The following is a list of current and potential research topics. They range from short term PhB projects, to year long Honours and graduate projects, to three year PhD projects.

It is neither definitive nor exhaustive, but rather is intended to give students an idea of the wide range of possibilities. Contact the supervisor for further discussion and ideas.

Project name Supervisor Research areasort descending
Moduli spaces for Elliptic PDEs from quantum physics and string theory Bryan Wang Algebra & topology
Analysis & geometry
Mathematical physics
Galois theory in topology Jim Borger Algebra & topology
Statistics of point clouds Amnon Neeman Algebra & topology
K-theory via simplicial sets Amnon Neeman Algebra & topology
Elliptic curves Amnon Neeman Algebra & topology
Homological algebra and derived categories Amnon Neeman Algebra & topology
Algebraic geometry of chiral Potts mode Amnon Neeman Algebra & topology
Topics in low-dimensional topology Joan Licata Algebra & topology
Differential topology Bryan Wang Algebra & topology
Topics in contact geometry Joan Licata Algebra & topology
Dirac operators and application Bryan Wang Algebra & topology
Morse theory in dimensions three and four Joan Licata Algebra & topology
Differential forms & de Rham cohomology Bryan Wang Algebra & topology
Surface mapping class groups Joan Licata Algebra & topology
Topics in Algebraic Geometry David Smyth Algebra & topology
Riemann zeta function & the distribution of primes Jim Borger Algebra & topology
Topics in Algebraic Complexity Theory David Smyth Algebra & topology
Computational mathematics
K-theory & generalized index theory Bryan Wang Algebra & topology
Model categories in algebraic topology Vigleik Angeltveit Algebra & topology
Geometry of Gauge fields Bryan Wang Algebra & topology
Kervaire invariant one problem Vigleik Angeltveit Algebra & topology
Dualities in algebra, geometry and physics Bryan Wang Algebra & topology
Analysis & geometry
Mathematical physics
Complex cobordism & stable homotopy Vigleik Angeltveit Algebra & topology
Number theory & algebraic geometry Jim Borger Algebra & topology
Algebraic toplogy Vigleik Angeltveit Algebra & topology
Interactive and automated theorem proving Scott Morrison Algebra & topology
Topics in Mathematical Economics David Smyth Algebra & topology
Fermat's last theorem Jim Borger Algebra & topology
Australian signals directorate summer research scholarship project Lilia Ferrario Algebra & topology
Crystallographic groups Jim Borger Algebra & topology
Enriched monoidal categories Scott Morrison Algebra & topology
Operators which preserve the spectrum Analysis & geometry
Spectral continuity Analysis & geometry
Geometry of gerbes & D-branes Bryan Wang Analysis & geometry
Gromov-Witten invariants and mirror symmetry Bryan Wang Analysis & geometry
Harmonic analysis and operator theory for partial differential equations Pierre Portal Analysis & geometry
Noncommutative geometry & physic Analysis & geometry
Hyperbolic geometry Andrew Hassell Analysis & geometry
Eigenfunction concentration Andrew Hassell Analysis & geometry
Wave diffraction Andrew Hassell Analysis & geometry
Scattering theory Andrew Hassell Analysis & geometry
Harmonic analysis of differential operators Pierre Portal Analysis & geometry
Nash's papers on game theory Andrew Hassell Analysis & geometry
Wavelets Andrew Hassell Analysis & geometry
Computational problems Andrew Hassell Analysis & geometry
Nonlinear heat equation Andrew Hassell Analysis & geometry
Group actions in complex geometry Alex Isaev Analysis & geometry
Analytic functions Analysis & geometry
The Monge mass transportation problem Qi-Rui Li Applied & nonlinear analysis
Viscosity solutions Neil Trudinger Applied & nonlinear analysis
Surfaces of prescribed Gauss curvature John Urbas Applied & nonlinear analysis
Isometric embedding of two dimensional Riemannian manifolds John Urbas Applied & nonlinear analysis
Mass transport problems John Urbas Applied & nonlinear analysis
Isoperimetric problems, shape optimization & curvature flows Applied & nonlinear analysis
Curve shortening flow Applied & nonlinear analysis
Eigenvalues of the Laplacian on Riemannian manifolds Applied & nonlinear analysis
Minimal surfaces in the sphere Applied & nonlinear analysis
Alignment-free biological sequence comparison Conrad Burden Bioinformation science
Mathematical aspects of population genetics Conrad Burden Bioinformation science
Bioinformatics Sue Wilson Bioinformation science
Mathematical Genetics: Epistasis Sue Wilson Bioinformation science
Numerical simulations of plasma flow Linda Stals Computational mathematics
ODE estimation Computational mathematics
Polyhedral optimization Computational mathematics
Domain decomposition/Multiscale physics Linda Stals Computational mathematics
Clustering techniques Markus Hegland Computational mathematics
Parallel high-dimensional density estimation Markus Hegland Computational mathematics
Adaptive sparse grids Markus Hegland Computational mathematics
Navier Stokes equation with free boundaries Steve Roberts Computational mathematics
Sensitivity Analysis of environmental models Barry Croke Computational mathematics
Fault tolerant algorithms Linda Stals Computational mathematics
Smoothing & rendering Linda Stals Computational mathematics
High dimensional approximation Steve Roberts Computational mathematics
Advanced computational techniques Markus Hegland Computational mathematics
Using methods from algebraic geometry to develop numerical approximations Markus Hegland Computational mathematics
Generalized Geometry and its Applications Peter Bouwknegt Mathematical physics
Chaos to structure in turbulent plasma & planetary flows Rowena Ball Mathematical physics
Energy transfer in biomolecules & molecular motors Rowena Ball Mathematical physics
Burning the biomass to sequester carbon dioxide Rowena Ball Mathematical physics
Dynamical systems, stability, & chaos Rowena Ball Mathematical physics
Fire, earth, air, & water Rowena Ball Mathematical physics
From chaos to structure in turbulent plasma & planetary flows Rowena Ball Mathematical physics
Fractal properties of Australia's river catchment boundaries Rowena Ball Mathematical physics
Introduction to String Theory Peter Bouwknegt Mathematical physics
Review of data mining literature John Maindonald Statistical science
Frequentist model averaging Alan Welsh Statistical science
Model selection in linear mixed models Alan Welsh Statistical science
The Bootstrap Alan Welsh Statistical science
Reduction Rank Regression Alan Welsh Statistical science
Residuals in linear mixed models Alan Welsh Statistical science
Smoothing Alan Welsh Statistical science
Composite Likelihood Alan Welsh Statistical science
Models for selection effects Alan Welsh Statistical science
LASSO asymptotics Alan Welsh Statistical science
Small Area estimation Alan Welsh Statistical science
Variational approximations for mixed models Alan Welsh Statistical science
Spherical data Alan Welsh Statistical science
Joint species distributions models in ecological statistics Alan Welsh Statistical science
Cox proportional hazards model Alan Welsh Statistical science
Simulation studies John Maindonald Statistical science
Polarised radiative transfer Lilia Ferrario Theoretical astrophysics
Radial velocity survey & non-LTE line profile modelling Lilia Ferrario Theoretical astrophysics
Model fitting to astronomical data Lilia Ferrario Theoretical astrophysics
Compact binary stars Lilia Ferrario Theoretical astrophysics
Pre-cataclysmic binaries Lilia Ferrario Theoretical astrophysics
Ultramassive white dwarfs Lilia Ferrario Theoretical astrophysics
Formation & detection of black holes Dayal Wickramasinghe Theoretical astrophysics
Circulalrly polarised radiation in early proto-planetary systems Lilia Ferrario Theoretical astrophysics

Updated:  26 April 2018/Responsible Officer:  Director/Page Contact:  School Manager