Potential Theory
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
Potential Theory
Potential theory has its origins in gravitational and electrostatic problems of mathematical physics. Today it is an important field of mathematical research that has rich connections with complex function theory, partial differential equations, fluid flow, stochastic analysis, ergodic theory and dynamical systems, and approximation theory. These varied links are reflected in the research activity of the UCD Potential Theory group.
Stephen Gardiner (Emeritus) has written monographs on classical potential theory and harmonic approximation, and also works on a range of problems concerning harmonic functions, free boundaries, and universal series expansions of holomorphic functions.
Hermann Render has published extensively on harmonic and polyharmonic functions, singularities of analytical solutions of PDEs, multivariate spline theory, wavelet analysis and quadrature formulae.
Marius Ghergu works at the interface of partial differential equations and potential theory. He has published monographs on isolated singularities in partial differential inequalities, nonlinear PDEs, and singular elliptic problems.
Neil Dobbs works in real and complex dynamics, examining the rich geometric structures and ergodic properties of such systems, and pursuing questions such as dependence of Hausdorff dimension of Julia sets on parameters.
People
Dr Neil Dobbs
Research Interests: Dynamical systems, Ergodic theory
(opens in a new window)Prof Stephen Gardiner (Emeritus):
Research Interests: Classical potential theory, harmonic approximation, harmonic functions, free boundaries, universal series expansions of holomorphic functions
Dr Marius Ghergu
Research Interests: Partial Differential Equations, Nonlinear Analysis, Potential Theory
Dr Myrto Manolaki
Research Interests: Potential Theory, Complex Analysis, Function Theory, Approximation, Universality
Dr Hermann Render
Research Interests: Computational Harmonic Analysis, Complex Analysis, Geometric Modelling
Group Contact (Email): (opens in a new window)Dr Myrto Manolaki