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 2012.

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

If you are interested in any of these research areas, you should contact the staff member directly prior to submitted a formal application. For full details on the application procedure, please see http://www.nuigalway.ie/hardiman-scholarships/. Please also read our information on Postgraduate Research degrees in Mathematics, Statistics and Applied Mathematics.

The deadline for applications is 5pm (GMT), Saturday January 7, 2012

Hardiman Research Scholar Supervisors

Name and Email	Area
Dr Javier Aramayona javier.aramayona@nuigalway.ie Geometry, Topology and Group Theory	I am interested in certain spaces of surfaces, known as moduli spaces, and their symmetries. There are a number of interesting open problems about the geometry and rigidity of these spaces. Such problems lie at the intersection of Geometry, Topology and Group Theory, and are quite often amenable at combinatorial arguments.
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), a highly active part of modern applicable mathematics. We will establish a new branch of CGT: computing with matrix groups over infinite domains. Specifically, we will develop innovative techniques for investigating solvable-by-finite and arithmetic groups, and compiling databases of finite linear groups.
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 Queenâs 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	This PhD project is in the area of Quantum Computation, more specifically, Quantum Random Walks (QRW). The main idea is to see how well we can simulate QRWs in 2 dimensions by using a 1-dimensional âcoinâ. The main application will be in the creation of new efficient algorithms in computing.
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	Clinical trial design, cluster randomized trials, tree based methods for developing clinical prediction rules, survival analysis and competing risks theory.
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.
Dr Claas Röver Claas.Roever@nuigalway.ie Group Theory, Computational Group Theory and Formal Languages and Automata	There are strong connections between Combinatorial Group Theory and Formal Language Theory and many open questions remain. They range from fundamental decidability problems to classification results. The aim of this project is to advance this area further by establishing theorems and devising new algorithms for infinite groups.
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.