Course Plan

Meeting 3
- Day 5 room D31, 14th November
  - material: Lecture slides Download Lecture slides
  - material: Exercise session Download Exercise session
  - tutorial: Notebook_Statistics Download Notebook_Statistics
  - 11:00-12:30 Lecture, Wojtek
    - Stable rank invariants for homologies
    - Summary of analysis pipeline
    - Stability results
  - 12:30 - 13:00 Lunch at Q Restaurant, next to Q1 lecture theater
    - pick up your voucher from Florian first.
  - 13:30-15:00 Lecture, Wojtek
    - Subsampling and statistical analysis
    - ML challenges for stable rank analysis
  - 15:00-15.30 Coffee break
  - 15:30-17:00 Exercises, Martina
  - 17:15-18:00 Exercises, Martina
  - 18:30 Social dinner at restaurant Cypern.
- Day 6 room D31, 15th November
  - material: <to be uploaded>
  - lecture: Multi_persistence Download Multi_persistence
  - 9:00-10:30 Lecture, Florian
    - Application research perspective: Applications of persistence in robotics and motion clustering
  - 10:30-11:00 Coffee break
  - 11:00-12:30 Lecture, Martina
    - Challenges of multi-parameter persistence
  - 12:30 - 13:30 Lunch at Q Restaurant, next to Q1 lecture theater
  - 13:30 - 15:00 Student presentations, Wojtek, Florian and Martina
    - Presentations of step 1 of the final project summaries
  - 15.00-15.15 Coffee break
  - 15:15-16:00 Student presentations, Wojtek, Florian and Martina
    - Presentations of step 1 of the final project summaries
    - Course evaluation, reflection on what can be improved, what worked well, etc

Activities between meeting 2 and 3
- Final Projects Step 1: Students are divided into groups of between 3 and 5. Each groups is supposed to turn in a written report whose content is an example of an analysis. Each group has to choose an analysis task, including data, that is suitable for analysis using the tools introduced in the course. Before meeting 3 each group is to prepare 15 minutes summaries of their suggested projects to be presented during the third meeting of the course. For the final grade a written report describing math ideas, the project, methods used, and results is to be turn in within a month after the 3rd meeting.

Meeting 2
- Day 3 room M3, 24th October
  - material: lecture slides part 1 Download lecture slides part 1
    , lecture slides part 2 Download lecture slides part 2
  - tutorial: ripser_tutorial.ipynb Download ripser_tutorial.ipynb
  - 11:00-12:30 Lecture, Wojtek
    - Simplicial complexes, maps between simplicial complexes, homotopy relation
    - Vietoris Rips complexes
  - 12:30 - 13:00 Lunch at Q Restaurant, next to Q1 lecture theater
    - pick up your voucher from Florian first.
  - 13:30-15:00 Lecture, Wojtek
    - Homology
    - Homology of Vietoris Rips complexes
    - Bar coding for higher homology
  - 15:00-15.30 Coffee break
  - 15:30-16:15 Lecture, Wojtek
  - 16:45-18:00 Exercises, Martina
  - 18:30 dinner at Sue Ellen restaurant Links to an external site..
- Day 4 room M3, 25th October
  - material: Exercises_Martina
  - lecture 1: seminar1.pdf Download seminar1.pdf
  - lecture 2: seminar2.pdf Download seminar2.pdf
  - 9:00-10:30 Lecture and Exercises, Florian
    - Various simplicial complex constructions
    - The computation of persistent homology and the complexity challenges of implementing and scaling persistent homology computations.
  - 10:30-11:00 Coffee break
  - 11:00-12:30 Lecture and Exercises, Florian
    - Various simplicial complex constructions.
    - The computation of persistent homology and the complexity challenges of implementing and scaling persistent homology computations.
  - 12:30 - 13:30 Lunch at Q Restaurant, next to Q1 lecture theater
  - 13:30-14:15 Exercises, Martina
  - 14:15-15:00 Student presentations, Wojtek, Florian and Martina
    - Presentations of projects summaries
  - 15.00-15.15 Coffee break
  - 15:15-16:00 Student presentations and Next tasks, Wojtek, Florian and Martina
    - Presentations of projects summaries
    - Suggestions for the final projects
Activities between meeting 1 and 2
- Projects: Students are divided into groups of 5. They choose one of the projects described on the page. Each group is to prepare 20 minutes summaries of their work on the project to be presented during the second meeting of the course.
Meeting 1
- Day 1
  - material: lecture slides Download lecture slides
    , exercises Download exercises
  - 11:00-12:30 Lecture, Wojtek room V3,
    - introduction, basic data sets used throughout the course as an illustration
    - recollection about partitions, distances, pseudometrics
    - piecewise constant functions
  - 12:30 - 13:00 Lunch at Q Restaurant, next to Q1 lecture theater
    - pick up your voucher from Florian first.
  - 13:30-15:00 Lecture, Wojtek room V3
    - comparing distances: fixed enumeration
    - comparing pseudometrics: Gromov-Hausdorff distance
    - ultra pseudometrics and dendrograms
  - 15:00-15.30 Coffee break room V3
  - 15:30-17:00 Exercises, Martina room M3
  - 17:15-18:00 Exercises, Martina room M3
  - 18:30 Social dinner at restaurant Cypern.
- Day 2
  - material: lecture slides Download lecture slides
    , exercises Download exercises
  - 9:00-10:30 Lecture, Wojtek room M3
    - hierarchical clustering methods
    - parametrised vector spaces, bar decompositions, interleaving distances.
  - 10:30-11:00 Coffee break
  - 11:00-12:30 Lecture, Wojtek roomM3
    - from dendrograms to bar codes,
    - from dendrograms to stable ranks,
    - H_0 clustering analysis
    - illustrations of analysis
  - 13:30-15:00 Exercises, Martina room M3
  - 15.00-15.15 Coffee break
  - 15:15-16:00 Next tasks, Wojtek and Martina room M3
    - Description of the projects between meetings 1 and 2

Activities before meeting 1
- Readings: The following are sections of the notes which are obligatory to read before the course starts. It is very important that you are familiar with basic definitions and notation contained in the following sections of the notes: