Algebraic Geometry between Tradition and Future An Italian Perspective

An incredible season for algebraic geometry flourished in Italy between 1860, when Luigi Cremona was assigned the chair of Geometria Superiore in Bologna, and 1959, when Francesco Severi published the last volume of the treatise on algebraic systems over a surface and an algebraic variety. This century-long season has had a prominent influence on the evolution of complex algebraic geometry - both at the national and international levels - and still inspires modern research in the area. "Algebraic geometry in Italy between tradition and future" is a collection of contributions aiming at presenting some of these powerful ideas and their connection to contemporary and, if possible, future developments, such as Cremonian transformations, birational classification of high-dimensional varieties starting from Gino Fano, the life and works of Guido Castelnuovo, Francesco Severi's mathematical library, etc. The presentation is enriched by the viewpoint of various researchers of the history of mathematics, who describe the cultural milieu and tell about the bios of some of the most famous mathematicians of those times.

1. Gilberto Bini (Palermo), Introduction.- 2. Claudio Fontanari (Trento), Stefano Gattei (Trento), Francesco Severi’s Mathematical Library.- 3. Angelo Guerraggio (Milano), Francesco Severi and the Fascist Regime.- 4. Maria Giulia Lugaresi (Ferrara), Fabio Conforto (1909-1954).His Scientific and Academic Career at the University of Rome.- 5. Livia Giacardi (Torino), Alessandro Terracini (1889-1968). Teaching and Research from the University Years to the Racial Laws.- 6. Marco Andreatta (Trento), Higher Dimensional Geometry from Fano to Mori and Beyond.- 7. Livia Giacardi (Torino), Erika Luciano (Torino), Elena Scalambro(Torino), Gino Fano (1871-1952). The scientific Trajectory of an Italian Geometer between Internationalism and Persecution.- 8. Alessandro Verra (Roma), From Enriques Surface to Artin-Mumford Counterexample.- 9. Ciro Ciliberto (Roma), The Theorem of Completeness the Characteristic Series: Enriques' Contribution.- 10. Edoardo Sernesi (Roma), Severi, Zappa and the Characteristic System.- 11. Ciro Ciliberto (Roma), Claudio Fontanari (Trento). Two letters by Guido Castelnuovo.- 12. Claudio Fontanari (Trento), Guido Castelnuovo and his Heritage: Geometry, Combinatorics, Teaching.- 13. Enrico Rogora (Roma), Guido Castelnuovo (1865-1952).- 14. Nicla Palladino (Perugia), Maria Alessandra Vaccaro (Palermo), The Genesis of the Italian School of Algebraic Geometry through the Correspondence between Luigi Cremona and Some of his Students.- 15. Aldo Brigaglia (Palermo), Veronese, Cremona and the Mystical Hexagram.

Gilberto Bini got his Ph.D. from Scuola Normale Superiore in July 2000. After that, he spent the following four years in the US (University of Michigan) and in the Netherlands (Universiteit van Amsterdam). He became a "Ricercatore di Geometria" at the Università degli Studi di Milano in 2004. In 2015, he started his job as an associate professor for Università degli Studi di Milano where he worked until 2019. The year afterwards, he moved to the Università degli Studi di Palermo where he started his job as a full professor of Geometry. His main research interests focus on projective geometry, especially the classification of complex projective varieties, as well as its application to Grassmann tensors and Computer Vision. He authored various peer-reviewed publications (proceedings, papers, books) on international journals. Through the years, he has organised different outreach activities (exhibitions, laboratories, public lectures, etc.). From 2015 until 2021, he was an editorof "Matematica, Cultura e Società", journal of the Unione Matematica Italiana. Last year, he co-organised with Claudio Fontanari the INdAM Workshop "Italian Algebraic Geometry between Tradition and Future".