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

MATH-GA 2360: Differential Geometry II, Spring 2025

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.

Basics

  • Instructor: Robert Young (ryoung@cims.nyu.edu)
  • Office: WWH 601
  • Office hours: Mondays, 11-12
  • Midterm exam: Mid-March
  • Final exam: Finals week

Problem Sets

Notes

Suggested texts

  • Milnor, Morse Theory
  • Lee, Introduction to Riemannian Manifolds
  • Cheeger and Ebin, Comparison Theorems in Riemannian Geometry
  • Warner, Foundations of Differentiable Manifolds and Lie Groups