## Introduction to Topological Data Analysis.

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

1st course: Introduction (September 7th 13-15)

2nd course: Simplicial homology (September 21st 13h-16h)

3rd course: Morse functions and bar codes and practical session (September 28th 13h-17h)

4rth course: Homology of surfaces (Monday October 3rd 10:15-12:15, no class this week on Wednesday)

5th course: More simplicial complexes and triangulations (October 12th 13h-17h)

6th course: Delaunay triangulations and midterm exam part 1 (October 19th 13h-16h)

7th course: alpha-complexes and Midterm exam part 2 (October 26 13h-16h)

8th course: Persistent homology, bottleneck distance and stability theorem. Practice on computer (November 9 13h-17h)

9th course: Practice on computer and quizz (November 16th 13h-16h)

10th course: Reach and triangulation of submanifolds, distance functions, gradient and weak feature size (November 23rd)

Final exam: December 5th, 10:15 in salle 2

#### Midterm exam:

A 2-5 pages report, with a 15 minutes presentation followed by a 5 minutes discussion on a topic of your choice among the ones given out in class.

#### Final exam:

A 2 hours in-class exam.

Grade: 40 percent on the final, 30 on the quizz and 30 on the midterm.
### References

- J.-D. Boissonnat, F. Chazal, M. Yvinec.
Geometric and Topological Inference. Cambridge Texts in Applied Mathematics, vol. 57,
Cambridge University Press, 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 for lectures 2 and 3.