Topics (as time permits)

1. Hodge decomposition for compact manifolds.
2. Compact manifolds with boundary - relative and absolute homology.
3. Stratified spaces and pseudomanifolds.
4. Resolutions of pseudomanifolds and iterated fibrations.
5. Manifolds with conic, horn-like and cusp-like boundaries.
6. Admissible metrics.
7. Self-adjoint extensions of , ideal boundary conditions.
8. Resolution of products and parametrices.
9. Hodge decomposition and cohomology.
10. Intersection homology and duality.
11. Kähler package.
12. Global invariants