Conical Refraction and Higher Microlocalization

The main topic of this text is higher analytic microlocalization and its application to problems of propagation of singularities. The section on higher microlocalization could serve as an introduction to the subject. The results on propagation refer to solutions of linear partial differential operators with characteristics of variable multiplicity and are of conical refraction type. The relation and interplay between these results and the results or constructions from geometrical optics in crystal theory is discussed. The notes are written foremost for researchers working in microlocal analysis, but it is hoped that they can also be of interest to mathematicians and physicists who work in propagation phenomena.