# Persistence modules and amplitudes

Persistence theory is a powerful branch of Topological Data Analysis with many applications. In this seminar, I will briefly introduce it, presupposing no previous knowledge of the topic. In particular, I will discuss some finiteness conditions on persistence modules. I will then introduce amplitudes, a special type of invariants that capture the idea of ‘‘size of persistence’’. Amplitudes can be defined on any abelian category and are particularly useful in the so-called multiparameter persistence, where there exists no discrete complete invariant. I will present some examples of amplitudes and discuss some of their properties.