In 1976 Keller formulated the following very general definition of inverse problems, which is often cited in the literature:

"We call two problems inverses of one another if the formulation of each involves all or part of the solution of the other. Often, for historical reasons, one of the two problems has been studied extensively for some time, while the other is newer and not so well understood. In such cases, the former problem is called the direct problem, while the latter is called the inverse problem."

Inverse problems appear in many situations in physics, engineering, biology and medicine. The main mathematical problem is the well (ill) – posedness of the inversion process. Indeed, in practice most inverse problems are ill-posed in terms of non-uniqueness or lack of stability of the inversion.

This one-day meeting is one of four LMS meetings on inverse problems every year that brings together researchers who work on advancing the field of inverse problems, both from a theoretical and from an applied point of view.

The meeting will concentrate on inverse problems in wave propagation. We will discuss recent advances in the analysis and numerical solution of the inverse spectral boundary value problem as well as inverse scattering.