Department of Mathematics
Research projects in Pure Mathematics

Voting procedures
Why is there no perfect voting system?

Symmetries of discrete objects
Shapes and symmetries of graphs, networks, maps and tessellations.

Foliations on Manifolds
The study and construction of foliations on nonmetrisable manifolds.

Differential Structures on Large Manifolds
The study of manifolds so large that it is impossible to impose a metric on them.

Conformal geometry, submanifolds, and natural partial differential equations
The study of global geometrical structure via analysis, with applications in a vast array of physical and natural phenomena, from particle equations to biological systems.

Elliptic Curves, Algorithms and Public Key Cryptography
Public key cryptography has important applications in ecommerce and internet security.

Algorithms for Group Theory
The development, analysis, and application of highquality algorithms to group theory and other areas of computational algebra

Modular Representation Theory of Finite Groups
What can we say about the group if we know the structure of a Sylow psubgroup?

Degenerate operators
The maths behind the evolution of heat in materials with nonuniform heat conductivity.

Bernstein operators on polytopes
In computer graphics (and the finite element method) surfaces are usually described as piecewise polynomial functions on a triangulation.

Applications of Topology to Analysis
Some very interesting results and concepts lie at the interface between these two disciplines.

Tight Frames and their Symmetries
If the one of the two cartesian coordinates of a battleship is lost, then its position can no longer be determined.

Regular Complex Polytopes
About these generalisations of the platonic solids and their symmetry spaces.

Generalised Inverse Limits
How do these differ from inverse limits and how can we resolve these differences?

The geometry of spaces of representations
Exploring the properties of groups using matrices and their geometry.

Simple games and secret sharing schemes
A secret sharing scheme `divides' the secret S into `shares'  one for every user  in such a way that S can be easily reconstructable by any authorised subset of users, but an unauthorised subset of users can extract absolutely no information about S.

Pluripotential theory
This is the study of potential theory on general spaces in several complex variables

Programmes, Centres and Partners
 Community for Understanding and Learning in the Mathematical Sciences (CULMS)
 Centre for Mathematical Social Science (CMSS)
 Department of Computer Science
 Department of Engineering Science
 Department of Physics
 Department of Statistics
 Auckland Bioengineering Institute
 New Zealand Journal of Mathematics

Programmes, Centres and Partners
 Community for Understanding and Learning in the Mathematical Sciences (CULMS)
 Centre for Mathematical Social Science (CMSS)
 Department of Computer Science
 Department of Engineering Science
 Department of Physics
 Department of Statistics
 Auckland Bioengineering Institute
 New Zealand Journal of Mathematics