Department of Mathematics
Postgraduate Research Topics in Applied Mathematics
There are numerous postgraduate research topics to choose from. For postgraduate students interested in Applied Mathematics please read here.
Current Bachelor (Honours) topics
Topic  Affiliation  Faculty and Dept  Supervisor  Special prerequisites 

Modelling particle movement and immune responses in the lymph node  FoS (Mathematics)  Dr Graham Donovan g.donovan@auckland.ac.nz 

Developing computational and theoretical models of the lung, particularly with regard to airway constriction and asthma  FoS (Mathematics)  Dr Graham Donovan g.donovan@auckland.ac.nz 

Deconvolution of astronomical images to find small targets  FoS (Mathematics)  Professor Jari Kaipio jari@math.auckland.ac.nz 
Matlab programming skills, solid computational linear algebra and basic probability and statistics 
Optimal stochastic control of onedimensional convectiondiffusion problems  FoS (Mathematics)  Professor Jari Kaipio jari@math.auckland.ac.nz 
Matlab programming skills, solid computational linear algebra and basic probability and statistics 
Bayesian approximation error approach for Xray tomography  FoS (Mathematics)  Professor Jari Kaipio jari@math.auckland.ac.nz 
Matlab programming skills, solid computational linear algebra and basic probability and statistics 
Local and global bifurcation theory for nonlinear ODEs  FoS (Mathematics)  Associate Professor Vivien Kirk v.kirk@auckland.ac.nz 

Bifurcation analysis of mathematical models of intracellular calcium dynamics  FoS (Mathematics)  Associate Professor Vivien Kirk v.kirk@auckland.ac.nz 

Dynamics near heteroclinic cycles and networks  FoS (Mathematics)  Associate Professor Vivien Kirk v.kirk@auckland.ac.nz 

Dynamics of biological systems with multiple timescales  FoS (Mathematics)  Professor Bernd Krauskopf b.krauskopf@auckland.ac.nz or Professor Hinke Osinga h.m.osinga@auckland.ac.nz  
Manifolds of systems with multiple time scales  FoS (Mathematics)  Professor Bernd Krauskopf b.krauskopf@auckland.ac.nz or Professor Hinke Osinga h.m.osinga@auckland.ac.nz  
The geometry of chaos  FoS (Mathematics)  Professor Bernd Krauskopf b.krauskopf@auckland.ac.nz or Professor Hinke Osinga h.m.osinga@auckland.ac.nz  
Intrinsic excitability and other transient effects  FoS (Mathematics)  Professor Hinke Osinga h.m.osinga@auckland.ac.nz  
Mathematical models of animal navigation  FoS (Mathematics)  Dr Claire Postlethwaite c.postlethwaite@math.auckland.ac.nz 
Familiarity with vector calculus (eg MATHS 340); some statistics and computing skills would be helpful; an interest in biology is essential (although no prior knowledge required 
A variety of topics in dynamical systems, including, but not limited to (a) switching on heteroclinic networks and (b) stabilisation using timedelayed feedback control  FoS (Mathematics)  Dr Claire Postlethwaite c.postlethwaite@math.auckland.ac.nz 
Some knowledge of differential equations (eg Maths 260); familiarity with computer programs such as Matlab. 
Comparison of numerical integrators for simulating the Solar System  FoS (Mathematics)  Dr Philip Sharp sharp@math.auckland.ac.nz 
Can solve ordinary differential equations using matlab. 
New algorithms for modelling the close approach of asteroids to planets  FoS (Mathematics)  Dr Philip Sharp sharp@math.auckland.ac.nz 
Can solve ordinary differential equations using matlab. 
Nonlinear dynamics of neuronal models or models of calcium dynamics  FoS (Mathematics)  Prof James Sneyd j.sneyd@math.auckland.ac.nz 
An interest in physiology and cell biology. No formal training in biology is required. 
Traveling waves in reactiondiffusion models, and their application  FoS (Mathematics)  Prof James Sneyd j.sneyd@math.auckland.ac.nz 
An interest in physiology and cell biology. No formal training in biology is required. 
Mathematical Physiology in general (cellular physiology models, organ models)  FoS (Mathematics)  Prof James Sneyd j.sneyd@math.auckland.ac.nz 
An interest in physiology and cell biology. No formal training in biology is required. 
Selforganisation models  FoS (Mathematics)  Prof James Sneyd j.sneyd@math.auckland.ac.nz 
An interest in biology. No formal training in biology is required. 
Computation and control of swirling flow  FoS (Mathematics)  Dr Steve Taylor taylor@math.auckland.ac.nz 

An entropy optimization problem  FoS (Mathematics)  Dr Steve Taylor taylor@math.auckland.ac.nz 

Hydrodynamic stability  FoS (Mathematics)  Dr Shixiao Wang wang@math.auckland.ac.nz 

Partial differential equations: Theory and computation  FoS (Mathematics)  Dr Shixiao Wang wang@math.auckland.ac.nz 
Current Masters topics
Topic  Affiliation  Faculty and Dept  Supervisor  Special prerequisites 

Modelling particle movement and immune responses in the lymph node  FoS (Mathematics)  Dr Graham Donovan g.donovan@auckland.ac.nz 

Developing computational and theoretical models of the lung, particularly with regard to airway constriction and asthma  FoS (Mathematics)  Dr Graham Donovan g.donovan@auckland.ac.nz 

Thermal tomography  FoS (Mathematics)  Professor Jari Kaipio jari@math.auckland.ac.nz 
Matlab programming skills, solid computational linear algebra and basic probability and statistics 
The discontinuous Galerkin method for wave propagation problems  FoS (Mathematics)  Professor Jari Kaipio jari@math.auckland.ac.nz 
Matlab programming skills, solid computational linear algebra and basic probability and statistics 
Local and global bifurcation theory for nonlinear ODEs  FoS (Mathematics)  Associate Professor Vivien Kirk v.kirk@auckland.ac.nz 

Bifurcation analysis of mathematical models of intracellular calcium dynamics  FoS (Mathematics)  Associate Professor Vivien Kirk v.kirk@auckland.ac.nz 

Dynamics near heteroclinic cycles and networks  FoS (Mathematics)  Associate Professor Vivien Kirk v.kirk@auckland.ac.nz 

Dynamics of biological systems with multiple timescales  FoS (Mathematics)  Professor Bernd Krauskopf b.krauskopf@auckland.ac.nz or Professor Hinke Osinga h.m.osinga@auckland.ac.nz  
Manifolds of systems with multiple time scales  FoS (Mathematics)  Professor Bernd Krauskopf b.krauskopf@auckland.ac.nz or Professor Hinke Osinga h.m.osinga@auckland.ac.nz  
The geometry of chaos  FoS (Mathematics)  Professor Bernd Krauskopf b.krauskopf@auckland.ac.nz or Professor Hinke Osinga h.m.osinga@auckland.ac.nz  
Intrinsic excitability and other transient effects  FoS (Mathematics)  Professor Hinke Osinga h.m.osinga@auckland.ac.nz  
Mathematical models of animal navigation  FoS (Mathematics)  Dr Claire Postlethwaite c.postlethwaite@math.auckland.ac.nz 
Familiarity with vector calculus (eg Maths 340); some statistics and computing skills would be helpful; an interest in biology is essential (although no prior knowledge required) 
A variety of topics in dynamical systems, including, but not limited to (a) switching on heteroclinic networks and (b) stabilisation using timedelayed feedback control  FoS (Mathematics)  Dr Claire Postlethwaite c.postlethwaite@math.auckland.ac.nz 
Some knowledge of differential equations (eg Maths 260); familiarity with computer programs such as Matlab. 
New integrators for simulating the Solar System  FoS (Mathematics)  Dr Philip Sharp sharp@math.auckland.ac.nz 
Graduate course in computational mathematics. 
Modelling the motion of the moons of the gas giants  FoS (Mathematics)  Dr Philip Sharp sharp@math.auckland.ac.nz 
Graduate course in computational mathematics 
Aspects of saliva secretion modelling. For example: Cell volume control, regulation of water flow through epithelial cells, calcium oscillations and water transport, Ion channels in secretory epithelia  FoS (Mathematics)  Prof James Sneyd j.sneyd@math.auckland.ac.nz 
Usually, my MSc students join one of my preexisting research groups, and learn the basics there while working on a small aspect of the overall problem. This project involves research groups in NZ and the USA. 
GnRH neurons. For example: 1. Calcium dynamics and electrical activity in GnRH neurons. 2. Electrical bursting, bifurcations, and multiple time scale analysis. 3. Nonlinear dynamics and excitability  FoS (Mathematics)  Prof James Sneyd j.sneyd@math.auckland.ac.nz 
A project involving research groups in Otago and Auckland. Usually, my MSc students join one of my preexisting research groups, and learn the basics there while working on a small aspect of the overall problem. This project involves research groups in NZ and the USA. 
Mathematical modeling of optics of vertebrate photoreceptors  FoS (Mathematics and Optometry)  Prof James Sneyd (Mathematics) j.sneyd@math.auckland.ac.nz Dr Misha Vorobyev (Optometry) m.vorobyev@auckland.ac.nz 
Vertebrate photoreceptors are small cells whose diameter is comparable with the wavelength of visible light. Therefore their properties cannot be modeled using geometric optics. In this project, we will apply waveguide theory to photoreceptors and study optics of photoreceptors by solving Maxwell equations numerically. It has been suggested that optical properties of vertebrate photoreceptors are adjusted to optimize resolution and sensitivity of eyes. The aim of this project is to test the hypothesis that the optics of photoreceptors is adapted to optimize vision. 
Information capacity of retinal ganglion cells  FoS (Mathematics and Optometry)  Prof James Sneyd (Mathematics) j.sneyd@math.auckland.ac.nz Dr Misha Vorobyev (Optometry) m.vorobyev@auckland.ac.nz 
Retinal ganglion cells send information from eye to brain as a message of spike trains. The information is encoded in the length of intervals between spikes. Variability of these intervals forms noise, against which signals are detected. The aim of this project is to develop analytical theory estimating the amount of information that ganglion cells can transmit depending on the level of noise and properties of input signal. 
Image reconstruction from noisy photoreceptor inputs  FoS (Mathematics and Optometry)  Prof James Sneyd (Mathematics) j.sneyd@math.auckland.ac.nz Dr Misha Vorobyev (Optometry) m.vorobyev@auckland.ac.nz 
Our brain reconstructs image from noisy inputs of photoreceptor cells. How the noise, optical blur and random arrangement of photoreceptors affect the accuracy of reconstruction? The aim of the project is to develop a method of optimal reconstruction of images. The method will take into account statistical properties of natural scenes. Both numerical and analytical methods will be used. 
Analysis computation and control of swirling flow  FoS (Mathematics)  Dr Steve Taylor taylor@math.auckland.ac.nz 

An entropy optimization problem  FoS (Mathematics)  Dr Steve Taylor taylor@math.auckland.ac.nz 

Nonlinear functional analysis and nonlinear PDEs  FoS (Mathematics)  Dr Shixiao Wang wang@math.auckland.ac.nz 

Vortex dynamics and stability  FoS (Mathematics)  Dr Shixiao Wang wang@math.auckland.ac.nz 
Current PhD topics
Topic  Affiliation  Faculty and Dept  Supervisor  Special prerequisites 

Topic  Affiliation  Faculty and Dept  Supervisor  Special prerequisites 
Modelling particle movement and immune responses in the lymph node  FoS (Mathematics)  Dr Graham Donovan g.donovan@auckland.ac.nz 

Developing computational and theoretical models of the lung, particularly with regard to airway constriction and asthma  FoS (Mathematics)  Dr Graham Donovan g.donovan@auckland.ac.nz 

Novel approaches to the numerical solution of ordinary differential equations  FoS (Mathematics)  Dr Robert Chan chan@math.auckland.ac.nz 

Computational models for stochastic boundary operators  FoS (Mathematics)  Professor Jari Kaipio jari@math.auckland.ac.nz 
Matlab programming skills, solid computational linear algebra and basic probability and statistics 
Markov chain Monte Carlo methods for inverse problems  FoS (Mathematics)  Professor Jari Kaipio jari@math.auckland.ac.nz 
Matlab programming skills, solid computational linear algebra and basic probability and statistics 
Local and global bifurcation theory for nonlinear ODEs  FoS (Mathematics)  Associate Professor Vivien Kirk v.kirk@auckland.ac.nz 

Bifurcation analysis of mathematical models of intracellular calcium dynamics  FoS (Mathematics)  Associate Professor Vivien Kirk v.kirk@auckland.ac.nz 

Dynamics near heteroclinic cycles and networks  FoS (Mathematics)  Associate Professor Vivien Kirk v.kirk@auckland.ac.nz 

Dynamics of biological systems with multiple timescales  FoS (Mathematics)  Professor Bernd Krauskopf b.krauskopf@auckland.ac.nz or Professor Hinke Osinga h.m.osinga@auckland.ac.nz  
Manifolds of systems with multiple time scales  FoS (Mathematics)  Professor Bernd Krauskopf b.krauskopf@auckland.ac.nz or Professor Hinke Osinga h.m.osinga@auckland.ac.nz  
The geometry of chaos  FoS (Mathematics)  Professor Bernd Krauskopf b.krauskopf@auckland.ac.nz or Professor Hinke Osinga h.m.osinga@auckland.ac.nz  
Intrinsic excitability and other transient effects  FoS (Mathematics)  Professor Hinke Osinga h.m.osinga@auckland.ac.nz  
Mathematical models of animal navigation  FoS (Mathematics)  Dr Claire Postlethwaite c.postlethwaite@math.auckland.ac.nz 
Familiarity with vector calculus (eg Maths 340); some statistics and computing skills would be helpful; an interest in biology is essential (although no prior knowledge required) 
A variety of topics in dynamical systems, including, but not limited to (a) switching on heteroclinic networks and (b) stabilisation using timedelayed feedback control  FoS (Mathematics)  Dr Claire Postlethwaite c.postlethwaite@math.auckland.ac.nz 
Some knowledge of differential equations (eg Maths 260); familiarity with computer programs such as Matlab 
Solving the million body problem  FoS (Mathematics)  Dr Philip Sharp sharp@math.auckland.ac.nz 
Good programming ability, graduate course in computational mathematics. 
Multipole methods for simulating the Solar System  FoS (Mathematics)  Dr Philip Sharp sharp@math.auckland.ac.nz 
Good programming ability, graduate course in computational mathematics. 
Efficient algorithms for simulating the Solar System  FoS (Mathematics)  Dr Philip Sharp sharp@math.auckland.ac.nz 
Good programming ability, graduate course in computational mathematics. 
A software package for simulating the Solar System  FoS (Mathematics)  Dr Philip Sharp sharp@math.auckland.ac.nz 
Good programming ability, graduate course in computational mathematics. 
Aspects of saliva secretion. For example: Cell volume control, regulation of water flow through epithelial cells, calcium oscillations and water transport, Ion channels in secretory epithelia  FoS (Mathematics)  Prof James Sneyd j.sneyd@math.auckland.ac.nz 
An interest in physiology. Knowledge of ordinary and partial differential equations. Some skill in scientific computing and numerical methods. 
Mathematical modelling of neurosecretory cells. For example: 1. Calcium dynamics and electrical activity in GnRH neurons. 2. Electrical bursting, bifurcations, and multiple time scale analysis. 3. Nonlinear dynamics and excitability  FoS (Mathematics)  Prof James Sneyd j.sneyd@math.auckland.ac.nz 
An interest in physiology. Knowledge of ordinary and partial differential equations. Some skill in scientific computing and numerical methods. 
Mathematical modelling of the lung. For example: 1. Calcium dynamics and airway smooth muscle. 2. Mechanical modelling of smooth muscle strips. 3. Crossbridge models of smooth muscle 
FoS (Mathematics)  Prof James Sneyd j.sneyd@math.auckland.ac.nz 
An interest in physiology. Knowledge of ordinary and partial differential equations. Some skill in scientific computing and numerical methods. 
Mathematical modeling of optics of vertebrate photoreceptors  FoS (Mathematics and Optometry)  Prof James Sneyd (Mathematics) j.sneyd@math.auckland.ac.nz Dr Misha Vorobyev (Optometry) m.vorobyev@auckland.ac.nz 
Vertebrate photoreceptors are small cells whose diameter is comparable with the wavelength of visible light. Therefore their properties cannot be modeled using geometric optics. In this project, we will apply waveguide theory to photoreceptors and study optics of photoreceptors by solving Maxwell equations numerically. It has been suggested that optical properties of vertebrate photoreceptors are adjusted to optimize resolution and sensitivity of eyes. The aim of this project is to test the hypothesis that the optics of photoreceptors is adapted to optimize vision. 
Information capacity of retinal ganglion cells  FoS (Mathematics and Optometry)  Prof James Sneyd (Mathematics) j.sneyd@math.auckland.ac.nz Dr Misha Vorobyev (Optometry) m.vorobyev@auckland.ac.nz 
Retinal ganglion cells send information from eye to brain as a message of spike trains. The information is encoded in the length of intervals between spikes. Variability of these intervals forms noise, against which signals are detected. The aim of this project is to develop analytical theory estimating the amount of information that ganglion cells can transmit depending on the level of noise and properties of input signal. 
Image reconstruction from noisy photoreceptor inputs  FoS (Mathematics and Optometry)  Prof James Sneyd (Mathematics) j.sneyd@math.auckland.ac.nz Dr Misha Vorobyev (Optometry) m.vorobyev@auckland.ac.nz 
Our brain reconstructs image from noisy inputs of photoreceptor cells. How the noise, optical blur and random arrangement of photoreceptors affect the accuracy of reconstruction? The aim of the project is to develop a method of optimal reconstruction of images. The method will take into account statistical properties of natural scenes. Both numerical and analytical methods will be used. 
An entropy optimization problem  FoS (Mathematics)  Dr Steve Taylor taylor@math.auckland.ac.nz 

Nonlinear functional analysis and nonlinear PDEs  FoS (Mathematics)  Dr Shixiao Wang wang@math.auckland.ac.nz 

Vortex dynamics and stability  FoS (Mathematics)  Dr Shixiao Wang wang@math.auckland.ac.nz 