Mathematical Sciences Research at QUT

The School of Mathematical Sciences is an innovative and thriving centre of excellence at QUT. Our research programs aim to solve real-world problems of global significance. In the Australian Government’s Excellence in Research for Australia (ERA) framework, our ambitious research programs have consistently been rated at the highest possible level: ‘well above world standard.’

Our research strengths are in statistical data science, computational modelling and simulation, decision theory and operations research.

We partner with businesses and organisations from start-ups to multinationals and our scope of application is inclusive, ranging from mathematical biology through climate change to engineering, natural resources, economics and finance.

Our research strengths

Using a range of mathematical, statistical, and computational modelling techniques, we aim to explore and understand various applications in medicine and biology. These applications include collective cell motion, wound healing, cancer progression, disease progression, signalling networks and tissue growth. We build mathematical models that are inspired by biological observations and measurements, and our research often involves close partnerships with life scientists.

Key researchers

  • Dr Adrianne Jenner
    Mathematical biology, specifically oncology, virotherapy and immunology, applied mathematics and computational mathematics.

  • Professor Matthew Simpson
    Continuous and discrete models of cell biology phenomena (tissue growth, cancer development); integration with experimental data, identifiability analysis, and parameter estimation.
  • Professor Scott McCue
    Analysis of reaction-diffusion models and random walk models for collective cell motion.
  • Dr David Warne
    Stochastic modelling of biochemical reaction networks, cell motility and proliferation, and epidemics.
  • Dr Brodie Lawson
    Bayesian inference, intersubject variability, simulation science, partial differential equations, cardiac electrophysiology, information geometry.
  • Dr Jesse Sharp
    Population growth models, ecological modelling, optimal control, numerical methods, Inference.

We aim to understand ecological systems and our environment by developing and applying new mathematical and statistical methods. Ecosystems and the way people interact with them are complex, with many moving parts and high uncertainties. We build models of these systems and use those models to optimise their management to improve ongoing sustainability. Learn about the Applied Mathematical Ecology Group.

Key researchers

  • Professor Michael Bode
    Ecological and evolutionary modelling, conservation decision-making, environmental economics.
  • Dr Matthew Adams
    Ecological modelling, mechanistic models, and Bayesian inference for model-data calibration, ecological networks, tipping points/regime shifts, and seagrass.
  • Dr David Warne
    Modelling of delays in coral reef recovery, statistical modelling of coral cover, and sampling design for reef monitoring.

We develop and apply mathematical and computational techniques to study the motion of fluids. Our focus is on interfacial fluid mechanics, which involves mathematical models where there are two or more fluids separated by interfaces, and flows through porous media.

Key researchers

  • Professor Scott McCue
    Stefan problems, free surface flows, Hele-Shaw flows, thin film flows, droplet impaction.
  • Professor Ian Turner
    Computational porous media flow, modelling the heat and mass transfer processes arising during the drying of porous media, smoothed-particle hydrodynamics, finite volume methods, meshfree methods, and multiscale modelling.
  • Professor Timothy Moroney
    Linear and nonlinear ship waves, droplet spreading, computational methods for solving moving boundary problems, computational porous media flow.
  • Dr Michael Dallaston
    Theoretical fluid dynamics, interfacial flows and instability, the thin film flows, flow in porous media, asymptotic methods and similarity solutions.
  • Dr Elliot Carr
    Heterogeneous porous media flow, heat and mass transport in porous media, multilayered diffusion.

We develop numerical and analytic solutions for space, time, and space-time fractional partial differential equations. There is a strong emphasis on the application of numerical analysis for studying the convergence and stability of the underlying numerical algorithms. We apply these fractional models to study the anomalous transport processes evident across a range of scales arising in many physical and biological processes.We develop and apply mathematical and computational techniques to study the motion of fluids. Our focus is on interfacial fluid mechanics, which involves mathematical models where there are two or more fluids separated by interfaces, and flows through porous media.

Key researchers

  • Dr Pamela Burrage
    Stochastic simulation algorithms, numerical solutions of ordinary and stochastic differential equations, parallel computing, data visualisation.
  • Dr Qianqian Yang
    Applied and computational mathematics, and fractional order partial differential equations.

  • Professor Kevin Burrage
    Multiscale modelling and simulation, cardiac electrophysiology modelling, stochastic simulation algorithms, numerical analysis.
  • Professor Ian Turner
    Computational modelling for simulating flow in porous media, finite volume methods, meshfree methods, multiscale modelling methods, and modelling anomalous transport phenomena in porous media using fractional partial differential equations.

  • Professor Timothy Moroney
    Finite volume methods, level set methods, surface reconstruction, fractional differential equations.
  • Dr Libo Feng
    Numerical methods, Numerical analysis, Fractional calculus, Non-Newtonian fluid models, Anomalous diffusion, Comb models.

Large-scale computational methods are used to model and optimise the design of material microstructure across a range of applications, including, for example, piezo-electric sensors for robots and bone implant prototypes.

Key researchers

  • Dr Vivien Challis
    Topology optimisation. Piezoelectric materials. Finite element methods. Solid Mechanics. High-performance computing.

We develop new computational methods and algorithms to solve challenging statistical problems, predominantly those related to Bayesian inference. Bayesian statistics is a popular inferential paradigm in many applied disciplines, but it is being constantly challenged by increases in model complexity and data size. Advances in statistical algorithms, combined with modern machine learning methods, further unlock the scope of applications that can benefit from Bayesian techniques.

Key researchers

  • Dr Leah South
    Monte Carlo methods, variance reduction, scalable Monte Carlo methods, Stein’s method in machine learning, statistical machine learning, Markov chain Monte Carlo, sequential Monte Carlo, and Bayesian synthetic likelihood.
  • Professor Chris Drovandi
    Approximate Bayesian computation, Bayesian experimental design, Bayesian synthetic likelihood, implicit models, likelihood-free inference, Monte Carlo methods, Markov chain Monte Carlo, sequential Monte Carlo, simulation-based inference, statistical data science, surrogate modelling, robust Bayesian inference.
  • Dr David Warne
    Monte Carlo methods, multi-fidelity methods, multilevel Monte Carlo, sequential Monte Carlo, intractable likelihoods, simulation-based inference, uncertainty quantification, parameter identifiability, computational inference, partially observed Markov processes.

Data science is a powerful force for addressing the challenges we face across all sectors — health, environment, business, society and industry. Its ability to solve global challenges is at the forefront of discussions and strategic activity in most commercial and government organisations, research entities and universities. The QUT Centre for Data Science draws together capabilities in data science from across Australia, providing a centralised hub for world-class data science research, unique training opportunities, and active external engagement.

Key researchers

  • Associate Professor Helen Thompson
    Optimal design of experiments, clinical trial design, Bayesian design, spatial modelling and sampling, Copula modelling, Stochastic frontier modelling and applied statistics.
  • Professor James McGree
    Bayesian adaptive clinical trials, Bayesian design, Bayesian sequential design, decision-theoretic design of experiments, loss functions, model discrepancy, optimal sub-sampling methods, robust design, and utility functions.
  • Dr Edgar Santos Fernandez
    Bayesian models, applied statistics, spatial statistics, spatio-temporal modelling, anomaly detection, complex data.

Optimisation and simulation relating to transport, logistics, manufacturing and supply chain for industry, agriculture, healthcare and natural resource management.

Key researcher

  • Dr Guvenc Dik
    Mixed integer programming, meta-heuristics, scheduling, routing, and discrete-event simulation.