Book
Rivoluzioni Matematiche · Vol. 35 · Le Scienze / Springer Nature Italia

Il teorema ergodico

Published August 2025, distributed with Le Scienze magazine

A book presenting the ergodic theorem, one of the most profound results in modern mathematics. The theorem says, in essence, that for many dynamical systems, time averages equal space averages: a gas in equilibrium eventually "visits" all its possible states proportionally. The book traces the theorem's history from Boltzmann's hypothesis to its rigorous proof by Birkhoff and von Neumann, and illuminates its deep connections to probability, physics, and our understanding of irreversibility and entropy. Accessible to a broad audience, the book requires only an introductory college-level foundation in mathematics and physics.

Articles & Blog Posts
2022
Essay · Book chapter
Metodi a confronto: Didattica Universitaria in USA e in Italia
Drawing on over a decade of personal experience studying and then teaching in both the United States and Italy, this essay compares the two university systems across curriculum structure, depth of content, and teaching and assessment methods. The central observation — that American undergraduate education in its early years resembles a well-organized Italian liceo — opens into a broader reflection on the trade-offs between the highly structured, resource-intensive US approach (frequent partial exams, weekly graded homework, mandatory attendance) and Italy's more autonomous model, on the different cultural attitudes toward higher education in the Anglo-Saxon and Latin traditions, and on the role of professional networks at elite American institutions. Published in the proceedings of a 2021 conference on pedagogy.
2022
Blog post · ParliamoneOra
Scienza e Cultura: impressioni
What does it mean, concretely, for science to be culture — not just through its technological applications, but through its lasting impact on how we think and reason as individuals and as a society? Starting from this question, the essay works through three simple examples to argue that even elementary scientific literacy changes how we face uncertainty, interpret data, and make decisions. The conclusion is pointed: science gives us tools for understanding phenomena we might directly experience otherwise, and choosing to engage with it seriously is itself a cultural act.
2020
Popular article · Zanichelli / Aula di Scienze
La matematica del distanziamento
Written during the COVID-19 pandemic for a general audience, this article explains the mathematical models behind social distancing recommendations — from epidemiological models to geometric tiling problems (the Lagrange–Thue–Fejes Tóth theorem). Includes supplementary material with proofs and problems for the curious reader.
2020
Blog post · ParliamoneOra
Chi ha paura della matematica?
Public expressions of pride in being poor at mathematics reveal a widespread cultural prejudice that would rarely be accepted toward other fields of knowledge. Such attitudes, often reinforced by public discourse in Italy, portray mathematics as inaccessible or suitable only for specialists. This perception contributes to the marginalization of mathematical literacy and obscures the discipline’s central role in scientific reasoning, critical thinking, and many aspects of contemporary society. Recognizing mathematics as a fundamental component of general education is therefore essential for strengthening broader intellectual and civic competence.
Community
2009
Co-founder & organiser
DinAmicI — The Community of Italian Dynamicists
DinAmicI is the informal community of Italian researchers in dynamical systems, ergodic theory, and related areas. Founded in 2009 with a series of workshops in Corinaldo, it has grown into a network of regular workshops, a DinAmicI Day series, and an active online presence. I co-founded and have co-organised many of its events, including workshops in Corinaldo, Pisa, L'Aquila, Varese, and Rio de Janeiro.
Formal Mathematics & Lean
Scientific committee · INdAM Meeting
Lean for the curious mathematician
September 7–11, 2026 · Palazzone di Cortona, Cortona. INdAM Meeting for Italian and international mathematicians curious about the Lean ecosystem and the growing Mathlib library. Member of the Scientific Committee.
Conference co-organiser
ItaLean 2025 — "Bridging Formal Mathematics and AI"
December 9–12, 2025 · Università di Bologna. A conference bringing together Italian and international mathematicians, computer scientists, and AI researchers around the Lean proof assistant and the future of computer-verified mathematics. Aimed at both specialists and curious newcomers to formal methods.
Workshop co-organiser
Computer-verified proofs: 48 hours in Rome
January 24–26, 2024 · Università di Roma Tor Vergata. An intensive two-day workshop introducing mathematicians to formal proof-writing in Lean 4 and Mathlib. Participants worked on formalising results from their own fields of research.