Topological data analysis

Goal:

In topological data analysis (TDA) one uses techniques from algebraic topology to study experimental data. Very generally, the idea is that the "shape"(= topology) of a dataset (or rather the space from which it is sampled) carries important information about the data. By trying to reconstruct the space from which the data came, one can compute algebraic invariants for datasets and use these invariants to compare different data.
In this project you will learn some of the basic tools used in TDA. The participants will use these to study a few small datasets in a simplified way. This could be done either from scratch in a programming language of the participants' choice or by using some pre-existing TDA software. The project will also serve as a very hands-on introduction to some mathematical concepts that are central also in many areas of theoretical mathematics.

Supervisors: Axel Siberov

Difficulty level: Advanced

Prerequisites: Knowledge corresponding to the courses Programming fundamentals 2 [F1-BAINFOR-15], Algèbre [BASI-289] and Topologie générale [BASI-210]

Tools: Python or similar language

FSTC -- University of Luxembourg