FGV/EMAp Summer Program: Topological Data Analysis: Foundations and Algorithms

This course introduces the fundamental mathematical concepts and algorithm from the emerging field of topological data analysis.

[Mon 16/01]
0 - Introduction: introduction and motivation for topological data analysis.
1 - Homology theory: simplicial complexes, simplicial homology, and some applications.

[Wed 18/01]
2 - Discrete Morse theory: introduction of discrete Morse theory as a mean to simplify simplicial complexes.

[Fri 20/01] -> holiday.

[Mon 23/01] -> technical issue

[Tue 24/01] -> same time
3 - Persistent homology: introduction of persistent homology as a multi-scale approach to homology.

[Wed 25/01]
5 - Stability and topology inference: the stability theorem of persistent homology, and application in topology inference. 4 - Stability and topology inference: the stability theorem of persistent homology, and application in topology inference.

[Fri 27/01]
5 - General topology: concepts of general topology, and in particular topological equivalences.

Parisian Master of Research in Computer Science (MPRI) - Computational Geometry Learning

The course is an introduction to the emerging field of Geometric and Topological Data Analysis. Fundamental questions to be addressed are: how can we represent complex shapes in high-dimensional spaces? how can we infer properties of shapes from samples? How can we handle noisy data? How can we walk around the curse of dimensionality?

Webpage of the course