# Invitation to Topological Data Analysis

##### Summer Term 2022

Modern topology has found its way through computations into applications. In this lecture we will discuss basic tools of topological data analysis: homology and persistent homology theory, discrete Morse theory, Reeb graphs and mapper algorithms and more. In particular, a number of applications of those techniques will be highlighted. We will show how those methods can be integrated with statistics and machine learning. By doing so will lay down solid theoretical foundations and learn to use the techniques in practice.Prior knowledge of algebraic topology is desired. Ability to program in Python or R is required.

#### Lecture

Fridays 12:00 - 13:30Paweł Dłotko

MIMUW, room 5840

USOS

#### Labs

Fridays 14:00 - 15:30Davide Gurnari, Niklas Hellmer

MIMUW, room 3045

USOS

#### Exercises

Students will need to present at least one theoretical and one practical exercise in class, ideally three exercises in total.

#### Final Presentations

Students will need to present a paper in the last two weeks of class. Please indicate your choice by 13.05. end of day by email to Niklas. The presentations should take no more than 30 minutes including time for questions.#### References

- Herbert Edelsbrunner and John Harer, Computational Topology, an introduction, AMS 2011.
- Paweł Dłotko, Applied and computational topology Tutorial, arXiv
- Mischaikow, Kaczynski, Mrozek, Computational Topology, Springer 2004.
- Gudhi library: gudhi.inria.fr