Mathematics 621, Spring 2013

Differential Geometry

Wednesdays and Fridays, 1:25-2:40 pm, Physics 227

Office hours are Wednesdays 4:20-5:00 and Thursdays 1:30-3:30 (please note these are shared with my Math 222 class), or please feel free to drop by.


Homework assignments

Roughly weekly problem sets, to be posted here once they are assigned.

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: differential manifolds, vector fields, tensors, differential forms, and vector bundles; 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 Perdig„o 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.