A more Fruitful view on the De-Rham Theorem

Abstract

In this presentation, I will demonstrate the utility of sheaf cohomology as it can be applied to broad problems in differential geometry. The De-Rham Theorem is a classical result which compares two notable invariants of differentiable manifolds. Despite its simplicity, it is notoriously difficult to prove without substantial departure. In this presentation, I will express these invariants in the language of sheaf cohomology in order to demonstrate the comparison in a more concise way than is classically known. Then, I will show some way this method extends to active topics in modern geometry.