Differential Geometry, Spring 2024

Lectures: TTh 12:30 -- 1:45, Hayes-Healy 117.

Office hours: Th 5-6, Hurley 283 (tentative), or by appointment.

Syllabus: We will loosely follow Lee's and do Carmo's books. We will aim to cover material in do Carmo up through chapter 10, and maybe beyond if we have time/inclination. We will cover: Riemannian metrics, connections, geodesics, curvature, submanifolds, Gauss-Bonnet theroem, Jacobi fields, curvature comparison theorems. Here are the lecture notes from when I taught the course in 2021.

Book: do Carmo, ``Riemannian geometry.'' Lee, ``Introduction to Riemannian manifolds.''

Grade: There will be one take-home midterm, and one take-home final. Your grade will be weighted by: 50% homework, 25% midterm, 25% final.

Midterm: Will take place the week of March 18. It will be a take-home midterm. You won't have homework for that week.

Homework: There will be regular (~weekly) homework assignments. I will post the homeworks and solutions here as they appear.