Fall 2026
Daniel Ketover
Course Description:
Introduciton to differential geometry
Text:
Lee, Smooth Manifolds and Do Carmo Riemannian geometry
Prerequisites:
Point set topology, linear algebra, real analysis
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Fall 2025
Facundo Mémoli
Course Description:
This is an introduction to Riemannian manifolds. We'll cover concepts such as distance, volume, covariant derivatives, the Levi-Civita connection, geodesics, different notions of curvature: sectional, Ricci, scalar; Jacobi fields, conjugate points and will build towards proving the Rauch comparison, Hopf-Rinow, and volume comparison theorems.
Text:
We'll use several sources including: Riemannian Geometry by Gallot, Hulin, and LaFontaine, Riemannian Geometry by Sakai, and Riemannian Geometry by Peter Petersen.
Prerequisites:
Advanced Calculus. Some elementary set theory and metric topology.
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Spring 2025
Daniel Ketover
Course Description:
Introduction to U8smooth manifolds and Riemannian geometry.
Text:
M. do Carmo's Riemannian geometry and J. Lee's Introduction to smooth manifolds.
Prerequisites:
Point Set Topology
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Fall 2023
Jian Song
Course Description:
Differential geometry is the study of geometric properties of curves, surfaces, and their higher dimensional analogues using the methods of calculus. It has a long and rich history, and, in addition to its intrinsic mathematical value and important connections with various other branches of mathematics, it has many applications in various physical sciences. In this course, we will study differential manifolds, Riemannian metrics, Levi-Civita connections, curvature tensors, geodesics and space forms and possibly comparison theorems in Riemannian geometry.
Text:
My own notes
Prerequisites:
Real Analysis
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Fall 2022
Daniel Ketover
Course Description:
We give an introduction to Riemannian geometry, beginning with the notion of a manifold. We'll study geodesics, Jacobi fields and the Morse index theorem, the curvature tensor and comparison theorems, connections between curvature and topology and time-permitting some selected topics in geometric analysis.
Text:
do Carmo, Riemannian Geometry
Prerequisites:
point set topology, multivariable calculus
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Fall 2021
Daniel Ketover
Course Description:
We give an introduction to Riemannian geometry, beginning with the notion of a manifold. We'll study geodesics, Jacobi fields and the Morse index theorem, the curvature tensor and comparison theorems, connections between curvature and topology and time-permitting some selected topics in geometric analysis.
Text:
do Carmo, Riemannian Geometry
Prerequisites:
point set topology, multivariable calculus
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Schedule of Sections:
16:640:532 Schedule of Classes