Monday

The first part of the talk will review briefly a number of current research areas in which “multivalued” solutions of elliptic equations appear. These are solutions taking values in a flat bundle over the complement of a codimension-2 submanifold. In particular, we will describe their relevance to adiabatic models for special holonomy manifolds fibred by hyperkahler 4-manifolds. In the second part of the talk we will discuss semi-explicit solutions in Euclidean space which can be found using classical integral representations and twistor theory—making connections with complex geometry--- and many open questions in this direction.