Title: Hodge Theory

Abstract. Hodge theory says, among other things, that in every de Rham cohomology class of a compact manifold there is a unique harmonic representative. It is one of the most satisfactory theories in the differential topology and geometry of a manifold.

In this highly informal talk all the necessary ingredients leading to understanding Hodge theory will be discussed: manifolds and submanifolds, tangent and cotangent bundles, differential forms, Riemannian metrics and volume forms, integration on manifolds, Stokes' theorem, the de Rham complex and cohomology, the Laplace-Beltrami operator, the Hodge *-isomorphism, harmonic forms.

The talk is primarily directed to the graduate students intending to sign-up for Math 6610 - Topics in Geometry, in Spring 2017.