## Thesis Topics and Supervisors

The following members of staff offer postgraduate supervision.

Please note: this is not an exhaustive list - please see individual staff pages for further research interests.

## Mathematics

- Topics in singularities and invariants of robot manipulators, including applications of singularity theory, Riemannian geometry and computational invariant theory (Masters and PhD level).

- Computability, complexity, combinatorics and algebra.

- Mathematical and philosophical logic, including model theory of modal and other intensional logics and algebraic logic.

- Algorithmic randomness, computability theory and models of set theory.

- Classical and higher computability theory (Masters, PhD) and set theory (Masters).

- Number theory with focus on arithmetic geometry (Masters).

- Banach algebra theory (Masters).

- Matroid theory (Masters and PhD).

- The growth of sea ice - mathematical modelling of the growth of first year sea ice, with particular attention paid to the ice/ocean boundary, where turbulent flow and billows of frazil ice crystals complicate the picture. (Note: A background in differential equations and numerical methods would be useful).
- Annealing steel coils - the radial transport of heat through layers of steel and hot gas is a limiting factor in factory furnaces, and a better mathematical understanding is needed. (Note: A background in differential equations and numerical methods would be useful).

- Model theory, applications to functional analysis, probability, ergodic theory and combinatorics.

- Combinatorics, matroid theory (Masters or PhD).

## Statistics

- Capture Recapure analysis (with Shirley Pledger), Bayesian statistics with applications to medicine and physics

- Bayesian statistics, logistic regression, Simpson's paradox, efficiency theory in mathematical economics and data envelopment analysis, non-parametric correlation coefficients and their relation to metrics on the symmetric group, applications of special functions to mathematical statistics, gamma and zeta functions, analysis of sorting algorithms, inequalities in mathematics and statistics.

- Missing Data in Semi-parametric Models, Profile Likelihood Estimation, Information Criteria and Model Selection, EM Algorithm and Variational Bayesian Methods.

- Statistical analysis of diversity, theory of large number of rare events
- Application of geometry in statistical problems, set-valued functions and statistics
- Goodness of fit theory, testing statistical models
- Statistical analysis of tails of distributions, extreme value theory and large deviations
- Stochastic processes in application to demography, finance and insurance
- Asymptotic statistical methods, Martingale methods in statistics
- Selected applications in biology, linguistics, finance.

- Ordinal Response Data Analysis

- Statistical genetics, Bayesian statistics (with applications in medicine and genetics), Statistical Process Control (with applications in healthcare and industry).

Note: A PhD Scholarship is available for work on newly discovered connections between set-valued analysis and statistics. For more information, see the description.

## Operations Research

Mark Johnston (All Masters projects)

- Insight from visualisation in combinatorial optimisation
- Integrating rewards with combinatorial optimisation problems
- Sports tournament scheduling and the travelling tournament problem
- Sensitivity of numerical simplification in genetic programming
- Addressing class imbalance in genetic programming for classification