• Welcome to differential geometry! We meet Monday and Wednesday 9-10 AM in SC Hall E.
• Bookmark this page. See Canvas for HW submission.
• Pre-requisites are 19a,b or 21a,b or 22a,b or 23a or 25a or 55a or an equivalent background.
• Weekly HW. First HW is due September 11, 2026
• Lecture notes consist of "units". Lectures and units do not correspond in general. The first 2 lectures cover 4 units and cover mostly material you know from calculus and linear algebra. We build on this!
• Grades: HW 40 percent, midterm 30 (in-class/take-home combined), final 30 (in-class/paper combined)

Lecture notes

• 09/02/26 Unit 1: Introduction ,
• 09/09/26 Unit 2: Preliminaries , Unit 3: Surfaces , Unit 4: Curves .

Homework

• PSet 1, Due September 11
• PSet 2, Due September 18

W1    1 Wednesday September 2:      Surfaces and curves

W2
      2 Monday   September 7:       Labor day, no class
      3 Wednesday September 9:      Relevant linear algebra and analysis 
W3
      4 Wednesday  September 14:    Frenet theorem in two and 3 dimensions
      4 Wednesday  September 16:    Frenet theorem in arbitrary dimensions

W4    6 Monday   September 21:      Hopf Umlaufsatz
      7 Wednesday  September 23:    Four vertex theorem

W5    8 Monday   September 28:      The fundamental forms I,II,III
      9 Wednesday  September 30:    The Gauss Map A and Curvature K

W6   10 Monday  October 5:          Discrete differential geometry 
     11 Wednesday October 7:        Review for midterm

W7   12 Monday  October 12:         Columbus day, no classes
     13 Wednesday October 14:       In-class part Midterm

W8   14 Monday  October 19:         Calculus of variations and Geodesics
     15 Wednesday October 21:       Exponential map and geodesic coordinates

W9   16 Monday  October 26:         Differential forms and Green's Theorem
     17 Wednesday October 28:       The Theorema Egregium

W10  18 Monday  November 2:         Local Gauss Bonnet theorem
     19 Wednesday November 4:       Global Gauss Bonnet theorem

W11  20 Monday  November 9:         Riemannian manifolds
     21 Wednesday November 11:      Discrete manifolds

W12  22 Monday  November 16:        Curvature and Ricci tensors
     23 Wednesday Novemer  18:      General relativity

W13  24 Monday  November 23:        Discrete general relativity
        November 25- November 29:   Thanksgiving

W14  25 Monday  December 2:         Final review
     26 Wednesday December 4:       In class part final