Research 

Members of the School are engaged in research in a number of fields within mathematics and statistics, including strong research interests in the area of biomathematics and computational mathematics. The School has researchers working in ring theory, geometry, combinatorics, harmonic analysis, the potential theory of differential operators, mathematical education, and the history of mathematics.

Broad groupings of the School’s research interests are highlighted below. Details of the School’s publications are available in the UC SPARK research site.

Areas of current research by the department include:

  • algebraic groups
  • representation theory
  • clifford algebras
  • automorphism groups
  • finite geometry
  • matroid theory, combinatorial and algorithmic phylogenetics
  • constructive analysis and topology
  • cryptography
  • foundations of mathematics
  • non-classical logics
  • number theory.

Staff actively working in these areas are Brendan Creutz, Hannes Diener, Jeanette McLeod, Maarten McKubre-Jordens, Charles Semple, Mike Steel, Günter Steinke and Felipe Voloch.

The School's research strengths in these areas include: approximation theory; topological geometry; constructive and non-classical analysis and topology; functional analysis (including applications to quantum theory); harmonic analysis; partial differential equations and potential theory; general topology; algebraic geometry.

Staff active in those areas are Rick Beatson, Brendan Creutz, Hannes Diener, Ngin-Tee Koh, Maarten McKubre-Jordens, Günter Steinke and Felipe Voloch.

Applied statistics broadly covers research where statistics is being used to help solve real-world problems. Examples include:

  • environmental monitoring
  • risk assessment and uncertainty analysis
  • medical and engineering applications
  • statistical genetics.

Within the School staff who work in this area are Jennifer Brown, Marco Reale, Blair Robertson and Carl Scarrott.

Broadly, tool building in the form of the development and analysis of algorithms and methods for numerical computation. Areas of current research in the School include:

  • numerical optimisation
  • approximation theory
  • algorithms for surface approximation
  • inverse problems
  • numerical linear algebra
  • rigorous set processing.

Staff currently working in these areas are Rick Beatson, Chris Price, Blair Robertson and David Wall.

Members of the School have interests in theoretical, computational and applied aspects of nonlinear differential equations and discrete time dynamical systems. Areas of particular activity include:

  • chaotic dynamics
  • ergodic theory
  • inverse problems
  • nonlinear models in ecology and medicine
  • symmetry methods.

Permanent staff include Mark Hickman, Alex James, Michael Plank and Rua Murray.

Broadly, the use of mathematics to understand economics and finance, and processes arising in industrial settings. Specific interests include:

  • econometrics
  • mathematical economics
  • fast surface fitting algorithms for applications in geophysics, image processing, computer graphics and custom manufacture
  • statistical design and analysis of communication systems
  • signal and image processing
  • acoustics
  • industrial applications of spatial statistics, extreme value methods and spectral analysis.

Faculty members with interests in this area include Rick Beatson, Michael Plank, Chris Price, Marco Reale, Carl Scarrott and Phil Wilson.

The School is active in health-related research in several areas, including:

  • physiological modelling
  • epidemiology
  • statistical models for clinical studies and trials and healthcare analytics.

Staff working in this area include Jennifer Brown, Alex James, Michael Plank and Carl Scarrott.

Areas of current research by the School include:

  • mathematics in the ancient Near East, ancient Greece, India, and Islam with an emphasis on editing mathematical texts from these cultures from the original primary sources
  • mathematics during the Italian renaissance
  • history of ancient mathematical astronomy
  • constructive and non-classical mathematics
  • foundations of mathematics
  • mathematics education in the tertiary sector
  • mathematics and communication.

Staff actively working in these areas are Hannes Diener, John Hannah,  Alex James, Maarten McKubre-Jordens, Clemency Montelle and Phil Wilson.

The School hosts the Biomathematics Research Centre, this focuses on three broad areas:

  • computational molecular biology and phylogenetics
  • ecological and physiological modelling
  • statistical applications in ecology and medicine.

Staff actively working in this area include Jennifer Brown, Alex James, Michael Plank, Charles Semple, Mike Steel and Phil Wilson.

The Statistics Group within the School has an active research programme in many aspects of theoretical and computational statistics.

Particular topics include:

  • stochastic processes
  • computational methods
  • Bayesian inference
  • statistical genetics
  • sampling theory
  • random matrices
  • extreme value theory
  • graphical models. 

Staff with research projects in this area include Jennifer Brown, Marco Reale, Blair Robertson, Carl Scarrott and Mike Steel.

Collaborations