The following projects or project areas are proposed for the consideration of prospective postgraduate research students.
If any of these appeal to you, please contact Dr. Mark Walsh (Mathematics Postgraduate Coordinator) or Dr. Catherine Hurley (Statistics Postgraduate Coordinator)
Maynooth University Department of Mathematics and Statistics
ToggleAlgebra and Number Theory
Professor Stephen Buckley - Ring Theory
Potential topics include:
- Combinatorial ring theory.
- Notions of isoclinism and isologism for rings.
- More details.
Dr. Ollie Mason - Algebra (Applied Linear Algebra)
Potential topics include:
- The matrix Riccati equation and applications to the stability of time-delay systems
- Matrix theory over the max algebra and general semirings
- Combinatorial and nonnegative matrix theory: applications to data privacy
Dr. Pat McCarthy - Combinatorics and Number Theory
One of Dr. McCarthy's interests is Number Theory, cryptography, and the implementation of cryptographic routines and cipher attacks on microprocessors.
Dr. John Murray - Character Theory of Finite Groups
Potential topics include:
- Recent conjectures concerning the ordinary characters of finite groups.
- Modular representations of sporadic simple groups.
- Structure of blocks with dihedral or quasidihedral defect group.
- Open problems in Jenning's theory.
- Noncommutative symmetric functions.
- Specht modules for the prime 2.
- Gelfand-Zetlin algebra for Coxeter groups.
- Integral representation theory:lattices and orders.
- Experimentation with GAP: an interactive computer programme for groups and algebras.
Professor Anthony O'Farrell - Real and Complex Analysis
Potential topics include:
Problems of approximation, capacities, function spaces, geometry, groups, algebras of functions, Functional Analysis, Dynamical Systems, Potential Theory and Partial Differential Equations.
Dr. David Redmond - Group Theory
Potential topics include:
- Study of Group theory, Ring theory, Galois theory, ordinary character theory and, in particular, Modular character theory to be able to understand and write an intelligent and intelligible report on some major results in the area of character theory, such as the Brauer-Suzuki theorem on Quaternion 2-sylow subgroups and/or the Glauberman 2* - theorem.
- Study of group theory, ordinary character theory and other algebraic techniques so as to understand and write an intelligent and intelligible report on both the classification of the Frobenius groups and the classification of the Zassenhaus groups.
Analysis
Dr. Detta Dickinson - Diophantine Approximation and Measure Theory
Potential topics include:
- Simultaneous Diophantine Approximation.
- Diophantine Approximation on Manifolds.
- Hausdorff Measure and Dimension.
Dr. Ollie Mason - Analysis (Stability Theory)
Potential topics include:
- Joint spectral radius for sets of positive operators
- Nonautonomous dynamical systems arising in population dynamics
- Stability theory of differential inclusions and functional differential equations
Dr. Pat McCarthy - Classical Analysis
Pat McCarthy is interested in Classical Function Spaces and the inequalities which arise in their study. Examples include HP, LP and Lipschitz spaces.
He has worked on convergence problems for Fourier series and extremal properties of certain orthogonal polynomials. Currently he is examining generalisations of Carleson Interpolation Sequences.
Professor Anthony O'Farrell - Real and Complex Analysis
Potential topics include:
Problems of approximation, capacities, function spaces, geometry, groups, algebras of functions, Functional Analysis, Dynamical Systems, Potential Theory and Partial Differential Equations.
Geometry and Algebraic Topology
Dr Stefan Bechtluft-Sachs - Differential Geometry/Algebraic Topology/Variational Methods
Potential topics:
- Invariants for Harmonic Maps into Homogeneous Spaces
- Numerical Analysis: Small Dirac-eigenvalues of homogeneous spaces
- Calculus of Variations: Tension field and Index of Energies with polynomial density
- Lie group actions and Curvature: G-manifolds with few orbit types
- More details
Potential topics in geometric analysis include:
- Poincaré-type inequalities.
- Curvature and convexity on metric spaces.
- Quasiconformal mappings and mappings of finite distortion.
- More details.
Professor Anthony O'Farrell - Real and Complex Analysis
Potential topics include:
Problems of approximation, capacities, function spaces, geometry, groups, algebras of functions, Functional Analysis, Dynamical Systems, Potential Theory and Partial Differential Equations.
Dr Anthony Small - Algebraic/Differential Geometry
Potential topics include:
- MSc/MA problems relating Constant Mean Curvature Surfaces
- MSc/MA problem in Gauge Theory/Complex Geometry
- PhD problems from the differential geometry of surfaces, twistor theory and Yang-Mills.
Professor David Wraith - Differential Geometry
Projects related to the geometry and topology of Riemannian manifolds with curvature bounds.
Mathematics Education
Dr. Fiacre Ó Cairbre - Maths Education / History of Mathematics
Fiacre Ó Cairbre's research interests are currently in the three areas of stability theory, history of mathematics and mathematics education. He is working on the stability of certain types of switching systems. He is also working on the history of mathematics and resource materials for second level mathematics teachers.
Dr. Ann O'Shea - Maths Education
Possible topics include:
- Task Design and Implementation
- Advanced Mathematical Thinking
Dr. Ciarán Mac an Bhaird - Maths Education / History of Mathematics
Potential topics include:
- Student Engagement and Motivation
- Evaluation of Teaching Initiatives
- Various topics from the History of Mathematics, including mathematical biography, a history of mathematical teaching and history resources for teaching
Statistics
Dr. Caroline Brophy - Statistical Modelling in Environmental and Ecological Science
My research interests are in the development and application of statistical modelling techniques to non-standard situations in Ecology and Environmental Science. The Statistical topics I am particularly interested in are mixture models, functional relationship models, multinomial models, mixed models, methods for modelling data with large numbers of missing or zero values, methods for predicting the mean response without bias from non-linear models and bootstrapping methods for assessing predictions from non-linear models. The Ecological and Environmental topics I am currently working on are climate change, biodiversity in grassland systems, competition in a range of ecological systems, and genotypic variability in allergenic plant species.
Dr. Niamh Cahill
Broadly, my research focuses on the development of statistical models for the analysis of time dependent, compositional and/or spatial data. I use a Bayesian approach to statistical modeling, which is suitable for developing complex hierarchical models, accounts of uncertainties related to model parameters, incorporates prior knowledge, and shares information across data populations. Specifically, my research interests lie in the analysis of reproductive health indicators and climate change. A future project will involve looking at the use of family planning service statistics to inform the estimation of trends in contraceptive use. See description below.
National-level data on modern contraceptive prevalence rates (mCPR) are commonly obtained through surveys. However, a primary reliance on surveys alone leaves many countries in a difficult situation due to an absence of recent survey information and gaps in knowledge of mCPR at the sub-national level. Family planning service statistics that are produced as a byproduct of service delivery have the potential to rectify this and provide information on recent trends. Unfortunately, the data are prone to biases and are without an uncertainty quantification, limiting their use. Understanding and accounting for these biases and the uncertainties that they introduce paves the way for the improved use of service statistics to inform national and sub-national trends in mCPR and method-specific contraceptive use.
Dr. Rafael de Andrade Moral - Statistical Modelling of Abundance Data in Ecology
Potential topics include:
- Multivariate covariance generalized linear models and applications to ecological data
- Mixture models to estimate species abundance
- Spatial modelling of species occurrence/abundance data
- Estimating correlation between species within different communities from abundance data
Dr. Katarina Domijan - Bayesian methods of Statistical Inference
Potential topics include:
- Dimension reduction methods for classification of micro-array data
- Semi-supervised kernel classification of high-dimensional data
- Fast approximations to posterior distributions that arise in the implementation of Bayesian kernel classifers
- Parameter estimation of large crop models.
Dr. Catherine Hurley - Statistical Computing and Graphics
Potential topics include:
- Applications of Grand Tour Methods.
- Regression Analysis: a graphical user interface.
- Interactive display methods for large datasets.