Much of our research is interdisciplinary with strong links to the rest of the sciences, especially biology. The mathematics we use spans the spectrum from applying differential equations to modelling the dynamics of Tasmanian Devil facial tumour and Ross River virus, to building statistical models of plant pollination strategies, to analysing the algebraic symmetries of bacterial gene rearrangement. We have an international reputation for our research in mathematical phylogenetics which makes use of DNA sequence data to infer the evolutionary tree of life.
Beyond biological applications we have applied techniques from Decision Science (Operations Research) to improve efficiency of hospital systems, we have numerically optimised the design of coils for magnetic resonance imaging, modelled the behaviour of planetary and gravity waves and constructed scuba diving decompression tables. Read on to find out more about our researchers’ activities and interests.
Postgraduate projects available for the current round are shown on the Research Degrees site under the School of Natural Sciences. However, other projects become available on a regular basis.
Research Specialisations and Key Strengths
The theory of group representations is an important branch of pure mathematics which has many applications in other areas, such as mathematical physics, number theory, chemistry, and phylogenetics. It offers techniques to study abstract algebraic structures by representing their elements as linear transformations of vector spaces (Banach or Hilbert spaces if locally compact groups are considered). In the foundational steps it reduces problems in abstract algebra to problems in linear algebra, a subject that is well-understood. Representation theory has led to many generalisations; for instance, we acknowledge that pure mathematics is enriched by its power to illuminate and generalize Fourier Analysis via harmonic analysis, an area that is fundamental to many applications in applied mathematics and physics (MRI studies, Partial Differential Equations to name a few). With the aid of measure and integration techniques on topological spaces, representation theory of groups has proven to be an important area of study/research in modern analysis.
Key researchers:
Kumudini Dharmadasa: Theory of representations
Jeremy Sumner: His research interests revolve around applications of algebraic methods to phylogenetic models. His specialty is exploiting the symmetries inherent in the problem by applying algebraic methods such as group representation theory to analyse and improve phylogenetic methodologies.
The area of applied mathematics broadly covers the application of mathematics to problems in science, engineering, and industry. Mathematical explanations of the complexities of the real world are constructed then used to predict behaviour. Such development often begins with a simple, idealised environment in which the mathematics itself is of prime importance. Models are then adapted to mimic real world scenarios.
Members of our research group have made significant contributions in both aspects of this process. Numerous fundamental advancements in fluid dynamics modelling have enabled us to confirm observations of star behaviour, simulate the atmospheric polar hexagon on Saturn, model the propagation of combustion waves and shock waves in gas, and model the behaviour of planetary and gravity waves. In biological applications we have modelled climate impacts on butterfly emergence, pollen dispersal by bees, and the spread and transmission of infectious diseases such as mange in wombats, facial tumour in Tasmanian devils, and Ross River virus. In magnetic resonance imaging (MRI) we have made significant contributions to the design of magnets and coils, the reduction of acoustic noise, and improvements in image reconstruction techniques in high-field imaging.
Key researchers:
Larry Forbes: He has worked on ship hydrodynamics, shock waves in gases, and outflows from underwater explosions or stars. Most recently, he has proposed a model of fluid turbulence. He has also worked on the design of magnetic and radiofrequency coils used in magnetic resonance imaging (MRI) machines in hospitals. Other research interests include modelling of disease spread and the behaviour of complex chemical reaction systems.
Andrew Bassom: Has interests in fluid mechanics, mathematical modelling and differential equations. He has solved several problems concerning the stability of time-periodic flows and has looked at the application of these results in a range of problems from ocean flows to the ventilation of premature babies. He has modelled a number of industrial and applied problems including the design of open-pit mines and the construction of novel scuba diving decompression tables. He interacts with researchers in other areas; principally geophysics and oceanography.
Michael Brideson: Michael’s research is focused on the design of magnets used in MRI machines as well as on image reconstruction techniques for MRI.
Jason Cosgrove: selective withdrawal from multi-layered fluid systems and numerical simulations of interacting atmospheric vortices using ‘tangent plane’ approximations.
Shane Richards: theoretical population and evolutionary ecology, conservation biology
Michael Charleston: is interested in analysis of biological networks of all kinds, molecular evolution and phylogenetics, epidemiology of infectious disease, the foraging behaviour of social insects, and co-evolution of parasites or pathogens and their hosts. He works with epidemiologists, computer scientists, ecologists, historians, statisticians, plant scientists, geneticists, and probably some more.
Operations Research (OR) is a field of expertise that is highly sought-after by industry, to which it contributes millions of dollars in benefits and savings each year. OR techniques such as mathematical modelling, statistical analysis, simulation, and optimisation, are used to find solutions to complex decision-making problems in a wide range of areas, including engineering, manufacturing, energy, environment, sustainability, transportation, economics, medicine, music, computer science, and artificial intelligence. OR is also often applied to problems in theoretical and applied biology. For example, OR has helped develop robust wildfire management strategies for conservation biology, and has been used to predict optimal life-history strategies, such as when to reproduce and when to grow.
Stochastic Modelling is a major sub-discipline of OR that focuses on developing methodologies for real-life systems under uncertainty. The work involves constructing models, analysing them analytically, deriving mathematical expressions for various performance measures, building efficient algorithms for their numerical evaluations, and simulations. Markov chains is the most important class of stochastic models due to their powerful modelling features, numerical tractability, and applicability to many real-life systems of great engineering or environmental significance.
Key Researchers:
Małgorzata O'Reilly: Her interests include applications of OR and stochastic models, for example in phylogenetics, modelling evolution, microsatellites, speciation, phylogenetic trees; conservation of endangered species; healthcare systems, patient flow, patient admission scheduling; internet networks, mobile networks; satellite data analysis, change detection. Theory of Markov chains, Markovian-modulated models, algorithms, random processes, queues, and other topics in matrix-analytic-methods, an area of applied probability that focuses on developing methodologies that are suitable for real-life applications using computers.
Shane Richards: theoretical population and evolutionary ecology, conservation biology
Phylogenetics is concerned with the problem of reconstructing the past evolutionary history of extant organisms from present day molecular data such as DNA. There is ongoing interest in further development of the mathematics that underlies computational phylogenetic methods.
Hidden from view, in the software packages used by biologists, are algorithms performing statistical inference using Markov models on binary trees. The mathematics involved represents a wonderful confluence of stochastic methods and probability theory (Markov chain models), discrete mathematics (combinatorics of tree space), statistical inference (maximum likelihood and Bayesian methods) and, more recently, methods taken from algebraic geometry and the representation theory of finite and infinite (Lie) groups. There are many important theoretical problems that arise, such as statistical identifiability of models, consistency and convergence of methods. These problems can only be solved using a multi-disciplinary approach.
Key researchers:
Barbara Holland: She is interested in developing tools that can assess if sequence data is well explained by a simple tree model or if more complex processes such as hybridisation, recombination or convergent selection are at work. The areas of mathematics/statistics that she uses frequently include stochastic models, continuous time Markov chains, combinatorial optimization, maximum likelihood, and simulation.
Michael Charleston: biological networks of all kinds, molecular evolution, co-evolution
Jeremy Sumner: His research interests revolve around applications of algebraic methods to phylogenetic models. His specialty is exploiting the symmetries inherent in the problem by applying algebraic methods such as group representation theory to analyse and improve phylogenetic methodologies.
Understanding the noisy world in which we live involves building probabilistic models and fitting them to real-world data, that may have been collected opportunistically, or the result of a well-planned manipulative scientific study. Mathematical models reflect hypotheses about how we think a system behaves and comparing the predictive ability of multiple models allows us to critically assess our hypotheses. Biology, and in particular ecology, have benefitted enormously from mathematical modelling and statistics. How mechanisms of interest can be explicitly incorporated into models and the best way to compare and select useful models is an important focus of statistics research. These research topics are addressed using frequentist and Bayesian frameworks.
Key researchers:
Shane Richards: statistical ecology
Honours Research and Summer Research Scholarship
If you have completed a mathematics focused Bachelor degree with a high level of academic achievement, the one year Mathematics Honours programme is an attractive option to further develop your skills. Combining a research project with advanced level coursework, Honours provides an excellent pathway into life as a professional mathematician.
The coursework gives more advanced applications of mathematics and a deeper understanding of mathematical concepts, whilst the research project exposes you to the frontiers of knowledge. The project is conducted under the direction of a supervisor in a theme area of the department and culminates with the submission of a thesis.
UTas Honours graduates have taken their skills into industry, financial institutions, government departments, and teaching. Others have used the year as preparation for a research higher degree, either at UTas or at universities across Australia and the world.
For enquiries about undertaking Honours, please contact: Dr Michael Brideson
The College of Sciences and Engineering offers the Dean's Summer Research Scholarship for eligible students. Research projects in Maths are generally completed over the summer of your second and/or third undergraduate year of study.
If you want to know more about what Summer Research can mean for a Maths student, check out Rhiannan's amazing story While an undergraduate student she travelled on a research voyage, continuing the same project from her first summer scholarship into a second, which then led to an honours year!
Visit the College website for general information on the Summer Research Scholarship.
If you're interested, the first step is to express interest to your Mathematics lecturers. They can help identify research opportunities and get you on track. It all starts with a conversation!
