The recently found synergy of Topological Data Analysis (TDA) and artificial intelligence is proving effective in many real-world scenarios. In this talk, we are going to present a new approach for the study of the shape of data by means of operators that originate from TDA and that we call Group Equivariant Non-Expansive Operators (GENEOs). The key idea of GENEOs is to allow TDA to be equivariant with respect to a subgroup of all homeomorphisms, potentially expanding the flexibility of the TDA framework. After introducing the key concepts of this mathematical setting, we are going to show that the computation of the persistence diagram is actually a GENEO. We conclude with a couple of real-world applications.

The seminar will be held in person at Inria Sophia Antipolis, and online on BigBlueButton