Research Groups

Research is a key part of our work at MSOR and a diverse range of projects are underway at any one time. We utilise our close ties between each discipline to create unique research partnerships with expertise across the mathematical sciences.

MSOR also publishes a Research Report series for working papers and technical reports. New additions to these are made available on-line.

Mathematics

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, 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 Dillon Mayhew, and Prof Geoff Whittle. There are strong links with the Department of Philosophy and with Computer Science; joint seminars involving staff and graduate students from all three fields are a frequent event.

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

Analysis, Topology and Geometry

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 and Numerical Mathematics

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, geothermal wellbore simulation, 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, and mathematical physics. A/Prof Mark McGuinness, Prof Matt Visser 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.

Gravity Group

The main theme of research for the Victoria University Gravity Group, the Generic Gravity Group, is the interface between classical gravity and quantum physics. This very broad topic is one aspect of the search for a theory of "quantum gravity", or more precisely a theory that in one limit approximately reproduces ordinary quantum physics and in another limit approximately reproduces classical Einstein gravity (the general relativity).

The web pages for the Victoria University Gravity Group can be found here.

Operations Research

The Operations Research group is currently interested in combinatorial optimisation, heuristic search methods for computational games and network optimisation, optimisation issues related to integer programming, analysis of scientific data using bayesian methods, reliability models, product warranty analysis and queueing models.

Dr Mark Johnston is investigating solution methods for combinatorial optimisation problems related to vehicle routing and scheduling. He is also developing heuristic search methods in connection with computational games and network optimisation.

A/Prof Stefanka Chukova 's main research is focused on product warranty analysis. She undertakes theoretical as well as applied projects in this area. In addition Stefanka is working on problems in reliability modelling and queueing theory.

Prof Tony Vignaux is interested in the analysis of scientific data using bayesian methods. He is a co-author of a book (Interpreting Evidence) on bayesian methods in forensic science and is a co-developer of the open-source simulation package SimPy.

Dr Tapas Sarkar is investigating optimisation issues related to networks and integer programming.

Statistics

Research in the Statistics group covers a wide range of areas in both theoretical and applied probability and statistics.

Our applied statistics projects include research into methods of estimating the sizes of finite population through capture-recapture modelling, the design and analysis of experiments, multivariate statistics and influence analysis. In categorical data analysis we are researching the analysis of multiple responses and the development of appropriate diagnostics. Our research interests in time series analysis involve projects in forecasting that include the development of tests for improved forecasting performance, endogenous detection of structural changes and the development of new evolutionary models for stochastically evolving seasonal patterns. We are applying Bayesian statistical methods to problems in Astronomy and Geophysics, providing improved solutions to estimation problems which had previously been intractable or only partly solved. Our research in stochastic point processes is being applied to models of the occurrence of earthquakes.

We have an active research programme in the asymptotic theory of empirical and point processes, martingale methods and differential geometry in statistics. Applications of this research can be found in goodness of fit diagnostics, distribution free methods in regression, the spatial analogue of the change-point problem, insurance mathematics and mathematical and historical demography.

Researchers associated with The Centre for Mathematics Education conduct research into Mathematics and Statistics Education with a particular emphasis on issues relating to cultural effects, the influence of socioeconomic status in schools, teachers' beliefs and attitudes to Mathematics education, and numeracy in early childhood education.

Interdisciplinary

While there are some strong links between groups within the School, there are also good ties to groups outside the School.

Centre for Logic, Language and Computation

The Centre for Logic, Language and Computation (CLLC) was established in February 2001. The aim of CLLC is:

• to promote research in logic, computation and the logical analysis of language (including related areas, such as formal syntax), particularly at the interface between these disciplines.

CLLC consists of people from mathematics, computer science, philosophy and linguistics.