Regularity aspects of variational problems

The project will investigate one or more of the various open questions in the regularity theory of minimal submanifolds and related areas. In particular, recent developments in the analysis of branch point singularities of stable minimal hypersurfaces, area minimising (integral and mod p) currents and multi-valued harmonic functions have generated an important circle of new ideas and techniques. These developments have thus opened up possibilities for further progress, such as extending the various interior regularity theories to the boundary, and potential applications of the methods to various PDE problems. The PhD project will eventually involve some aspect of these questions, after an initial period of time in which the candidate will be required to aquire the substantial Goemetric Measure Theory background necessary to tackle these regularity questions.