# PhD Projects in Analysis

### Singular Integral Operators in Potential Theory: at the Analysis/Numerical Analysis Interface

Supervisors: Prof Simon Chandler-Wilde, Prof Jani Virtanen, and Dr Raffael Hagger

Short description: In this project we will attack a long-standing conjecture in potential theory of (Kenig, 1994) regarding the so-called double-layer potential operator K on a closed curve Γ in the plane. The conjecture is that K has essential spectral radius < ½ whenever Γ is the boundary of a bounded Lipschitz domain.

Full description: PDF