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
- Comparison geometry
- The Cartan-Hadamard theorem and the geometry of nonpositively curved manifolds
- The geometry of Lie groups and symmetric spaces

- Instructor: Robert Young (ryoung@cims.nyu.edu)
- Office: WWH 601
- Office hours: WWH 601, Wednesdays, 3:15--4:30
- Lectures: WWH 517, Wednesdays, 1:25--3:15
- Sources:
- Milnor,
*Morse theory* - Lee,
*Introduction to Riemannian Manifolds*(Springer) - Cheeger and Ebin,
*Comparison Theorems in Riemannian Geometry* - Bridson and Haefliger,
*Metric spaces of non-positive curvature*

- Milnor,

- March 11: Minimizing geodesics and the Morse index theorem
- May 6: Lower curvature bounds and Toponogov's Theorem