MATS4120 Geometry of geodesics

• Course page in Sisu
• Instructor: Joonas Ilmavirta, MaD310, first.last@jyu.fi
• Lecture and exercise schedule: see Sisu
• Ratkomo sessions: upon request
• Lecture notes:
  1. First version, March 17
  2. Second version, April 30

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 Wednesday (or the one exceptional Tuesday). Exercises returned electronically must be sent by email by 9 pm the previous evening with the subject starting with "MATS4120".

Other exercises can be done at any time. All the exercises must be turned in two weeks after the last exercise session, by Wednesday 29th of May. Adjustments are negotiable, but only in advance.

Passing the course

The course is graded with a numerical grade 1–5. Passing requires the following:

• Returning weekly important exercises in writing electronically or on paper.
• Returning at least 50 % of all exercises by Wednesday 29th of May. Adjustments are negotiable. This amounts to a minimum of 94 exercises.
• Grading:
  50 % (70/139 exercises) for 1/5.
  60 % (84/139 exercises) for 2/5.
  70 % (98/139 exercises) for 3/5.
  80 % (112/139 exercises) for 4/5.
  90 % (126/139 exercises) for 5/5.
  

When returning exercises, please mention the total number of exercises completed and your grade goal. That makes grading faster by eliminating the typical cases where a grader needs to reach out to a student.

Lecture attendance is not mandatory. The course can be completed remotely by returning exercises (the important ones weekly and the rest after the course). The lectures are not recorded or broadcast.