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: Tuesdays, 1--2 or by appointment
- Lectures: CIWW 201, Thursdays, 1:25--3:15
- Sources:
- Milnor,
*Morse theory* - Lee,
*Riemannian Manifolds: An Introduction to Curvature*(Springer) - Bridson and Haefliger,
*Metric Spaces of Non-Positive Curvature* - Cheeger and Ebin,
*Comparison Theorems in Riemannian Geometry*

- Milnor,

- Problem Set 1 (due Feb. 9) (2017-02-06: corrected some typos)
- Problem Set 2 (due Feb. 23) (2017-02-23: corrected a typo in question 2 (extra 2 in the denominator))
- Problem Set 3 (due Mar. 2)
- Problem Set 4 (due Mar. 23)
- Problem Set 5 (due Apr. 13) (2017-04-12: minor corrections)
- Problem Set 6 (due Apr. 27)