C*-rigidity: a bridge between coarse geometry and C*-algebras

With every proper metric space are associated C*-algebras of special geometric importance (Roe algebras), originally defined for index-theoretic considerations. It is a simple observation that metric spaces that are coarsely equivalent give rise to isomorphic C*-algebras. Much more surprisingly, the converse also holds: a C*-rigidity Theorem shows that spaces with isomorphic Roe algebras must be coarsely equivalent. This establishes a strong connection between the categories of coarse spaces and C*-algebras. In this introductory talk I aim to properly introduce the C*-rigidity question and illustrate the roadmap of the proof of rigidity.