# Differential Geometry II

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

## Basic information

- Instructor: Robert Young (ryoung@cims.nyu.edu)
- Office: CIWW 601
- Office hours: Mondays, 1--3 or by appointment
- Lectures: CIWW 517, Tuesdays, 1:25--3:15
- Sources:
- Milnor,
*Morse theory*
- Lee,
*Introduction to Riemannian Manifolds* (Springer)
- Cheeger and Ebin,
*Comparison Theorems in Riemannian Geometry*

## Problem sets