Multidimensional inverse problems and applications to, for example, medical imaging and geophysics. Geometric measure theory. Mathematical and numerical approaches to the spectral theory of partial differential operators (e.g. Schrodinger operator), diffraction and scattering theory and applications. Probability theory. Partial differential equations, including asymptotic and multiscale analysis and homogenisation, microlocal analysis, blow-ups in evolutionary equations. Numerical analysis of partial differential equations including problems arising in applications involving wave dynamics. Finite and boundary element methods.