Sede ufficiale: LARGO BRUNO PONTECORVO, 3, 56127 PISA
Email: patrizio.frosini@unipi.it
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Sede ufficiale: LARGO BRUNO PONTECORVO, 3, 56127 PISA
Email: patrizio.frosini@unipi.it
Struttura: Dipartimento di Informatica
Settore scientifico-disciplinare: Geometria MATH-02/B
Modalità:
Luogo: Dipartimento di Informatica.
Orario: Il ricevimento si tiene su appuntamento.
My research primarily focuses on the topological and geometric properties of manifolds and topological spaces equipped with filtering functions taking values in Rn, particularly in the presence of symmetry groups. In the early 1990s, I introduced and began studying the first theoretical elements of topological data analysis and persistent homology, as acknowledged in Herbert Edelsbrunner's plenary lecture at the 2012 European Congress of Mathematics. For further information on my mathematical contributions in this field, you can consult the online page: Topological data analysis - Wikipedia. As of now, Scopus reports over 5,000 documents under the term “topological data analysis” and more than 6,000 under “persistent homology.”
Regarding persistent topology, I am particularly interested in extending the theory in the presence of a subgroup G of the topological group of all homeomorphisms of the space in question, and in studying the natural pseudo-distance associated with G, both for real-valued and vector-valued functions. I introduced and began developing the topological theory of spaces of Group Equivariant Non-Expansive Operators (GENEOs) with respect to groups of homeomorphisms, as well as their application to topological data analysis, machine learning, and artificial intelligence (https://www.nature.com/articles/s42256-019-0087-3). Together with several collaborators, I am currently extending the GENEO framework to graphs (https://www.nature.com/articles/s41598-025-90152-7) and collaborating with various research groups, a major pharmaceutical company, and a large multinational mobile telecommunications company for the application of GENEO theory to deep learning and related areas.