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

本课题主要研究光滑流形、具有群作用的流形和轨道流形上的正数量曲率黎曼度量。这种度量存在的障碍，以及正数量曲率度量空间的拓扑(如果非空的话)是这种上下文中的特殊问题。将特别注意来自微分几何、整体分析、代数拓扑学和粗略几何学的方法的相互作用。正标量曲率问题也将是研究这些特定领域中感兴趣的其他问题的动力，独立于正标量曲率问题。

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.