Mini-Workshop: L2-Spectral Invariants and the Integrated Density of States

Abstract

L2 -spectral invariants play an increasingly important role in the analysis of infinite geometric objects allowing for the action of a group. Typical such objects are covering spaces like Riemannian manifolds and graphs. The aim is to understand the group and the geometry of the object. The associated L2 -invariants can all be derived from the integrated density of states —also known as spectral distribution function— of a suitable geometrically induced equivariant Laplacian. On the other hand, the integrated density of states is also a most prominent quantity in the study of Laplacians with