MATH 0072 (Riemannian Geometry)

This plan below is very schematic.

How to contact me: by email, or stop by my office (better to ask in advance if I'm going to be in).

Weeks below are numbered accordingly to the UCL academic calendar to avoid any confusion.

• WEEK 6
  Lecture 1, 04/10 - Manifolds: basics
  Lecture 1 notes
  Lecture 2, 07/10 - Tangent space and tangent bundle
  Lecture 2 notes
• WEEK 7
  Lecture 3, 11/10 - Differential forms, exterior algebra
  Lecture 3 notes
  Lecture 4, 14/10 - Vector bundles, Lie bracket
  Lecture 4 notes
  
• WEEK 8
  Lecture 5, 18/10 - Lie derivative, differential forms
  Lecture 5 notes
  Lecture 6, 21/10 - Riemannian manifolds, connections, Levi-Civita connection
  Lecture 6 notes
  
• WEEK 9
  Lecture 7, 25/10 - Levi-Civita connection
  Lecture 7 notes
  Lecture 8, 28/10 - Parallel transport, geodesics, exponential maps
  Lecture 8 notes
  
• WEEK 10
  Lecture 9, 01/11 - Gauss' lemma, Hopf-Rinow theorem
  Lecture 9 notes
  Lecture 10, 04/11 - Proof of Hopf-Rinow theorem, curvature
  Lecture 10 notes
  
• WEEK 12
  Lecture 11, 15/11 - Ricci and sectional curvature
  Lecture 11 notes
  Lecture 12, 18/10 - Spaces of constant curvature: hyperbolic space
  Lecture 12 notes
  
• WEEK 13
  Lecture 13, 22/11 - Jacobi fields
  Lecture 13 notes
  Lecture 14, 25/11 - Conjugate points and the Cartan-Hadamard Theorem
  Lecture 14 notes
  
• WEEK 14
  Lecture 15, 29/11 - Variations of energy
  Lecture 15 notes
  Lecture 16, 02/12 - Symplectic geometry of Jacobi fields, Bonnet-Myers theorem, Synge theorem
  Lecture 16 notes
  
• WEEK 15
  Lecture 17, 06/12 - Cut locus, Sphere theorems
  Lecture 17 notes
  Lecture 18, 09/12 - Lie groups and homogeneous spaces
  Lecture 18 notes
  
• WEEK 16
  Lecture 19, 13/12 - Riemannian metrics on the Lie groups
  Lecture 19 notes
  Lecture 20, 16/12 - Cheeger-Gromoll splitting theorem
  Lecture 20 notes