Analysis and PDEs

Analysis and the theory of partial differential equations are classical fields that have a wide range of application both within mathematics and in other fields. These include applications to number theory, group theory, geometry and topology, physics, engineering and chemistry.

Research interests in the Analysis and PDEs group currently include spectral theory, inverse problems, harmonic analysis on manifolds, PDEs and their numerical approximation and geometric analysis.

Analysis seminars

Members of our group are part of the following LMS (scheme 3) funded networks:

Dr Jean-Claude Cuenin is organiser of the Harmonic Analysis and Partial Differential Operators conference taking place on 16 July 2021. To find out more visit the conference website.

Marco Discacciati is organiser of the UKACM 2021 Conference on Computational Mechanics taking place from 14th to 16th April 2021. To find out more visit the conference website.

Marco Discacciati is the UK representative on the ECCOMAS Computational Applied Mathematics committee and a member of the scientific organising committee of the 20th International Conference on Fluid Flow Problems.

Dr Jean-Claude Cuenin

Spectral theory of selfadjoint and non-selfadjoint partial differential operators, especially Lieb-Thirring inequalities, spectral asymptotics and questions related to embedded eigenvalues and resonances.

Dr Marco Discacciati

Mathematical and numerical analysis of elliptic and parabolic boundary value problems involving PDEs. Domain decomposition methods. Theory and application of the finite element method to incompressible fluid mechanics. Preconditioners for iterative methods in numerical linear algebra.

Dr Jonathan Eckhardt

Direct and inverse spectral theory for ordinary differential equations, in particular generalised indefinite strings and canonical systems; Inverse spectral/scattering transform method for integrable partial differential equations, and long-time asymptotics.

Dr Lukas Schimmer

Spectral theory of self-adjoint discrete and continuous differential operators arising from Mathematical Physics with particular interest in trace formulae, Lieb–Thirring inequalities, Weyl-type asymptotics, resolvent estimates, variational principles and self-adjoint extensions

Dr Martin de Borbon

Kähler Geometry. Geometric Analysis.

Dr Alex Kyriakis

Domain decomposition methods for partial differential equations

Dr Xiaoyan Su

  • Costas Loizou (supervised by Dr Claudia Garetto).  Weakly hyperbolic equations in the presence of multiplicities and singularities via analytical and numerical methods.
  • Solomon Keedle-Isack (supervised by Dr. Jean-Claude Cuenin). Spectral properties of non-self-adjoint Schrödinger operators.