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.


Fridays 12:00 - 13:30
Paweł Dłotko
MIMUW, room 5840


Fridays 14:00 - 15:30
Davide Gurnari, Niklas Hellmer
MIMUW, room 3045


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.


  • 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: