\(\newcommand{\R}{\mathbb{R}} \newcommand{\C}{\mathbb{C}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\K}{\mathbb{K}} \newcommand{\N}{\mathbb{N}} \newcommand{\cV}{\mathcal{V}} \DeclareMathOperator{\id}{id} \DeclareMathOperator{\Ric}{Ric} \newcommand{\from}{\colon\;} \newcommand{\II}{\mathrm {I\!I}} \newcommand{\Q}{\mathbb{Q}}\)

MATH-GA 2360: Differential Geometry II, Spring 2026

Overview

Differential geometry studies Riemannian manifolds and their local and global properties. One of the fundamental questions of differential geometry is how local properties like curvature, which describes the shape of a manifold on infinitesimal balls, can be used to describe the global structure.

In this class, I plan to cover:

  • Smooth and Riemannian manifolds
  • Geodesics and curvature
  • Variational formulas and Jacobi fields
  • Model spaces and comparison geometry
  • Gromov-Hausdorff convergence and limits of manifolds

Basics

  • Instructor: Robert Young (ryoung@cims.nyu.edu)
  • Office: WWH 601
  • Office hours: Wednesdays, 1-2pm
  • Midterm exam: March 12, in class
  • Final exam: Finals week

Problem Sets

Suggested texts

  • Lee, Introduction to Riemannian Manifolds
  • Milnor, Morse Theory
  • Cheeger and Ebin, Comparison Theorems in Riemannian Geometry