Coarse Geometry, Index theory and singularities

Coarse Geometry, as introduced by Higson and Roe in the context of index Theory for non compact manifolds, has a number of developments and crossways with Singularity theory. Grupoids and Stacks constitute vast conceptual generalizations which allow to formulate index theoretical or algebraic-geometric information which is relevant to moduli in a general sense.

We will present a panorama of topics which are present at the intersection of these ideas and which look to put in motion Coarse Geometry tools in the study of topological groups as large-scale geometric objects.