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Potential Theory

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.


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

UCD School of Mathematics and Statistics

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