Functional Analysis
Research Groups
- Actuarial and Financial Mathematics
- Applied Algebra and Information Theory
- Bayesian Statistics
- Computational Mathematics and High-Performance Computing
- Enumerative Combinatorics
- Fluid Dynamics
- Functional Analysis
- Mathematics Education
- Matrix Analysis
- Number Theory
- Potential Theory
- Probability
- Quantum Information and Computation
- Real Algebra
- Relativity and Mathematical Physics
- Statistical Genetics and Bioinformatics
- Statistical Modelling
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.
People
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