Speaker
Edward McDonald, Penn State
Abstract
The density of states (DOS) is a Borel measure on the real line associated to a Schrödinger operator on Euclidean space. The DOS is supported on the essential spectrum of the Schrödinger operator and is insensitive to localised perturbations of the potential. Several years ago my coauthors and I discovered a connection between the DOS and Connes’ trace formula in the form of a Dixmier trace formula. In more recent work with E. Hekkelman we have placed this formula in its proper context and proved several generalisations. In this talk I will explain the formula, some of its implications and the ideas behind the proof.