Abstract: 

In this talk, we will highlight the role played by partial differential equations in studying the geometry of manifolds. More specifically, we will introduce harmonic forms on a compact Riemannian manifold and use relevant partial differential equations' results  to deduce certain important properties of its de-Rham cohomology.  This can very well serve as a motivation to study partial differential equations, the first encounter of which in the standard curriculum is an overwhelming experience for many students, if not for all.