Analysis on spaces with fibred cusps, II

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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.