Topological Data Analysis (TDA) is a recent area of computer science that focuses on discovering intrinsic structures hidden in data. Based on sound mathematical foundations such as Morse theory and Persistent Homology, TDA enables the robust extraction of the main features of a data set into stable, concise, and multi-scale descriptors that facilitate data analysis and visualization.

In this talk, I will give an intuitive overview of the main tools used in TDA (persistence diagrams, Reeb graphs, Morse-Smale complexes, etc) with applications to concrete use cases in computational fluid dynamics, medical imaging, quantum chemistry, and climate modeling. This talk will be illustrated with results produced with the "Topology ToolKit" (TTK), an open-source library (BSD license) that we develop with collaborators to showcase our research. Tutorials for re-producing these experiments are available on the TTK website: https://topology-tool-kit.github.io/