"Microlocal Analysis: an Introduction to the Theory and its Applications"
Microlocal Analysis arose in the 60’s as a fundamental tool for the understanding of Partial Differential Equations, providing beautiful connections between Analysis, Differential Geometry and Geometrical Optics. Over recent decades, it has also been used as a technique for the study of Inverse Problems, with profound impacts in Medical and Geophysical Imaging.
n this talk, I will introduce the main ideas and motivation behind Microlocal Analsysis, explaining how it is used in the analysis of inverse problems. I will then present my research in extending this theory to hyperbolic equations with memory; in particular I will describe a novel parametrix construction and a theorem on the propagation of singularities with applications to inverse source problems.