We have left 9 lectures 

Feb 12, 19, 24, 26 and mar 3, 5 10 12 and 17

Plan:  

2/12: Integration pairing.  Define singular homology
and thus cohomology by duality. The deRham isomorphism.
A bit of Hodge theory, time permitting

2/19 and 24.  Frobenius, the dual version. Chow, the dual version.
A bit of EDS

2/26.  Homogeneous space intro.  G acts transitively on M $\implies$ M = G/H
A few examples: spheres, projective space, Grassmannians, hyperbolic space.
The space forms

3/3 and 3/5.  Structure equations: for surfaces. For curves.  For Riemannian manifolds.
Perhaps for submanifolds.  Cartan's lemma. The frame bundle.

3/10 and 3/12:  beginning Riemannian geometry

3/17: how this course relates to my work.