## Introduction to Topological Data Analysis.

M2 MPA: Topics in computational algebra and geometry by Indira Chatterji, indira@unice.fr, office 607 2nd floor. Practical sessions by Antoine Commaret.

1st course: Introduction (September 11th 13-16)

2nd course: Practical session (September 18th 13-15)

3rd course: September 25th 13-16: Simplicial complexes and functors

4th course: October 2nd, 13-16: Simplicial homology

5th course: October 9th, 13h-16: Simplicial approximation, mesh and Mayer-Vietoris

6th course: October 16th 13h-17: Quizz (20 min). Homology of surfaces and homotopy invariance

7th course: October 23rd 13h-16: Delaunay triangulations. Short presentations.

8th course: November 6th 13h-16: Midterm exam (1h). Persistent homology, bottleneck distance and stability results.

9th course: November 13th 13h-16: Reach and triangulation of submanifolds

10th course: November 20th, 13-16: Quizz (20 min). Practice session (with a practice grade)

Final exam: To be fixed

**Presentation:** A max 2 pages report, with a 10 minutes presentation of an exercise of your choice among the ones given out in class, or an interesting exercise that you would like to share with the class.

**Quizzes:** Two 20-minutes quizzes with a simple exercise and definitions will be given during the semester.

**Final exam:** A 4p max essay on a chosen topic, date to be decided.

**Final Grade: ** 40 percent on the final, 20 on the midterm exam, 20 on the quizzes, 10 on the presentation and 10 on the practice.
### References

- J.-D. Boissonnat, F. Chazal, M. Yvinec.
Geometric and Topological Inference. Cambridge Texts in Applied Mathematics, vol. 57, (2018) public version.
- F. Chazal, Vin da Silva, Marc Glisse, Steve Oudot.
The structure and stability of persistence modules public version.
- J.R. Munkres.
Elements of Algebraic Topology, Addison-Wesley, 1984.
- A. Hatcher. Algebraic Topology. Cambridge University Press 2002.
public version.
- Fred Chazal's notes available here
- Henry Wilton's class notes by Dexter Chua especially part 6 and 7.