Mathematics 621, Spring 2017

Differential Geometry

Wednesdays and Fridays, 4:40-5:55, Physics 205

Office hours are Mondays 11-12 and Fridays 3:30-4:30.

The final day of class will be Friday April 21. The take-home final exam will be handed out (in my office) on April 24 between 3:00 and 5:00 pm, and it is due on May 2.

Course notes part 1; course notes part 2

Homework assignments

Please note: these links are no longer operative.

Course synopsis:

This course is a graduate-level introduction to foundational material in differential geometry. Differential geometry underlies modern treatments of many areas of mathematics and physics, including geometric analysis, topology, gauge theory, general relativity, and string theory. The main topics of study will be organized into two overall sections, differential topology (differential manifolds, vector fields, tensors, differential forms, and vector bundles) and Riemannian geometry (Riemannian metrics, connections, geodesics, curvature, and topological curvature theorems). Additional advanced topics will be considered if time permits.

The textbook for this course is Riemannian Geometry by Manfredo Perdigao do Carmo. As a supplementary source, some of the material covered in the class can be found in Riemannian Geometry by Gallot, Hulin, and Lafontaine, and Smooth Manifolds by Lee.