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In this talk, we will explore the relation between C* actions and Morse theory and will include themes in Representation Theory, Topology, Symplectic Geometry, Algebraic Geometry, Cohomological Algebra and Integrable Systems. Namely, we will show that a C* action on a symplectic manifold leads to a Morse function on your manifold. (Are these two notions equivalent in this setting?) From this, we can use this action to study the cohomology of the manifold. In particular, if time allows, we use these techniques to determine the Poincare polynomial of a family of Hilbert Schemes of points on a surface.