MATS4120 Geometry of geodesics

• Course page in SISU
• Instructor: Joonas Ilmavirta, MaD310, first.last@jyu.fi
• Lectures: Thursdays Jan 9–Feb 20 at 12:15–14:00 in MaD380 and Fridays Jan 10–Feb 21 at 12:15–14:00 in MaD381
• Exercise sessions: Thursdays Jan 16–Feb 27 at 08:30–10:00 in MaD381
• Ratkomo sessions: Mondays and Tuesdays at 16–18 during the course, but not 27 Jan–4 Feb.
• Lecture notes:
  1. First version, Jan 9
  2. Second version, Jan 21
  3. Third version, Feb 6
  4. Fourth version, Feb 7
  5. Fifth version, Feb 12

This course focuses on the geometry of geodesics on Riemannian manifolds, including topics like the exponential map, Jacobi fields, and the geodesic flow.

Exercises

Exercises are included in the lecture notes. Each lecture covers one section and every week has two lectures. Therefore the first week covers exercises of sections 1 and 2, the second week sections 3 and 4, and so on. The exercises are discussed in the exercise session the week after the corresponding lectures.

The ones marked important should be returned to the instructor at latest during the exercise session on Thursday.

Other exercises can be done at any time. All the exercises must be turned in two weeks after the last exercise session, by Friday 13th of March. Adjustments are negotiable.

Passing the course

The course is graded as pass/fail without a numerical grade. Passing requires the following:

• Returning weekly important exercises in writing electronically or on paper.
• Returning at least 70 % of all exercises by Friday 13th of March. This amounts to a minimum of 94 exercises.
• Preparing a short presentation on a topic related to the course.