## 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.

### Homework assignments

Please note: these links are no longer operative.

- HW 1, due Wednesday 1/25; solutions to HW 1

- HW 2, due Wednesday 2/1; solutions to HW 2

- HW 3, due Wednesday 2/8; solutions to HW 3

- HW 4, due Wednesday 2/15; solutions to HW 4

- HW 5, due Wednesday 3/1; solutions to HW 5

- HW 6, due Wednesday 3/8; solutions to HW 6

- HW 7, due Wednesday 3/22; solutions to HW 7

- HW 8, due Wednesday 3/29; solutions to HW 8

- HW 9, due Wednesday 4/5; solutions to HW 9

- HW 10, due Wednesday 4/12; solutions to HW 10

- HW 11, due Wednesday 4/19; solutions to HW 11

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.