Files for download
Introductory lecture:
- Introduction to Homology and Basic Combinatorial Structures (Bartosz Furmanek, Jagiellonian University in Kraków)
- Topology in Dynamics (Jakub Leśkiewicz, Jagiellonian University in Kraków)
Thomas Wanner, George Mason University. Combinatorial Topological Dynamics.
Paweł Dłotko, Dioscuri centre in TDA. Topological Data Analysis and beyond.
- Slides
- Software examples
- GUDHI library
- Computational and applied topology, tutorial (arXiv)
- GUDHI tutorials
- pyEulerCurves GitHub project
- Knot invariants and their relations: a topological perspective
- When two distributions have the same expected ECC? (arXiv)
- On the shape that matters – topology and geometry in data science (popular science article)
- Visualizing Maps in Practice (popular science article)
Bogdan Batko, Jagiellonian University in Kraków. Conley index methods in data-driven dynamics.
- Slides part 1: Conley index theory for discrete multivalued dynamical systems
- Slides part 2: Conley index approach to sampled dynamics
- Slides part 3: Identifying nonlinear dynamics with high confidence from sparse data
Michał Lipiński, IST Austria & Jagiellonian University in Kraków. Conley-Morse barcodes
Conley-Morse barcodes. Combinatorial continuation of a Morse decomposition via persistent homology (joint work with Tamal K. Dey and Manuel Soriano-Trigueros).