Metric Embeddings Fall 2022



Welcome to the course on metric embeddings, MATH-513. A metric embedding is a mapping from one metric space to another. Special interest is on such embeddings that are distance preserving or approximately distance preserving. We focus on such embeddings of finite metric spaces.

Basic Information

Mailing List: News, updates and general information on the course will be disseminated via the mailing list [email protected] 
  Literature: We will largely follow the lecture notes of Matousek: You are expected to read the corresponding chapters as we progress during the course 
Format of the Lectures: This course will be a flipped-classroom format. I will record around 40-50 minutes of video material each week that you are asked to watch before the course. Watching the video is not enough. It is absolutely necessary to read, in-depth, the corresponding parts of the lecture notes. 
Exercises: Exercises are mostly  taken from the notes and announced one day before the lecture. In the exercise session, we will discuss the exercises and present solutions. You are requested to do the exercises at home. We will not publish written solutions to the exercises. You are expected to take notes of the solutions yourself. 
Exam: There is an oral exam at the end of the semester. 10% of the grade is determined by your participation in the exercises: Each student has to present the solution to three exercises and receives a grade A or B for the respective presentation. AAA is corresponds to 6.0 BBB to 3.5 The grade of  two presentations can be dropped and replaced by the grade of two additional exercise presentations. The goal of this format is to foster discussion and to have a lively participation. 
Schedule:  We meet each Friday (room  ELG120) according to the following schedule:
  • 9:00 – 9:50     Discussion of additional course material (Questions, variations of proofs, examples, etc…) 
  • 10:00: 11:30  Exercise session. 
Videos: The videos from the last edition are found here and will be updated, as we deviate from the content.

Covered material

  • 23.09.: Metric spaces, the cone of L_1

Problem sets