| (1) Differential forms and DeRham cohomology. Here the text will be Bott and Tu. I will introduce smooth manifolds and differential forms and use them to construct DeRham cohomology. We will explore Poincare duality, integration, intersection theory, and more.
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(2) Connections, curvature, and Chern-Weil theory. I will introduce vector bundles and connections on vector bundles and use them to construct characteristic classes in DeRham cohomology. I do not have a particular text in mind, I will mostly be lecturing from my own notes.
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(3) Time permitting, I will do the Cartan model for equivariant cohomology and Atiyah-Bott localization. At the end of the term, there will be student projects --- either written projects or student lectures.
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