Colloquium Mathematics - Prof. S. Holman

Title:
Microlocal Analysis in Inverse Problems

Abstract:
Microlocal analysis has found many different applications in the field of inverse problems, and in this talk I will aim to describe some of these. In microlocal analysis both the position and orientation of singularities are captured through the concept of the wavefront set. It is possible to study the manner in which the wavefront set propagates through the forward operator of an inverse problem, and such analysis can result in stability (or non-stability) results, and in some cases injectivity results for the inversion. It is also possible to understand and predict the presence of certain artefacts that appear in numerical reconstructions. I will give an overview of these applications of microlocal analysis to inverse problems.