Mathematics lies at the heart of much modern science and technology and has strong connections with philosophy and the humanities. It has its own rich history of ideas and problems and is a dynamic subject with many new and developing branches. Building on a core of algebra, geometry and calculus, students of mathematics may progress to more advanced courses in logic, geometry, analysis and calculus, algebra, combinatorics, applied mathematics and mathematical physics, and theoretical computer science.
Mathematics is a vital discipline within the School and research activity in the group is both diverse and of an international calibre. Four mathematicians at Victoria lead prestigious Marsden Fund research projects and they and others have research collaborations with researchers both in New Zealand and around the world. There are regular research seminars by staff in the School and by visiting mathematicians. Research activity in mathematics at Victoria can be broadly divided into three categories.
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, logics of programs, model theory, matroid theory, graph theory, set theory, universal algebra, Hopf algebras, lattices and more. Staff particularly involved with this research include Dr Colin Bailey, Prof Rod Downey, Prof Rob Goldblatt, Dr Yinhuo Zhang, and Prof Geoff Whittle. There are strong links with the Department of Philosophy and with the School's Computer Science group; joint seminars involving staff and graduate students from all three fields are a frequent event.
These fields belong largely to the domain of continuous mathematics, having strong connections with calculus but also incorporating many ideas from algebra too. Research currently undertaken by mathematicians in this group include functional and global analysis, differential geometry, topological dynamics, singularity theory with applications to robotics, non-standard analysis, synthetic geometry and also the history of mathematics. Staff working in these areas are Dr Christopher Atkin, Dr Peter Donelan, Dr Ken Pledger and Prof Rob Goldblatt. There are valuable connections with staff in economics and finance and in statistics and probability.
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. In particular, research interests and activity undertaken by this group include black holes, cosmology, quantum field theory, general relativity, fluid mechanics of bubbles and drops, water waves, modelling of two-phase fluid flow in porous media, cooking of cereal grains, heat and light transport in sea ice, modelling the volatilisation of coal, modelling the performance of lead-acid batteries, modelling human cardiorespiratory systems, nonlinear dynamics and fractals, mathematical physics, numerical computation and wavelets. A/Prof Mark McGuinness, A/Prof Philip Rhodes-Robinson, Prof Matt Visser, Dr Lindsay Johnston and Prof John Harper work in this section. They maintain a lively interaction with scientists and mathematicians in several government research organisations and universities, in NZ and around the world, as well as with physicists and geophysicists at Victoria.
The web pages for the Victoria University Gravity Group can be found here.
A detailed of list staff research interests (and potential areas for PhD Study) can be found on the Mathematics Staff Research Profiles page.