Pure and applied analysis

Project ID: 2531ad1557

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UCL Lead department: Mathematics

Project Summary:

This project will concern the analysis and spectral theory of linear and nonlinear ordinary and partial differential and difference equations. This includes overlap with neighbouring fields of pure maths such as number theory, mathematical physics and probability theory, as well as applications in areas such as fluid dynamics, geophysics, medical imaging, relativity theory, finance, and social science.

Specific topics that may be investigated include spectral geometry, spectral problems, Toeplitz operators, geometric scattering theory, random operators, Nevanlinna Theory, high frequency wave propagation and scattering, integral equations and operator theory, matched asymptotic expansions, multiscale techniques, singular perturbation theory, Sobolev spaces on non-smooth domains, and stochastic PDEs.