Macroscopic invariants of manifolds

• Applicant: Professor Dr. Alexander Engel
• Subject Area: Mathematics
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 441426261

This project is concerned with non-compact Riemannian manifolds which are so-called "large". Concretely, we consider macroscopic dimension as a measure of largeness, and being hypereuclidean as a strong form of having full macroscopic dimension. The goals are to investigate the behaviour of these two notions in geometric situations where we have a suitable large submanifold, to relate them to macroscopic positive scalar curvature, and to explore them in the world of simplicial non-positive curvature.

• DFG Programme: Priority Programmes
• Subproject of: SPP 2026: Geometry at Infinity