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. John Murray - Representation Theory of Finite Groups
Potential topics include:
- Recent conjectures on the ordinary characters of finite groups.
- Modular representations of solvable groups.
- Frobenius-Schur indicators of characters in blocks.
- Littlewood-Richardson coefficients.
- Types of self-dual modules.
- Experimentation with computer software such as GAP and SageMath.
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.
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
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
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.
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
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.
Dr. Keefe Murphy - Model-based Clustering of High-Dimensional Data
Potential topics include:
- Clustering longitudinal categorical sequences with time-varying covariates.
- A mixtures of experts model for mixed continuous and categorical data.
- Automatic variable selection in parsimonious Gaussian mixtures of experts models.
- Alternative covariance decompositions in parsimonious Gaussian mixtures of experts models.
- Shrinkage priors in Bayesian non-parametric factor-analytic mixtures.
- Applications of model-based clustering to learning analytics data.