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

MATH-GA 2360: Differential Geometry II

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.

This semester, we will cover some topics in differential geometry, possibly including:

  • Calculus of variations and Morse theory on the space of paths
  • Comparison geometry
  • The geometry of nonpositively curved manifolds
  • Lie groups and symmetric spaces
  • Cohomology and Hodge theory

Basics

  • Instructor: Robert Young (ryoung@cims.nyu.edu)
  • Office: WWH 601
  • Office hours: Mondays, 1-2, WWH 601
  • Midterm exam: First half of 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