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The research activity in Mathematics at University of 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.

Recent graduates are working as (a) lecturers and postdoctoral researcher at third-level institutes, (b) in industry, including banking and finance, and (c) in the Meteorological Service.

As part of the doctoral training available on the Structured PhD programme, students avail themselves of a range of taught modules. The wide menu of available options includes:

• 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.

Research Areas

Algebra:

• 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.

Mathematics Education