What is...?

Persistence modules offer a way to analyze how features, such as connected components or holes, evolve as a space is gradually changed. One can think of a persistence module as a sequence of vector spaces, each corresponding to a particular stage of this process, together with linear maps that describe how features at one stage carry over to the next. This approach helps identify which features are robust (persisting over many stages) and which are transient, making it a powerful tool for understanding the structure of geometric spaces and data.
Persistence modules emerged in 2005 within topological data analysis. They now lie at the intersection of several fields, including metric geometry and the calculus of variations. In recent years, they have been fruitfully integrated into pure mathematics, particularly in disciplines such as function theory and symplectic geometry.
The talk will be accessible to all audiences, with no prior knowledge required.