mathematics, Sir Horace Lamb. We are involved in leading edge research in areas such as dynamical systems, mathematical biology, fluid mechanics and solid mechanics. Our research aims to develop a fundamental understanding of the behaviour of mechanical and biological systems through the use of advanced mathematical techniques and the use of modern computing technologies.

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