Mathematics - Structured
The research activity in Mathematics at NUI Galway covers a broad range of topics spanning Algebra, Analysis, Geometry and Topology. There is a particular strength in Computational Algebra, which has led to the establishment of de Brún Centre, whose mission is to support research in broad areas of algebra and its applications.
The various research groups within the discipline of Mathematics host a wide range of workshops, seminars and graduate courses, resulting in a unique and thriving graduate research programme with a strong international dimension.
As part of the doctoral training available on the Structured PhD programme, students select from a range of taught modules, including:
- graduate-level courses in Mathematics covering topics such as Advanced Algebra and Analysis, Geometry, Topology/Set Theory and Computational Mathematics;
- modules in Statistics, Bioinformatics and Applied Mathematics available from the cognate disciplines within the School of Maths;
- a wide range of interdisciplinary modules from other schools in the College of Arts, Humanities and Social Sciences;
- modules on core skills such as research methods, computing, communications, and languages;
- modules acknowledging a student's professional development, including presentation of posters and paper at an International Conference
- modules to enhance a student's employability through generic training e.g. Careers' Workshops, computing skills, etc.
Each student is assigned a primary Supervisor(s) and a Graduate Research Committee made up of experienced researchers to plan their programme of study and to provide on-going support to their research.
Candidates for the degree of PhD or MSc by research must have reached a high honours standard (minimum H2.2 [or equivalent international qualification] for an MSc) at the examination for the primary degree, or presented such other evidence as will satisfy the Head of School and the College of his/her fitness.
Areas of interest
Group theory including group varieties, representation theory of finite groups, associative and non-associative rings, and group rings, coding theory and cryptography.
Computational algebra including computational homological algebra, computational group theory, computational representation theory.
Linear and Multilinear Algebra
Finite Field Theory
Analysis and Numerical Analysis:
Functional analysis, in particular tensor products, multilinear forms, polynomials and holomorphic functions on Banach spaces.
Non-linear analysis, including differential and integral equations, and fixed point theory.
Numerical analysis and computational differential equations.
Geometry and Topology:
Differential geometry and the geometry and topology of Lie groups and homogeneous spaces
Analytic topology and order.