## Mathematics

Mathematics research in the School builds around three broad and overlapping research groupings.

### Discrete Mathematics, Theoretical Computer Science and Logic

Research in this group builds on ideas from combinatorics, mathematical logic and general algebra.

Areas that are actively being developed include recursion theory, complexity of computation, reverse mathematics, algorithmic randomness, algebraic logic, modal logic, model theory, matroid theory, graph theory, set theory, universal algebra, Hopf algebras, lattices and more.

We have strong links with the Philosophy programme and the School of Engineering and Computer Science and joint seminars involving staff and postgraduate students from all three Schools are held frequently.

The School also holds a regular informal seminar series on matroid theory. Anyone interested in participating should contact Geoff Whittle.

### Analysis, Geometry and Number Theory

These research areas belong largely to the domains of continuous mathematics and number fields, having strong connections with calculus but also incorporating many ideas from algebra.

Research currently undertaken by mathematicians in this group includes Banach algebras, elliptic curves, functional and global analysis, invariant theory and singularity theory with applications to robotics and non-standard analysis.

### Applied Mathematics, Theoretical Physics and Modelling

Applied mathematics ranges from theoretical physics to industrial mathematics and from geophysics to fractal geometry. The mathematical ideas involved are equally varied, from structures on manifolds, through differential equations to numerical methods and techniques of modelling.

Research interests of this group include black holes, cosmology, quantum field theory, general relativity, industrial, geophysical, medical and biophysical applied mathematics, mathematical physics and robot kinematics.

The group collaborates with physicists and geophysicists at Victoria University and maintains lively interactions with scientists and mathematicians in government research organisations and universities in New Zealand around the world.

The Gravity Group also contributes to research in mathematics.