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 Supervisor Special prerequisites
Dynamics of climate models Dr Anna Barry An interest in paleoclimate; Some knowledge of differential equations (eg Maths 260); familiarity with computer programs such as Matlab would be helpful
Modelling particle movement and immune responses in the lymph node Dr Graham Donovan
 
Developing computational and theoretical models of the lung, particularly with regard to airway constriction and asthma Dr Graham Donovan  
Deconvolution of astronomical images to find small targets Prof Jari Kaipio
Matlab programming skills, solid computational linear algebra and basic probability and statistics
Optimal stochastic control of one-dimensional convection-diffusion problems Prof Jari Kaipio Matlab programming skills, solid computational linear algebra and basic probability and statistics
Bayesian approximation error approach for X-ray tomography Prof Jari Kaipio Matlab programming skills, solid computational linear algebra and basic probability and statistics
Local and global bifurcation theory for nonlinear ODEs Assoc Prof Vivien Kirk  
Bifurcation analysis of mathematical models of intracellular calcium dynamics Assoc Prof Vivien Kirk  
Dynamics near heteroclinic cycles and networks Assoc Prof Vivien Kirk  
Dynamics of biological systems with multiple time-scales

Prof Bernd Krauskopf or

Prof Hinke Osinga

 
Manifolds of systems with multiple time scales

Prof Bernd Krauskopf or

Prof Hinke Osinga

 
The geometry of chaos

Prof Bernd Krauskopf or

Prof Hinke Osinga

 
Intrinsic excitability and other transient effects Prof Hinke Osinga  
Modelling EEG data with heteroclinic networks Dr Claire Postlethwaite 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
Rock-paper-scissors as a model for interacting populations Dr Claire Postlethwaite Some knowledge of differential equations (eg Maths 260); familiarity with computer programs such as Matlab.
Comparison of numerical integrators for simulating the Solar System Dr Philip Sharp
Can solve ordinary differential equations using matlab.
New algorithms for modelling the close approach of asteroids to planets Dr Philip Sharp Can solve ordinary differential equations using matlab.
Nonlinear dynamics of neuronal models or models of calcium dynamics Prof James Sneyd An interest in physiology and cell biology. No formal training in biology is required.
Mathematical Physiology in general (cellular physiology models, organ models) Prof James Sneyd An interest in physiology and cell biology. No formal training in biology is required.
Computation and control of swirling flow Dr Steve Taylor  
An entropy optimization problem Dr Steve Taylor  
Hydrodynamic stability Dr Shixiao Wang  
Partial differential equations: Theory and computation Dr Shixiao Wang  
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Current Masters topics


Topic Supervisor Special prerequisites
Dynamics of climate models Dr Anna Barry An interest in paleoclimate; Some knowledge of differential equations (eg Maths 260); familiarity with computer programs such as Matlab would be helpful
Modelling particle movement and immune responses in the lymph node Dr Graham Donovan  
Developing computational and theoretical models of the lung, particularly with regard to airway constriction and asthma Dr Graham Donovan  
Thermal tomography Prof Jari Kaipio Matlab programming skills, solid computational linear algebra and basic probability and statistics
The discontinuous Galerkin method for wave propagation problems Prof Jari Kaipio Matlab programming skills, solid computational linear algebra and basic probability and statistics
Local and global bifurcation theory for nonlinear ODEs Assoc Prof Vivien Kirk  
Bifurcation analysis of mathematical models of intracellular calcium dynamics Assoc Prof Vivien Kirk  
Dynamics near heteroclinic cycles and networks Assoc Prof Vivien Kirk  
Dynamics of biological systems with multiple time-scales

Prof Bernd Krauskopf or

Prof Hinke Osinga

 
Manifolds of systems with multiple time scales

Prof Bernd Krauskopf or

Prof Hinke Osinga

 
The geometry of chaos

Prof Bernd Krauskopf or

Prof Hinke Osinga

 
Intrinsic excitability and other transient effects Prof Hinke Osinga  
Modelling EEG data with heteroclinic networks Dr Claire Postlethwaite 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)
Non-Markovian models of animal behaviour Dr Claire Postlethwaite Some knowledge of differential equations (eg Maths 260); familiarity with computer programs such as Matlab.
New integrators for simulating the Solar System Dr Philip Sharp Graduate course in computational mathematics.
Modelling the motion of the moons of the gas giants Dr Philip Sharp 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 Prof James Sneyd Usually, my MSc students join one of my pre-existing 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 Prof James Sneyd A project involving research groups in Otago and Auckland. Usually, my MSc students join one of my pre-existing 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.
Analysis computation and control of swirling flow Dr Steve Taylor  
An entropy optimization problem Dr Steve Taylor  
Nonlinear functional analysis and nonlinear PDEs Dr Shixiao Wang  
Vortex dynamics and stability Dr Shixiao Wang  
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Current PhD topics


Topic Supervisor Special prerequisites
Dynamics of climate models Dr Anna Barry An interest in paleoclimate; Some knowledge of differential equations (eg Maths 260); familiarity with computer programs such as Matlab would be helpful
Modelling particle movement and immune responses in the lymph node Dr Graham Donovan  
Developing computational and theoretical models of the lung, particularly with regard to airway constriction and asthma Dr Graham Donovan  
Computational models for stochastic boundary operators Prof Jari Kaipio Matlab programming skills, solid computational linear algebra and basic probability and statistics
Markov chain Monte Carlo methods for inverse problems Prof Jari Kaipio Matlab programming skills, solid computational linear algebra and basic probability and statistics
Local and global bifurcation theory for nonlinear ODEs Assoc Prof Vivien Kirk
 
Bifurcation analysis of mathematical models of intracellular calcium dynamics Assoc Prof Vivien Kirk  
Dynamics near heteroclinic cycles and networks Assoc Prof Vivien Kirk  
Dynamics of biological systems with multiple time-scales

Prof Bernd Krauskopf or

Prof Hinke Osinga

 
Manifolds of systems with multiple time scales

Prof Bernd Krauskopf or

Prof Hinke Osinga

 
The geometry of chaos

Prof Bernd Krauskopf or

Prof Hinke Osinga

 
Intrinsic excitability and other transient effects Prof Hinke Osinga  
Mathematical modelling of circatidal rhythms Dr Claire Postlethwaite 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)
Switching on heteroclinic networks Dr Claire Postlethwaite Some knowledge of differential equations (eg Maths 260); familiarity with computer programs such as Matlab
Solving the million body problem Dr Philip Sharp Good programming ability, graduate course in computational mathematics.
Efficient algorithms for simulating the Solar System Dr Philip Sharp 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 Prof James Sneyd 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 Prof James Sneyd 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
Prof James Sneyd An interest in physiology. Knowledge of ordinary and partial differential equations. Some skill in scientific computing and numerical methods.
An entropy optimization problem Dr Steve Taylor
 
Nonlinear functional analysis and nonlinear PDEs Dr Shixiao Wang  
Vortex dynamics and stability Dr Shixiao Wang
 
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