Analysis on spaces with fibred cusps, II

• Applicant: Professor Dr. Daniel Grieser
• Subject Area: Mathematics
• Term: since 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 340035557

Fibred cusp metrics and their generalization, the iterated multiple fibred cusp metrics, are a class of complete Riemannian metrics which occur for example on locally symmetric spaces. The closely related (iterated multiple) fibred boundary metrics occur in many contexts of geometry and physics, e.g. Kähler geometry, Hilbert schemes and moduli spaces of monopoles.The goals of this project are to develop analytic tools for analyzing the natural geometric differential operators associated to these metrics and to apply these tools to questions of global analysis and spectral theory. Central to our approach is geometric microlocal analysis, and part of the project is to extend its scope and methods.

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