Positive scalar curvature at the intersection of global analysis, geometric topology and coarse geometry

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This project deals with the investigation of Riemannian metrics of positive scalar curvature on smooth manifolds, on manifolds with groups actions and on orbifolds. Obstructions to the existence of such metrics, and the topology of the space of positive scalar curvature metrics (if non-empty) are particular questions in this context. Special attention will be paid to the interaction of methods from differential geometry, global analysis, algebraic topology and coarse geometry. The positive scalar curvature question will also be a motivation to investigate other problems that are of interest in these specific areas, independently of the positive scalar curvature question.