Title: Hodge theory and Cohomology
Abstract: Hodge theory is bridge between the topological properties of a smooth manifold, its cohomology, and its analytical properties, namely harmonic forms. This bridge enables the study of spaces whose topology break down yet still have a sensible notion of a smooth function space. I will review the classical example of this bridge: showing that every cohomology class on a smooth manifold has a unique harmonic form. Afterwards I will highlight some examples where this bridge can study generalized our singular spaces.
