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Functional Analysis

Functional Analysis

The beginnings of functional analysis go back to the end of the 19th century, and came about in response to questions emerging from other areas of mathematics such as linear algebra, differential equations, calculus of variations, approximation theory and integral equations. Many brilliant mathematicians contributed to its development, but arguably functional analysis emerged as a field in its own right in the 1920s, with the work of Stefan Banach and the Lwów School in Poland. Other major contributors include Hilbert, von Neumann, Grothendieck, and more recently Bourgain and Gowers. Loosely speaking, the subject is the study of linear spaces having infinitely many dimensions. Such things do not exist in reality of course, but intriguingly, it turns out that many mathematical phenomena that are motivated by real world problems, such as solutions of differential equations and wavefunctions in quantum mechanics, are best viewed in the context of these infinite dimensional spaces. The subject itself is an intricate blend of linear and abstract algebra, metric space theory, topology, set theory, combinatorics and probability.

The members of the UCD research group in functional analysis have a diverse range of interests, such as the geometry of Banach spaces, interactions with topology and set theory, operator algebras, infinite dimensional real and complex analysis, bounded symmetric domains and Jordan structures.

Modern applications of functional analysis are many and varied, including the axiomatic foundations of financial mathematics, the existence and the form of solutions to equations of infinitely many variables that arise in physical and engineering and financial models.


Professor Pauline Mellon
Research Interests‌: Complex Analysis, Symmetric Manifolds and Jordan Triple Systems

Dr Michael Mackey
Research Interests‌: ‌Jordan Structures in Analysis

Dr Rupert Levene
Research Interests‌: ‌Functional Analysis, Operator Algebras, Operator Spaces, Quantum Information Theory, Matrix Analysis

Dr Richard Smith
Research Interests‌: Banach Space Geometry and Structure, and connections with Set theory and Topology

Assoc Prof Christopher Boyd 
Research Interests‌: Geometry of Banach Spaces, Analytic Mappings on Infinite Dimensional Banach Spaces, Functional Analysis Methods in Function

Group Contact (Email): (opens in a new window)Assoc Professor Christopher Boyd

UCD School of Mathematics and Statistics

Room S3.04, Science Centre South, University College Dublin, Belfield, Dublin 4, Ireland.