Hardiman Research Scholarships at the
School of Mathematics, Statistics and Applied Mathematics
NUI Galway

NUI Galway is now offering Hardiman Research Scholarships for structured PhD programmes. These are fully-funded four-year PhD scholarships, providing a stipend of € 16,000 per year plus fees, starting in September 2014.

Applicants must provide names of up to three proposed supervisors: a list of supervisors from the School of Mathematics, Statistics, Applied Mathematics and Statistics is given below, along with their research interests. These include

The deadline for applications is 5pm (GMT), Monday, November 18, 2013

The School of Mathematics, Statistics and Applied Mathematics at NUI Galway has an excellent track record of securing funding for applicants for these scholarships, and for the Government of Ireland Postgraduate Scholarship Scheme offered by the Irish Research Council. We have one of the largest graduates schools in the mathematical sciences in Ireland, and offer structured PhD programmes in Mathematics, Statistics, Applied Mathematics and Bioinformatics.

To begin your application process, contact one of our staff members listed below to discuss a project idea, prior to submitting a formal application. For full details on the application procedure, please see http://www.nuigalway.ie/hardiman-scholarships/.

Hardiman Research Scholar Supervisors

Name and Email	Area
Dr John Burns john.burns@nuigalway.ie Differential Geometry, Algebra.	Project Title: Compact homogeneous spaces with positive Euler characteristic. The project will be concerned with the study of a topological invariant of the class of manifolds in the title. This invariant was introduced by Salamon (motivated by the study of hyper-Kaehlar structures) and was computed for several classes of symmetric spaces. These computations will be extended to equal rank homogeneous spaces. The relation of this invariant to the Chern classes of these spaces and the exponents of the corresponding Lie group will be studied.
Dr James Cruickshank james.cruickshank@nuigalway.ie Polytopes, realisation spaces, geometry, algebraic and geometric topology	Rigid frameworks and mechanical linkages arise naturally in many scientific and engineering contexts. We propose to investigate sufficient conditions for a three dimensional framework to be rigid and in the case when it is not rigid to investigate the topology of the configuration space.
Prof. Michel Destrade michel.destrade@nuigalway.ie Elastic waves and stability, nonlinear solid biomechanics	Elastic waves and stability; mechanics of soft solids; biomechanics of soft tissues.
Prof. Graham Ellis graham.ellis@nuigalway.ie Algorithmic algebraic topology	This project is aimed at designing practical algorithms for making computations in algebraic topology. One goal is to use perturbation techniques for computing integral cohomology ring structures of large data sets.
Dr Dane Flannery dane.flannery@nuigalway.ie Linear (matrix) groups, computational group theory, algebraic design theory	This project is in computational group theory (CGT), an active and applicable branch of modern mathematics. We are establishing an entirely new area of CGT: computing with matrix groups over infinite domains. Specifically, we will develop practical techniques for investigating arithmetic groups, linear groups of finite rank, and groups defined over various classes of rings.
Prof. John Hinde john.hinde@nuigalway.ie Methodology, computation and application of statistical modelling.	General interests in the theory and practice of statistical modelling and statistical computing. Specific areas include random effects and mixture models, overdispersion, model-based clustering, the EM algorithm and models for discrete data. Possible application areas include biological, environmental and agricultural sciences, clinical research, social sciences and educational research.
Dr Kevin Jennings Kevin.Jennings@NUIGalway.ie Finite fields, Difference sets in abelian groups, Sequences with ideal correlation properties.	Hunting for Perfectly Nonlinear Polynomials over Finite Fields: If a polynomial's effect is to permute the elements of a finite field we call it a permutation polynomial. A perfectly nonlinear function, f, is one for which f(x+h)-f(x) is a permutation polynomial for each element h in the field. These are rare, elusive and useful.
Dr Milovan Krnjajić milovan.krnjajic@nuigalway.ie Statistical modelling, Bayesian non-parametrics, stochastic simulation.	Bayesian non-parametric models allow for specification of prior distributions on function spaces which results in flexible statistical analyses of complex data. The project involves development of such models and implementation of corresponding inference engines using Markov chain Monte Carlo simulations in a variety of application settings.
Dr Niall Madden Niall.Madden@NUIGalway.ie Numerical analysis, computational mathematics, singularly perturbed problems	Numerical analysis: the design and analysis of novel methods to solving differential equations and linear systems, and the application of these methods in numerical modelling and simulation.
Dr Aisling McCluskey aisling.mccluskey@nuigalway.ie Set-theoretic topology, Order theory, Mathematics Education	This research proposal resides within the field of Mathematics Education. It proposes to undertake an in-depth study of the mathematical ability and creativity of mathematics students across two institutions, NUI Galway and Queen's University Belfast (QUB) against the backdrop of very different education systems. Additionally, I have ongoing and keen research interest in problems within analytic topology and order theory.
Dr Michael Mc Gettrick Michael.McGettrick@NUIGalway.ie Quantum Computation and Quantum Information, Computer Algebra, Tropical Geometry	I am interested in supervising a PhD student in either 1) quantum random walks or 2) quantum evolutionary game theory. Specific problems in 1) include asymptotics of "higher order" walks, entanglement generation, walks on Cayley graphs. In 2) specific problems include quantum strategy/policy optimization, the effect of the network structure on the game dynamics, and models with local/global entanglement. Please see http://maths.nuigalway.ie/~gettrick/ for further details on current research.
Dr Martin Meere Martin.Meere@NUIGalway.ie Mathematics of diffusion, modelling and analysis of impurity diffusion mechanisms in semiconductors	Quantum dots are small (nanometre scale) fluorescent semiconductor crystals that are used to image dynamic processes in cells. This project will involve developing mathematical models for the uptake and re-distribution of quantum dots in cells. The work will be in collaboration with experimentalists working in the NCBES at NUI Galway.
Dr John Newell john.newell@NUIGalway.ie Biostatistics, statistical modelling, clinical trials	Research interests include statistical modelling, statistical computing, design and analysis of cluster randomised trials, smoothing techniques and derivative estimation, survival analysis involving dependent observations, tree based classification problems and the application of statistics in Clinical Research and Sports Science.
Prof. Donal O'Regan donal.oregan@nuigalway.ie Differential equations, non-linear analysis and Fixed Point Theory	Differential equations, non-linear analysis and Fixed Point Theory.
Dr Götz Pfeiffer goetz.pfeiffer@nuigalway.ie Finite Groups, Representation Theory, Computer Algebra	Computational Algebra, representation of finite groups, Finite Coxeter groups and related combinatorial and algebraic structures
Dr Petri Piiroinen petri.piiroinennuigalway.ie Multibody system dynamics, Numerical bifurcation analysis, Piecewise smooth dynamical systems	Periodic orbits of mechanical systems with impacts have the possibility to undergo grazing bifurcations caused by low-velocity impacts. This project will shed a light on these phenomena by using a novel approach called discontinuity geometry to develop analysis and control methods for the overall dynamics in impacting systems.
Dr Rachel Quinlan Rachel.Quinlan@NUIGalway.ie Linear algebra and combinatorics, group representation theory; university level mathematics education.	My research interests are in linear algebra and its interactions with such areas as combinatorics, representation theory, field theory, and finite group theory. Details available on my website I am also interested in mathematics education research at university level. I would welcome applications in either of these areas.
Prof. Cathal Seoighe Cathal.Seoighe@NUIGalway.ie Modeling molecular biological data, including gene expression, alternative mRNA splicing, and viral evolution.	Research spans several areas of bioinformatics/computational biology: Genomics and epigenetics, including gene expression analysis, mRNA splicing and analysis of chromatin structure using deep sequencing data, and implications in cancer. Development and application of probabilistic models of evolution - especially the use of evolutionary models to identify immune epitopes in HIV-1.
Dr Emil Sköldberg Emil.Skoldberg@nuigalway.ie Homology of combinatorially defined objects such as monomial algebras, partially ordered sets	I am interested in homological properties of combinatorial objects such as algebras with monomial relations, incidence algebras of partially ordered sets etc. A suggested topic for a PhD project would be the use of homotopical methods, such as colimits of diagrams, for constructing resolutions in commutative algebra. I am also interested in computational techniques such as Grobner bases for homological computations.
Dr Ray Ryan ray.ryannuigalway.ie Functional Analysis	Functional Analysis - in particular, tensor products, multilinear forms
Dr Michael Tuite michael.tuitenuigalway.ie Vertex Operator Algebras and Conformal Field Theory, Monstrous Moonshine, Riemann Surfaces	Vertex Operator Algebras (VOAs) on Riemann surfaces. A VOA is a mathematical formulation of ideas in string theory in physics. VOA theory has deep connections to algebra, number theory, geometry, group theory and combinatorics. This project seeks to develop my recent research in relating general Riemann surfaces to VOAs.
Dr Haixuan Yang haixuan.yangnuigalway.ie Bioinformatics and Statistical Modelling.	I would be interested in supervising a student working in the areas of bioinformatics and statistical modelling, especially of network data such as protein-protein interaction, co-expression, and functional similarity. Example of concrete project: "Inferring valuable information about proteins and tissues from bio-molecular networks by integrating large scale heterogeneous data". The potential candidate may choose to work on one of the sub-problems in the project: building high-quality bio-molecular networks; predicting protein functions; and disease gene selection and disease type prediction. The potential candidate can also work on your own problems as long as they are linked to my current research.