### Teaching

#### 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*