{"id":147618,"date":"2025-05-12T14:02:56","date_gmt":"2025-05-12T14:02:56","guid":{"rendered":"https:\/\/www-test.unipi.it\/ateneo\/organizzazione\/persone\/patrizio-frosini-198939-en\/"},"modified":"2026-03-31T14:43:10","modified_gmt":"2026-03-31T12:43:10","slug":"patrizio-frosini-198939-en","status":"publish","type":"unipi_persone","link":"https:\/\/www-test.unipi.it\/en\/abous-us\/organization\/people\/patrizio-frosini-198939-en\/","title":{"rendered":"Patrizio Frosini"},"content":{"rendered":"<p>Professore Associato &#8211; Dipartimento di Informatica | Email: patrizio.frosini@unipi.it<\/p>\n","protected":false},"template":"","meta":{"unipi-persone-chiave":"198939","unipi-persone-nome":"Patrizio","unipi-persone-cognome":"Frosini","unipi-persone-email":"patrizio.frosini@unipi.it","unipi-persone-cv":"CURRICULUM VITAE OF PATRIZIO FROSINI (short version)<br \/>\r\n<br \/>\r\nORCID: 0000-0001-6711-1926<br \/>\r\nDate of Birth: September 20, 1960<br \/>\r\nNationality: Italian<br \/>\r\n<br \/>\r\nEDUCATION AND PROFESSIONAL EXPERIENCE<br \/>\r\n1991 \u2013 PhD in Mathematics, University of Florence.<br \/>\r\n1993\u20132014 \u2013 Assistant Professor of Geometry, University of Bologna.<br \/>\r\n2014\u20132024 \u2013 Associate Professor of Geometry, University of Bologna.<br \/>\r\n2024\u2013present \u2013 Associate Professor of Geometry, University of Pisa.<br \/>\r\n2019 \u2013 National scientific qualification for Full Professor (01\/A2 \u2013 Geometry and Algebra; valid until September 4, 2030).<br \/>\r\n<br \/>\r\nACTIVITY AS A REVIEWER. Referee for many well-known journals, including Advances in Data Analysis and Classification; Applicable Algebra in Engineering, Communication and Computing; Artificial Intelligence Review; Computer Vision and Image Understanding; Computer-Aided Design; Computers & Graphics; Computers & Mathematics with Applications; Discrete & Computational Geometry; Foundations of Computational Mathematics; IEE Proceedings - Vision, Image & Signal Processing; IEEE Transactions on Image Processing; IEEE Transactions on Pattern Analysis and Machine Intelligence; IEEE Transactions on Signal Processing; International Journal of Computer Vision; International Journal of Shape Modeling; Japan Journal of Industrial and Applied Mathematics; Journal of Applied and Computational Topology; Journal of Geometric Analysis; Journal of Mathematical Imaging and Vision; Journal of Pure and Applied Algebra; Nature Machine Intelligence; Pattern Recognition; Pattern Recognition Letters; Topological Methods in Nonlinear Analysis.<br \/>\r\n<br \/>\r\nAuthor\/coauthor of more than 70 scientific papers <br \/>\r\nCitations: 1352 (Scopus - 2 May 2025) <br \/>\r\nh-index: 20 (Scopus - 2 May 2025)<br \/>\r\nSupervisor of 5 Ph.D. students <br \/>\r\n<br \/>\r\nRESEARCH INTERESTS. My research primarily focuses on the topological and geometric properties of manifolds and topological spaces equipped with filtering functions taking values in &#8477;&#8319;, 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: Wikipedia \u2013 Topological Data Analysis. As of now, Scopus reports over 5,000 documents under the term \u201ctopological data analysis\u201d and more than 6,000 under \u201cpersistent homology.\u201d<br \/>\r\nRegarding 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.<br \/>\r\n<br \/>\r\nINVITED TALKS AND SEMINARS. I have been invited to deliver approximately 50 presentations at conferences, workshops, webinars, and international meetings, and I have received invitations to give seminars from more than 20 universities and internationally recognized institutions. I have been invited to teach four minicourses at international scientific schools. Additionally, I have served as a member of 15 program\/scientific\/organizing committees for international workshops, c","unipi-persone-link-esterno-cv":"","unipi-persone-modalita-ricevimento":"Si prega di confermare via email l'intenzione di partecipare al ricevimento.\nPlease confirm your intention to attend the reception by email.","unipi-persone-luogo-ricevimento":"Dipartimento di Informatica.\nDepartment of Computer Science.","unipi-persone-ore-ricevimento":"Il ricevimento si tiene ogni mercoled\u00ec dalle 11:30 alle 13:00.\nThe office hour is held every Wednesday from 11:30 to 13:00.","unipi-persone-telefono":"","unipi-persone-sitoweb":"","unipi-persone-cariche":"","unipi-persone-link-orario-lezioni":"https:\/\/unipi.prod.up.cineca.it\/calendarioPubblico\/matricola=064094","unipi-persone-link-registro-lezioni":"https:\/\/unimap.unipi.it\/registri\/registri.php?ri=064094&tmplt=principale.tpl","unipi-persone-settore-scientifico":"Geometria MATH-02\/B","unipi-persone-ruolo":"Professore Associato","unipi-persone-arpi":"https:\/\/arpi.unipi.it\/cris\/rp\/rp318383","unipi-persone-pubblicazioni":"<ul class=\"pubblicazioni-list\"><li><a href=\"https:\/\/arpi.unipi.it\/handle\/11568\/1328567\" target=\"_blank\" rel=\"noopener noreferrer\">Mathematical Foundation of\u00a0Interpretable Equivariant Surrogate Models<\/a> <span class=\"pub-details\">(Colombini, Jacopo Joy; Bonchi, Filippo; Giannini, Francesco; Giannotti, Fosca; Pellungrini, Roberto; Frosini, Patrizio - 2026 - 4.1 Contributo in Atti di convegno)<\/span><\/li><li><a href=\"https:\/\/arpi.unipi.it\/handle\/11568\/1313590\" target=\"_blank\" rel=\"noopener noreferrer\">A novel approach to graph distinction through GENEOs and permutants<\/a> <span class=\"pub-details\">(Bocchi, Giovanni; Ferri, Massimo; Frosini, Patrizio - 2025 - 1.1 Articolo in rivista)<\/span><\/li><li><a href=\"https:\/\/arpi.unipi.it\/handle\/11568\/1336067\" target=\"_blank\" rel=\"noopener noreferrer\">SCENE-Net: Geometric induction for interpretable and low-resource 3D pole detection with Group-Equivariant Non-Expansive Operators<\/a> <span class=\"pub-details\">(Lavado, Diogo; Micheletti, Alessandra; Bocchi, Giovanni; Frosini, Patrizio; Soares, Cl\u00e1udia - 2025 - 1.1 Articolo in rivista)<\/span><\/li><li><a href=\"https:\/\/arpi.unipi.it\/handle\/11568\/1326009\" target=\"_blank\" rel=\"noopener noreferrer\">GENEOnet: statistical analysis supporting explainability and trustworthiness<\/a> <span class=\"pub-details\">(Bocchi, Giovanni; Frosini, Patrizio; Micheletti, Alessandra; Pedretti, Alessandro; Gratteri, Carmen; Lunghini, Filippo; Beccari, Andrea R.; Talarico, Carmine - 2025 - 1.1 Articolo in rivista)<\/span><\/li><li><a href=\"https:\/\/arpi.unipi.it\/handle\/11568\/1326003\" target=\"_blank\" rel=\"noopener noreferrer\">GENEOnet: a breakthrough in protein binding pocket detection using group equivariant non-expansive operators<\/a> <span class=\"pub-details\">(Bocchi, Giovanni; Frosini, Patrizio; Micheletti, Alessandra; Pedretti, Alessandro; Palermo, Gianluca; Gadioli, Davide; Gratteri, Carmen; Lunghini, Filippo; Biswas, Akash Deep; Stouten, Pieter F. W.; Beccari, Andrea R.; Fava, Anna; Talarico, Carmine - 2025 - 1.1 Articolo in rivista)<\/span><\/li><li><a href=\"https:\/\/arpi.unipi.it\/handle\/11568\/1320227\" target=\"_blank\" rel=\"noopener noreferrer\">Matching Distance via the Extended Pareto Grid<\/a> <span class=\"pub-details\">(Frosini, Patrizio; Garc\u00eda, Eloy M\u00f3sig; Quercioli, Nicola; Tombari, Francesca - 2025 - 1.1 Articolo in rivista)<\/span><\/li><li><a href=\"https:\/\/arpi.unipi.it\/handle\/11568\/1264205\" target=\"_blank\" rel=\"noopener noreferrer\">Geometry of the matching distance for 2D filtering functions<\/a> <span class=\"pub-details\">(Ethier, M.; Frosini, P.; Quercioli, N.; Tombari, F. - 2023 - 1.1 Articolo in rivista)<\/span><\/li><li><a href=\"https:\/\/arpi.unipi.it\/handle\/11568\/1264191\" target=\"_blank\" rel=\"noopener noreferrer\">On the finite representation of linear group equivariant operators via permutant measures<\/a> <span class=\"pub-details\">(Bocchi, G.; Botteghi, S.; Brasini, M.; Frosini, P.; Quercioli, N. - 2023 - 1.1 Articolo in rivista)<\/span><\/li><li><a href=\"https:\/\/arpi.unipi.it\/handle\/11568\/1264229\" target=\"_blank\" rel=\"noopener noreferrer\">On the geometrical properties of the coherent matching distance in 2D persistent homology<\/a> <span class=\"pub-details\">(Cerri, Andrea; Ethier, Marc; Frosini, Patrizio - 2019 - 1.1 Articolo in rivista)<\/span><\/li><li><a href=\"https:\/\/arpi.unipi.it\/handle\/11568\/1264212\" target=\"_blank\" rel=\"noopener noreferrer\">Towards a topological\u2013geometrical theory of group equivariant non-expansive operators for data analysis and machine learning<\/a> <span class=\"pub-details\">(Bergomi, MATTIA GIUSEPPE; Frosini, Patrizio; Giorgi, Daniela; Quercioli, Nicola - 2019 - 1.1 Articolo in rivista)<\/span><\/li><li><a href=\"https:\/\/arpi.unipi.it\/handle\/11568\/1264197\" target=\"_blank\" rel=\"noopener noreferrer\">Combining Persistent Homology and Invariance Groups for Shape Comparison<\/a> <span class=\"pub-details\">(Frosini, Patrizio; Jablonski, Grzegorz - 2016 - 1.1 Articolo in rivista)<\/span><\/li><li><a href=\"https:\/\/arpi.unipi.it\/handle\/11568\/1264240\" target=\"_blank\" rel=\"noopener noreferrer\">Betti numbers in multidimensional persistent homology are stable functions<\/a> <span class=\"pub-details\">(Cerri, Andrea; DI FABIO, Barbara; Ferri, Massimo; Frosini, Patrizio; Landi, Claudia - 2013 - 1.1 Articolo in rivista)<\/span><\/li><li><a href=\"https:\/\/arpi.unipi.it\/handle\/11568\/1264198\" target=\"_blank\" rel=\"noopener noreferrer\">Uniqueness of models in persistent homology: the case of curves<\/a> <span class=\"pub-details\">(Frosini, P; Landi, C - 2011 - 1.1 Articolo in rivista)<\/span><\/li><li><a href=\"https:\/\/arpi.unipi.it\/handle\/11568\/1264192\" target=\"_blank\" rel=\"noopener noreferrer\">Does intelligence imply contradiction?<\/a> <span class=\"pub-details\">(Frosini, Patrizio - 2009 - 1.1 Articolo in rivista)<\/span><\/li><li><a href=\"https:\/\/arpi.unipi.it\/handle\/11568\/1264252\" target=\"_blank\" rel=\"noopener noreferrer\">Natural pseudodistances between closed surfaces<\/a> <span class=\"pub-details\">(Donatini, Pietro; Frosini, Patrizio - 2007 - 1.1 Articolo in rivista)<\/span><\/li><\/ul>","unipi-persone-didattica":"<ul class=\"registri-list\"><li>Algebra lineare - corso a (cod. 723AA) per Laurea in Informatica<\/li><li>Algebra (cod. 722AA) per Laurea in Informatica<\/li><\/ul>","unipi-persone-codocenze":"","unipi-persone-interessi-ricerca":"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:&nbsp;<a title=\"Topological Data Analysis - Wikipedia\" href=\"https:\/\/en.wikipedia.org\/wiki\/Topological_data_analysis\">Topological data analysis - Wikipedia<\/a>. As of now, Scopus reports over 5,000 documents under the term &ldquo;topological data analysis&rdquo; and more than 6,000 under &ldquo;persistent homology.&rdquo;<br \/>\r\n&nbsp;<br \/>\r\nRegarding 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.","_wpml_word_count":"12","_last_translation_edit_mode":"translation-editor"},"organizzazioni":[11455],"class_list":["post-147618","unipi_persone","type-unipi_persone","status-publish","hentry","organizzazioni-dipartimento-di-informatica-489999-en"],"email":"patrizio.frosini@unipi.it","telefono":null,"content_plain":"Professore Associato &#8211; Dipartimento di Informatica | Email: patrizio.frosini@unipi.it","photo_url":null,"ruoli_tags":[{"id":759,"name":"PA","slug":"pa"}],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Patrizio Frosini ~ UNIPI<\/title>\n<meta name=\"robots\" content=\"noindex, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Patrizio Frosini ~ UNIPI\" \/>\n<meta property=\"og:description\" content=\"Professore Associato &#8211; 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