Boundary value problems and homogenization for singular Schrödinger operators

This project aims to build on exciting new developments in harmonic analysis for minimal regularity elliptic PDE in order to solve minimal regularity boundary value problems for equations with highly singular and rapidly oscillating coefficients. The approach will combine a recent framework for singular Schrödinger equations, based on holomorphic functional calculus for first-order systems, with state-of-the-art techniques in elliptic PDE. A strong record in undergraduate analysis is therefore essential, whilst expertise across any of functional analysis, partial differential equations, homogenization theory, and harmonic analysis, would be especially advantageous.