In this talk, I will give a brief tutorial on the topological methods used in scientific visualization for the analysis of scalar data. I will present algorithms with practical efficiency for the computation of topological abstractions (Reeb graphs, Morse-Smale complexes, persistence diagrams, etc.) in low dimensions (typically 2 or 3). I will also illustrate these notions with concrete use cases in astrophysics, fluid dynamics, molecular chemistry or combustion.

This seminar will be followed by a second tutorial, on May 4th, related to the design and usage of the open-source C++ library "the Topology ToolKit" (https://topology-tool-kit.github.io/), which implements most of the algorithms discussed in the first talk.