Below is a sample of some of the PhD research projects offered by staff members in the School of Mathematics and Statistics (updated September 2021). Please note that this is not an exhaustive list of all potential projects and supervisors available in the School.
Information about PhD research offerings and potential supervisors can be found in various locations. It's worth browsing the Current Research Students list to see what research our PhD students are currently working on, and with whom.
There is also a Past Research Students list which provides links to the theses of former students and the names of their supervisors.
It's also recommended to browse our Staff Directory, where our staff members' names are linked to their research profiles which provide details about their areas of research and often include the topics they are open to supervising students in.
We host PhD information sessions in the School of Mathematics and Statistics twice a year. Keep an eye on our Events webpage for session information. The next one is planed for Term 1, 2022.

Projects in:
Applied Mathematics
Full list of staff in the Department of Applied Mathematics
Adelle Coster

Real world problem solving using dynamical systems, stochastic modelling and queueing theory for stochastic transport and signalling in cells.
Gary Froyland
 Dynamical Systems and Ergodic Theory:
Projects that combine techniques from nonlinear dynamics, ergodic theory, functional analysis, or differential geometry and can range from pure mathematical theory through to numerical techniques and applications (including ocean/atmosphere/blood flow), depending on the student.  Optimisation:
Projects are occasionally available in optimisation, mainly using either techniques from mixed integer programming to solve applied problems (e.g. transport, medicine,…) or mathematical problems arising from dynamics.
Mark Holzer
 Modelling and analysis of ocean biogeochemical cycles including isotope dynamics, inverse modelling of hydrographic data to detect climatedriven circulation changes, and analysis of largescale ocean transport.
PhD students should be highly motivated, have a strong background in applied mathematics and/or theoretical physics, and will have the opportunity to contribute to shaping their project.
Jeya Jeyakumar
 DataDriven Multistage Robust Optimization:
The aim of this study is to develop mathematical principles for multistage robust optimization problems, which can identify true optimal solutions and can readily be validated by common computer algorithms, to design associated datadriven numerical methods to locate these solutions and to provide an advanced optimization framework to solve a wide range of reallife optimization models of multistage technical decisionmaking under evolving uncertainty.  Semialgebraic Global Optimization:
The goal of this study is to examine classes of semialgebraic global optimization problems, where the constraints are defined by polynomial equations and inequalities. These problems have numerous locally best solutions that are not globally best. We develop mathematical principles and numerical methods which can identify and locate the globally best solutions.
Shane Keating
 Detection and cloaking of surface water waves created by submerged objects
 Decomposition of ocean currents into wavelike and eddylike components
Frances Kuo
 Theory and application of QuasiMonte Carlo methods:
for high dimensional integration, approximation, and related problems.
Quoc Thong Le Gia
 Computational Mathematics:
with specialised topics in radial basis functions, random fields, uncertainty quantification, partial differential equations on spheres and manifolds, stochastic partial differential equations.
John Roberts
 Discrete Integrable Systems:
These are birational maps with particularly ordered dynamics and their study is a nice motivation for using algebraic geometry, symmetry, ideal theory and number theory in the study of dynamical systems.  Arithmetic Dynamics:
This field is the study of iterated rational maps over the integers or rationals or over finite fields, rather than the complex or real numbers. I am particularly interested in how the usual structures present in dynamical systems over the continuum manifest themselves over discrete spaces.
Vera Roshchina
 Convex geometry:
Focused on the study of the facial structure of convex sets and the relations between the geometry of convex optimisation problems and performance of numerical methods. The project can be oriented towards convex algebraic geometry, experimental mathematics or classical convex analysis.  Projection methods and fixedpoint theory:
This project is associated with the ARC grant “Geometry in projection methods and fixedpoint theory.” The objectives are to capture the geometry of feasible sets affecting the convergence of projection methods, accelerate the convergence of projection and hybrid optimisationprojection algorithms and solve specific problems related to fixedpoint iterations of nonexpansive mappings.
Wolfgang Schief

Algebraic and Geometric Aspects of Integrable Systems:
The ubiquitous nature of integrable systems is reflected in their (apparent or disguised) presence in a wide range of areas in both mathematics and (mathematical) physics. Projects focus on the algebraic and/or geometric aspects of discrete and/or continuous integrable systems, depending on the individual student's background and preferences.
Chris Tisdell
 Fluid flow in channels with porous walls
 Mathematics education
 Nonlinear differential equations
 Difference equations
 Dynamic equations on time scales
Jan Zika
 How many oceans are there? Using novel statistical and machine learning techniques to characterise oceanic zones and provide a blueprint for quantifying the ocean's role in a changing climate.
 How does heat get into the ocean? An investigation of the physical mechanisms that control the ocean's uptake of heat and its effect on climate.
 Making climate models work better: Developing new methods to validate and improve the inner workings of numerical climate models and improve their projections of global warming and its impacts.
 Will it mix? New perspectives on turbulence in rotating fluid flows and how we estimate mixing from observations.
Pure Mathematics
Full list of staff in the Department of Pure Mathematics
Thomas Britz
 Combinatorics
 Graph theory
 Coding theory
 Extremal set theory
Arnaud Brothier
 Operator algebras
 Mathematical physics
 Group theory
 Jones subfactor theory
 Quantum field theory
 von Neumann algebras

Connection re: Vaughan Jones between conformal field theory, Thompson groups and knot theory.
Daniel Chan
 Noncommutative algebra
 Algebraic geometry
Catherine Greenhill
 Random graphs
 Asymptotic enumeration
 Randomized combinatorial algorithms
Anita Liebenau

Extremal and probabilistic combinatorics:
Possible subjects therein include Ramsey theory, random graphs, positional games and hypergraphs.
Alina Ostafe
 Unlikely Intersection in Number Theory and Diophantine Geometry:
These are problems of showing that arithmetic “correlations" between specialisations of algebraic functions are rare unless there is some obvious reason why they happen. These “correlations” may refer to common values or to values factored into essentially the same set of prime ideals and similar.  Arithmetic Dynamics:
This area is concerned with algebraic and arithmetic aspects of iterations of rational functions over domains of number theoretic interest.
Igor Shparlinski
 Counting integral and rational solutions to Diophantine equations and congruences.
The goal is to obtain upper bounds on the number of integer solutions to some multivariate equations and congruences in variables from a given interval [M, M+N]. Similarly, for rational solutions one restricts both numerators and denominators to certain intervals.  Kloostermania: Kloosterman and Salie sums and their applications.
A classical direction in analytic number theory where the goal is to obtain new bounds on bilinear sums of Kloosterman and Salie sums and apply them to various arithmetic problems, such as the Dirichlet divisor problem in progressions. 
Exponential sums and applications. This topic is about understanding the behaviour (e.g. extreme and typical values) of some most important exponential sums, in particular of Weyl sums.
Fedor Sukochev
 Noncommutative functional analysis and its applications to noncommutative geometry, particularly those related to quantised calculus and index theorems.
 Singular (Dixmier) traces and their applications
 Noncommutative integration theory
 Noncommutative probability theory
 Various aspects of Banach space geometry and its applications
Mircea Voineagu
 Motivic cohomology and algebraic Ktheory  an intersection of algebraic geometry and algebraic topology
 Equivariant algebraic topology
Statistics
Full list of staff in the Department of Statistics
Boris Beranger
 Extreme Value Analysis:
Projects available on the modelling of the dependence of multivariate and spatial extremes, spatiotemporal modelling, highdimensional inference. Interests in environmental/climate applications.  Symbolic Data Analysis:
Projects available on symbol design, distributional symbols and others. Applications in big and complex data analysis.
Rohitash Chandra
 Ancient river systems and landscape dynamics with Bayeslands framework
 Bayesian inference and machine learning for reef modelling
 Deep learning for the reconstruction of 3D orebodies for mineral exploration
 Bayesian deep learning for protein function detection
 COVID19 modelling with deep learning
 Variational Bayes for surrogate assisted deep learning
 Bayesian deep learning for incomplete information
Feng Chen
 Computational Statistics
 Event sequence data analysis
 Hidden Markov Models and StateSpace Models and their inference and applications
 Financial data analysis and modelling
 Point processes and their inference and applications
 Semi and nonparametric inference
Gery Geenens
 Nonparametric and semiparametric statistics:
Nonparametric dependence modelling (copulas) and nonparametric functional data analysis.
Clara Grazian
 Bayesian extension of the BlackLitterman model through copulas, for portfolio optimisation
 Nonparametric spatiotemporal clustering via Dirichlet processes
 Copula factor models
 Bayesian spatial clustering with application in animal behaviour and ecology
 Approximate Bayesian computation: choice of summary statistics, approximation of the likelihood, estimation of longmemory processes, problems of modelchoice
 Analysis of highdimensional genomic datasets: analysis of geneexpression data, study of the direction of the expression, singlecell technologies, GWAS.
 For some examples of my current projects, have a look at my research profile page.
Pavel Krivitsky
 Social network analysis for epidemiology, social sciences, and other areas
 Statistical models for dependent categorical data
 Survey sampling (design and inference), particularly for network data
 Statistical computing, particularly MCMCbased methods
Maarit Laaksonen
 The development and application of burden of disease methods, especially population attributable fraction.
 Topics include: modelling continuous exposures, repeated measurements, measurement error, competing risks, different study designs, metaanalysis and pooled analysis, future burden projections, comparison of different methods, novel applications.
Pierre Lafaye de Micheaux
 Dependence measures
 Complexvalued random variables
 Goodnessoffit tests
 Machine learning (with potential applications in medical imaging)
 Time series analysis
 Realtime analytics with the Raspberry Pi
 For some examples of my current projects, have a look at my personal webpage.
Jake Olivier
 The development of statistical methods for epidemiologic research:
Topics include regression to the mean, interrupted time series, metaanalysis, and population attributable fractions.
Scott Sisson
 Bayesian statistics and applications
 Computational statistics and algorithms
 Data privacy
 Data science, theory and application
 Defence (Australian citizens only)
 Extreme value theory and applications
 Machine learning
 Symbolic data analysis
Jakub Stoklosa
 Analysis of capturerecapture data
 Estimation of animal abundance
 Measurement error modelling
 Model selection for multivariate data
 Nonparametric smoothing
David Warton
 Statistical ecology
 Highdimensional data analysis
 Computational statistics
 Simulationbased inference
 EcoStats project ideas