765 - Differential Geometry | Department of Mathematics, University of Wisconsin

Instructor:

Sean Paul

Time and Place:

MWF 9:55-10:45 am

textbooks:

1) "Differential geometric structures" by Walter Poor.
2) "Lie groups and symmetric spaces" by Helgason.
3) My notes on Kahler Geometry.

Course Content:

The primary emphasis in the course is on examples and explicit computations (when possible).
1) Introduction to real and complex manifolds: projective spaces, grassmannians, flags, quadrics . Closed oriented surfaces as algebraic curves.
2) Riemannian and Kahler metrics: The model spaces of constant curvature. Kahler Einstein metrics. Geodesics .
3) Introduction to symmetric spaces and the elementary representation theory of lie groups and lie algebras . In particular sl(2,C).
4) Real and holomorphic vector bundles . Fiber bundles. Connections on vector bundles. Curvature.
5) Hodge Theory .