Matania Ben-Artzi (Hebrew University, Jerusalem)
From crystal optics to Dirac operators: a spectral theory of first-order systems
Abstract: First-order systems of partial differential equations appear in many areas of physics, from the Maxwell equations to the Dirac operator. The aim of the talk is to describe a general method for the study of the spectral density of all such systems, connecting it to traces on the (geometric-optical) "slowness surfaces". The Holder continuity of the spectral density leads to a derivation of the limiting absorption principle and global spacetime estimates. (Based on joint work with Tomio Umeda).