Advanced Differential Geometry

Harvard FAS

About half of the second semester will be a focus on Riemannian geometry: theory of geodesics, relations between curvature and topology, theorems ofHopf–Rinow, Cartan–Hadamard, Bonnet–Myers, etc. I will also introduce some basic linear PDE and prove the Hodge theorem. Beyond that the instructor has not yet decided and is open to student input. Spin geometry is one likely topic.