Differential geometry is the study of Riemannian manifolds and their local and global properties.

In this course, we will cover some topics in differential geometry, possibly including:

- Calculus of variations and Morse theory on the space of paths
- The Cartan-Hadamard theorem and the geometry of nonpositively curved manifolds
- The geometry of Lie groups and symmetric spaces
- Comparison geometry

- Instructor: Robert Young (ryoung@cims.nyu.edu)
- Office: CIWW 601
- Office hours: Mondays, 1:30--2:30 or by appointment
- Lectures: CIWW 201, Wednesdays 1:25--3:15
- Sources:
- Milnor,
*Morse theory* - Lee,
*Riemannian Manifolds: An Introduction to Curvature* - Bridson and Haefliger,
*Metric Spaces of Non-Positive Curvature* - Cheeger and Ebin,
*Comparison Theorems in Riemannian Geometry*

- Milnor,

- Week 1-2
- A different proof that flat manifolds are locally euclidean can be found in
*Riemannian Manifolds*, page 119-121. - Week 3-7
- Week 8-10
- Week 11-13