Configuration spaces and exotic spheres

Given a smooth manifold, one can consider the spaces of (framed) configurations in that manifold, and a natural question can be formed along the following lines: how much do the homotopy types of these spaces of configurations remember about the manifold? In this talk, we will focus on whether these spaces of configurations can distinguish the various exotic smooth structures on spheres, and formulate an answer based on the Kervaire-Milnor classification of said exotic spheres. The content of this talk is based on joint work with Manuel Krannich and Alexander Kupers.