Structured PhD (Mathematics)

Short summary of the research area.

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, with a 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.

Some subjects in this course are:-

1. 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.

2. Linear and Multilinear Algebra

• 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.

3. Geometry and Topology

• Differential geometry and the geometry and topology of Lie groups and homogeneous spaces,
• Analytic topology and order