Several School members offer supervision for PhD research projects in the School of Mathematics and Statistics.
Navigate via the tabs below to view project offerings by School members in the areas of Applied Mathematics, Pure Mathematics and Statistics. (This list was updated September 2022.)
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 page for session information.
 Applied mathematics
 Pure mathematics
 Statistics

 Real world problem solving using dynamical systems, stochastic modelling and queueing theory for stochastic transport and signalling in cells.

 Real & Computational Algebraic Geometry: Possible subjects include nonnegativity of real polynomials, polynomial system solving, semialgebraic sets, and algorithmic aspects of real algebraic & convex geometry.
 Polynomial & Convex Optimization: Potential topics include convex relaxations, designing algorithms, exploiting structure (e.g. sparsity), and applications in science & engineering.
 Real & Computational Algebraic Geometry: Possible subjects include nonnegativity of real polynomials, polynomial system solving, semialgebraic sets, and algorithmic aspects of real algebraic & convex geometry.

 Dynamical Systems and Ergodic Theory: Projects that combine techniques from nonlinear dynamics, ergodic theory, functional analysis, differential geometry, or machine learning and can range from pure mathematical theory through to numerical techniques and applications (including ocean/atmosphere/fluids/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.

 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.

 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.
 DataDriven Multistage Robust Optimization:

 Detection and cloaking of surface water waves created by submerged objects
 Decomposition of ocean currents into wavelike and eddylike components

 Theory and application of QuasiMonte Carlo methods:
for high dimensional integration, approximation, and related problems.
 Theory and application of QuasiMonte Carlo methods:

 Computational Mathematics:
with specialised topics in radial basis functions, random fields, uncertainty quantification, partial differential equations on spheres and manifolds, stochastic partial differential equations.
 Computational Mathematics:

 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.
 Discrete Integrable Systems:

 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.
 Convex geometry:

 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.
 Algebraic and Geometric Aspects of Integrable Systems:

 Analysis of multiscale problems in stochastic systems: These projects will involve an analytical study of certain multiscale problems arising in Markov chains and stochastic differential equations. These projects are suited for those interested in both analysis and probability, and will employ tools from differential equations, functional analysis and stochastic processes.
 Numerical methods for sampling constrained distributions: These projects are aimed at sampling problems arising in molecular dynamics. They will deal with designing and analysing numerical schemes to sample constrained probability distributions using stochastic differential equations.

 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.

 Combinatorics
 Graph theory
 Coding theory
 Extremal set theory

 Operator algebras (von Neumann algebras)
 Mathematical physics (quantum field theory)
 Group theory
 Jones subfactor theory
 Vaughan Jones' connection between conformal field theory, Richard Thompson's groups and knot theory.

 Noncommutative algebra
 Algebraic geometry

 Quantum groups/supergroups
 The SchurWeyl duality
 Representation Theory

 Random graphs
 Asymptotic enumeration
 Randomized combinatorial algorithms

Extremal and probabilistic combinatorics:
Possible subjects therein include Ramsey theory, random graphs, positional games and hypergraphs.

 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.
 Unlikely Intersection in Number Theory and Diophantine Geometry:

 Isometries, conformal mappings, and other special mappings on metric Lie groups
 Complex structures on Lie groups and their Lie algebras

 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.
 Counting integral and rational solutions to Diophantine equations and congruences.

 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

 Algebraic geometry (birational geometry and moduli)
 Hodge theory
 Transcendental methods in algebraic geometry

 Motivic cohomology and algebraic Ktheory  an intersection of algebraic geometry and algebraic topology
 Equivariant algebraic topology

 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.
 Extreme Value Analysis:

 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

 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

 Bayesian statistical inference
 Computational statistics and algorithms
 Approximate Bayesian inference
 Quantile regression method
 Statistical text analyses
 Applications to climate science, social science, image analyses
*Yanan Fan is an Adjunct A/Prof in the School and is able to cosupervise students (not as primary supervisor)

 Nonparametric and semiparametric statistics:
Nonparametric dependence modelling (copulas) and nonparametric functional data analysis.
 Nonparametric and semiparametric statistics:

 Social network analysis for epidemiology, social sciences, defence, national security, and other areas
 Statistical models for dependent categorical data
 Survey sampling (design and inference), particularly for network data
 Statistical computing, particularly MCMCbased methods

 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.

 Fast and efficient model selection for highdimensional data
 Development of efficient estimation and sampling algorithms for random graphs and spatial point processes
 Development of model compression methods for deep neural networks.

 The development of statistical methods for epidemiologic research:
Topics include regression to the mean, interrupted time series, metaanalysis, and population attributable fractions.
 The development of statistical methods for epidemiologic research:

Monte Carlo and Uncertainty Quantification
 Projects on the stochastic analysis and development of modern Monte Carlo methods for uncertainty quantification, sequential Bayesian inference, high dimensional sampling, particle based Variational Inference (knowledge/experience with stochastic analysis and SDE & PDE theory highly desired).
Machine learning and generative modelling
 Projects with a focus on (but not restricted to) medical imaging and machine learning methods for uncertainty quantification of image segmentation
 Theoretical analysis of modern machine learning methods (knowledge/experience with functional and stochastic analysis highly desired).
Mathematics of sustainability
 Projects on stochastic games, agent based models, network science and their applications in sustainability science.

 Automating data analyses via natural language queries
 Bayesian statistics, algorithms and applications
 Building software tools, services and packages
 Computational statistics and algorithms
 Data privacy and synthetic data
 Data science, theory and application
 Defence applications (nationality restrictions may apply)
 Extreme value theory and applications
 Machine learning
 Symbolic data analysis

 Developing statistical methods for point processes
 Financial data modeling
 Computational statistics

 Analysis of capturerecapture data
 Estimation of animal abundance
 Measurement error modelling
 Model selection for multivariate data
 Nonparametric smoothing

 Statistical ecology
 Highdimensional data analysis
 Computational statistics
 Simulationbased inference
 EcoStats project ideas