Aula Riunioni, Dipartimento di Matematica
Since the early 1990s, the theory that has subsequently taken the name of Topological Data Analysis has developed as a tool for the stable evaluation of data with respect to appropriate metrics, proving valuable in many applications. The main idea is to study the objects of interest by examining the topological properties of the functions defined on the spaces representing these objects. In this talk I will describe my research on topological data analysis and its natural relationship with geometric deep learning through the theory of group equivariant non-expansive operators (GENEOs), showing that Big Data and Artificial Intelligence require us to progressively shift the attention from data spaces to observer spaces. The talk will focus on expository clarity, avoiding as much as possible the use of technicalities. Some recent lines of research will also be briefly illustrated, concerning the applications of TDA and the theory of GENEOs to the automatic identification of pockets in proteins and the analysis of signals produced by the sixth generation of mobile telephony (6G).