Department of Mathematics and Applications
On 07/11/23, the 3rd meeting of the cycle Please don’t Delete: Maths Dialogues was held with Prof. Antonio GIORGILLI as speaker.
Title: The harmony of the spheres, the whisper of chaos
Abstract: Since ancient times, descriptions of the birth and evolution of our world have focused on the concepts of Order and Chaos. The traditional model is based on the idea that planetary motions are perfect, orderly and immutable. This idea has been systematically refuted by reality.
This talk seeks to illustrate how order and chaos are, in fact, inextricably mixed and how complete order and global chaos are just abstract simplifications.
The meeting was held in Room Martini U6-4 (U6 Building | Piazza dell'Ateneo Nuovo 1, Milano) and was introduced by Prof. Gianmario Tessitore, Director of the Department.
Antonio Giorgilli, Professor at the University of Milano-Bicocca and the University of Milano. Member of the Lombardo Institute, Academy of Sciences and Letters. In 1998, he was an Invited Speaker at the International Congress of Mathematicians (ICM98) in Berlin. In 2007, he was awarded the "Gili-Agostinelli" Prize by the Turin Academy of Sciences. In 2009, the asteroid 27855, discovered in 1995, was named Giorgilli.
Research interests: dynamical systems, classical mechanics and celestial mechanics; numerical methods for characterising chaos in dynamics.
On 08/06/23, the 2nd meeting of the cycle Please don’t Delete: Maths Dialogues was held with Prof. Claudio BARTOCCI as speaker.
Title: From Riemann to Queneau. Interweavings between mathematics and literature
Abstract: Both literary and mathematical creation – both, though in different ways, manifestations of Homo sapiens’ linguistic intelligence – seem to arise from the essential tension that exists between freedom, apparently infinite, of invention, composition, variation and the limitations imposed by formal and structural constraints.
Since the second half of the 19th century, the new universes of non-euclidean geometries, the transfinite hierarchies of set theory, the paradoxes of logic and the abstractions of algebra have opened up boundless spaces to the imagination of writers who have almost nothing in common except a shared sensitivity to the rarefied atmospheres of mathematics: among the most famous, Edwin Abbott, Paul Valéry, Robert Musil, Hermann Broch, Leonardo Sinisgalli, Carlo Emilio Gadda, Raymond Queneau, Georges Perec.
The fictional worlds of literature – we will try to show – are not fundamentally dissimilar to those of mathematics: they offer tools to explore reality and invent other ways of being, to sharpen the intellect and unlock the imagination.
The meeting was held at the University Library Headquarters (U6 Building | Piazza dell'Ateneo Nuovo 1, Milano) and was introduced by Prof. Gianmario Tessitore, Director of the Department.
Claudio Bartocci (Rome, 1962) is an associate professor of Mathematical Physics in the Department of Mathematics at the University of Genova. After graduating in Mathematics, he obtained a PhD in Mathematics (University of Milano, 1990) and a PhD in Mathematics at the University of Warwick (1993). He was a research fellow in Mathematical Physics from 1990 to 1999. In addition to having spent periods of research at universities and institutes such as SISSA (Trieste), the Tata Institute of Fundamental Research (Bombay) the Institut Henri Poincaré (Paris), the University of Salamanca and Boston University, he has also been a visiting professor at the State University of New York at Stony Brook, the University of Paris VII, the University of Pennsylvania (Philadelphia), the École des Hautes Études en Sciences Sociales in Paris and SISSA (Trieste). From 2004 to 2007, he was coordinator of the PhD Programme in Mathematics at the University of Genova.
His research interests focus primarily on methods of differential and algebraic geometry in physical theories. Together with U. Bruzzo and D. Hernández Ruipérez, he has published the monographs The Geometry of Supermanifolds (Kluwer, 1991) and Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics (Birkhäuser, 2008, in press), and is the author of some forty research articles in international journals. From 1999 to 2006, he was coordinator of the University of Genova's local unit for the co-funded national project "Algebraically Integrable Systems". He is a member of the editorial board of the journal "Lettera matematica", published by the Pristem centre at Bocconi University.
He also works as a literary consultant and has translated and edited many books, including: A. Weil, Teoria dei numeri (Einaudi, 2002) and Ricordi di apprendistato (Einaudi, 1994), B. Greene, L'universo elegante (Einaudi, 2000) and La trama del cosmo (Einaudi, 2004). He specialises in the history of mathematical thought and the relationship between mathematics and literature, subjects on which he has published various essays. He has edited Henri Poincaré’s collected writings on Geometria e caso: scritti di matematica e fisica (Bollati Boringhieri, 1995) and Scienza e metodo (Einaudi, 1997); together with Giulio Giorello, he edited the volume T. Kuhn, La tensione essenziale e altri saggi (Einaudi, 2006) and contributed the essay “Laicità e ricerca scientifica” nell’opera, edited by Giovanni Boniolo, Laicità (Einaudi, 2006); he published the anthology Racconti matematici (Einaudi, 2006); together with R. Betti, A. Guerraggio and R. Lucchetti, he edited the volume Vite matematiche. Protagonisti del ‘900 da Hilbert a Wiles (Springer-Verlag Italia, 2007). Together with Piergiorgio Odifreddi, he directs Einaudi’s “Grande Opera” La matematica (4 volumes, the first of which, I luoghi e i tempi, was published in 2007). He has contributed to “Le Scienze” and “Il Manifesto”; since 2001, he has been writing for the culture pages of “La Stampa” and “Tuttolibri”.
On 11/05/23, the 1st meeting of the cycle Please don’t Delete: Maths Dialogues was held with Prof. Lucio RUSSO as speaker.
Title: A partial reconstruction of a lost Hellenistic dynamic theory
Abstract: Plutarch, in his dialogue “De facie”, mentions a dynamic theory that would be applicable both to astronomy and to the motion of a body free to move within the Earth. A partial reconstruction of the mathematical aspects of the theory is proposed, based on works by various authors.
The meeting was held in Room Camatini (U36 Building | Viale Sarca 232, Milano) and was introduced by Prof. Gianmario Tessitore, Director of the Department.
Lucio Russo (Venice, 1944) studied in Naples, where he obtained his high school diploma and a degree in physics. He has worked in the fields of statistical mechanics, probability theory, the history of science and history. He has taught at the universities of Naples, Modena and Roma Tor Vergata and has spent periods of study at the Institut des Hautes Études Scientifiques (Bures-sur-Yvette, France), Princeton University (New Jersey, USA) and the Laboratoire de Probabilités at the Université Pierre et Marie Curie (Paris, France).
His main achievements in the exact sciences have concerned the rigorous theory of phase transitions, percolation theory and the study of threshold phenomena, while in the field of the history of science he has focused primarily on reconstructing the results of Hellenistic science and their influence on modern science.
His historical contributions are characterised by his approach to historiographical problems, also with the support of methods specific to the exact sciences and sometimes starting from the study of the history of science. He has also spoken on many topics related to cultural policy.
His books include: La rivoluzione dimenticata. Il pensiero scientifico greco e la scienza moderna (Feltrinelli, latest edition 2021, translated into many languages) and Segmenti e bastoncini. Dove sta andando la scuola? (Feltrinelli, 1998); La cultura componibile (Liguori, 2008); and Ingegni minuti. Una storia della scienza in Italia (with Emanuela Santoni, Feltrinelli, 2010, also translated into Chinese), L’America dimenticata. I rapporti tra le civiltà e un errore di Tolomeo (Mondadori Università, 2013, translated into several languages), Stelle, atomi e velieri (Mondadori Università 2015), Flussi e riflussi. Indagine sull’origine di una teoria scientifica (latest edition Mondadori Università, 2020), Perché la cultura classica. La risposta di un non classicista (Mondadori 2018), Archimede. Un grande scienziato antico (Carocci 2019). Notre culture scientifique. Le Monde antique en héritage (Les Belles Lettres, 2020), Il tracollo culturale. La conquista romana del Mediterraneo (146-145 a.C.) (Carocci, 2022).
On 24/10/24, the 6th meeting of the cycle Please don’t Delete: Maths Dialogues was held with Prof. Mimmo IANNELLI as speaker.
Title: One hundred years of Biomathematics: a pathway along the path traced by Volterra and Lotka
Abstract: A few years ago, the European Society for Mathematical and Theoretical Biology celebrated 2018 as the centenary of the birth of Biomathematics. At the time, it was decided that the birth of the discipline could be identified with the publication of the monograph ‘On Growth and Form’ by D'Arcy Thompson in 1917. In the essay, biological morphology was discussed on the basis of mathematical transformations. One hundred years since then, the interaction between Mathematics and Biology has undergone such a varied development that it is difficult to say today what Biomathematics is. In this talk I will therefore follow a particular track, which begins with the approach and insights of Volterra and Lotka in the field of Population Dynamics, where Mathematics and Biology interacted successfully and to mutual benefit. For a century, the mathematical approach of Population Dynamics has shaped the development of fields such as Ecology, Epidemiology, Cytology and Immunology. Nowadays, mathematical modelling is the common ground where the joint labours of Mathematics and Biology take place.
The meeting was held at the University Library Headquarters (U6 Building | Piazza dell'Ateneo Nuovo 1, Milano) and was introduced by Prof. Gianmario Tessitore, Director of the Department.
Mimmo Iannelli (Rome, 1946) graduated with a degree in Physics in 1968, he was a CNR researcher at the Institute for Computational Applications in Rome, and later a professor in Rome and Trento. His scientific work focuses on evolution equations and has long been oriented towards the analysis of mathematical models in population theory.
He has participated in various research projects funded by the MIUR and CNR. In particular, he was the national coordinator of the CNR Strategic Project “Mathematical Methods and Models in the Study of Biological Phenomena” (1998–2000), national coordinator of the PRIN project “Mathematical Population Theory: methods, models, comparison with data” (2007), and coordinator of the EPICO project “Epidemics description and control” (2004–2008) funded by the Autonomous Province of Trento.
He has organised schools and conferences, including “Mathematics of Biology” (Cortona 1979), “Mathematical Problems in Environmental Protection and Ecology” (Trento 1991), “Evolution Equation 2000: applications to physics, industry, life sciences and economy” (Trento 2000), “Mathematical Methods and Models in the Study of Biological Phenomena” (Rome 2001), “International Conference on Computational and Mathematical Population Dynamics” (Trento 2004).
He has been a visiting professor at Harvey Mudd College (Claremont, California), the University of Texas at Arlington, Purdue University, Arizona State University, University of Bordeaux II and the CRM centre in Barcelona.
He is the author of various publications on evolution equations and mathematical models in ecology and epidemiology. In particular, the books “Mathematical theory of age-structured population dynamics” (Giardini, Pisa 1995), “Gender-structured population modelling: mathematical methods, numerics and simulations” (SIAM 2005, with M. Martcheva and F. Milner), “An Introduction to Mathematical Biology” (Springer 2014, with A. Pugliese), and “The basic approach to age-structured population dynamics” (Springer 2017, with F. Milner).
On 23/05/24, the 5th meeting of the cycle Please don’t Delete: Maths Dialogues was held with Prof. Athanase PAPADOPOULOS as speaker.
Title: Drawing Geographical Maps: From Ptolemy to Milnor and Thurston
Abstract: Geographical maps involve many aspects of our lives: art, science, and imagination. We will explain why mathematicians and artists since antiquity were interested in the art of drawing geographical maps. We will also show how several important problems in geometry originate in questions arising from map drawing. We will describe some works on geography by eminent mathematicians such as Ptolemy, Euler, Lagrange, Chebyshev and Milnor. Each of them brought his talent to this beautiful field.
The meeting was held in Room Camatini (U36 Building | Viale Sarca 232, Milano) and was introduced by Prof. Gianmario Tessitore, Director of the Department.
Athanase Papadopoulos is Director of Research at the Institut de Recherche Mathématique Avancée and at the Centre de Recherche et Expérimentation sur l'Acte Artistique in Strasbourg. His main field of research is topology and geometry, and he has also published on the history and philosophy of mathematics, music theory, and the relationship between mathematics and art.
He has taught at various universities around the world, including Brown University, the City University of New York, the University of Southern California, Banaras Hindu University, Tsinghua University in Beijing and others, and has been a research fellow at the Institute for Advanced Study in Princeton, the Max Planck Institute in Bonn, the Erwin Schrödinger Institute in Vienna, the Tata Institute in Mumbai and several other institutions worldwide.
He is the author of over 200 articles and 40 monographs and edited volumes, mainly on mathematics, but also on history, philosophy and music theory.
On 18/01/24, the 4th meeting of the cycle Please don’t Delete: Maths Dialogues was held with Prof. Frederic PATRAS as speaker.
Title: Have we lost the structures? What is and what has become structuralism
Abstract: Structuralism was one of the most influential intellectual and scientific movements of the 20th century. This applies to mathematics, but also to the natural sciences, linguistics, economics… and even artistic creation, with Italo Calvino’s (and others’) Oulipo (Ouvroir de littérature potentielle). We will attempt to understand what it was, what it produced (both positive and less convincing), and what it might mean today.
The meeting was held at the University Library Headquarters (U6 Building | Piazza dell'Ateneo Nuovo 1, Milano) and was introduced by Prof. Gianmario Tessitore, Director of the Department.
Frédéric Patras, mathematician and philosopher, is Research Director at the CNRS at the University of Côte d’Azur in Nice. His work focuses on algebra and its various applications, as well as the philosophy of mathematics, within which he has been particularly interested in structuralism and phenomenology.
He has published, in Italian, Il pensiero matematico contemporaneo (Bollati Boringhieri, 2006, paperback edition 2017), and La Possibilité des nombres/The Essence of Numbers (2014, 2020) and, with P. Cartier, Classical Hopf Algebras (2021).
On 27/11/25, the 9th meeting of the cycle Please don’t Delete: Maths Dialogues was held with Prof. Paolo ZELLINI as speaker.
Title: From infinity to actual computation
Abstract: In the last century, the development of automatic computation and the importance of research into the nature of effective procedures for solving large-scale problems stem from the philosophy of the infinite that emerged in the late 19th century, as well as from earlier philosophical trends, particularly in France, regarding the potential convergence of spiritualism and positivism. Among the consequences of this historical juncture are today’s theoretical and practical research on computational efficiency, particularly regarding matrix computation, which is also of crucial importance for machine learning strategies based on neural networks.
The meeting was held at the University Library Headquarters (U6 Building | Piazza dell'Ateneo Nuovo 1, Milano) and was introduced by Prof. Gianmario Tessitore, Director of the Department.
Paolo Zellini is an Italian mathematician and essayist, one of the most original voices in contemporary thinking on the meaning of mathematics. Born in Rome in 1946 and graduating in Mathematics at the Università di Roma La Sapienza, he has carried out research in various Italian and international locations, including Rome, Pisa and the United States. During his career, he has taught at the Universities of Pisa, Udine and finally Rome Tor Vergata, where he is now emeritus professor of numerical analysis.
His scientific contributions concern numerical linear algebra, matrix theory, algorithm complexity and numerical optimisation. Alongside these interests, he has carried out in-depth reflection on the very meaning of mathematical research, placing it in a broader historical and philosophical perspective, attentive to the evolution of ideas.
In his best-known essays, such as Brief History of Infinity and The Mathematics of the Gods and the Algorithms of Men, Zellini has investigated the evolution of mathematical thinking through the concept of infinity and the notion of number, approaching these issues with a perspective that spans not only the history of mathematics but the history of thinking as a whole, even outside the western tradition. In this intellectual path, he recognised the decisive influence of the work of Elémire Zolla.
He is one of the founders of an interdepartmental centre for the study of ancient thinking at the Università di Roma Tor Vergata and regularly collaborates with the cultural pages of various national newspapers. His work combines scientific rigour and philosophical depth in a continuous dialogue between science and humanistic tradition.
On 29/10/25, the 8th meeting of the cycle Please don’t Delete: Maths Dialogues was held with Prof. Ciro CILIBERTO as speaker.
Title: Enumeration in geometry: a charming millennial history and recent developments
Abstract: The enumeration of geometric objects that verify certain specific properties is an ancient and venerable topic, which began its history more than two thousand years ago with the well-known Apollonius problem. Enumerative geometry is characterised by dealing with problems that are frequently easy to formulate but equally frequently very difficult to solve. In this talk, I aim to examine part of the very interesting and millennial history of this charming topic and its problems. In recent decades, enumerative geometry has seen the rise of new problems, more difficult than the already complex ones of the past, and has undergone a huge change in perspective and spectacular progress, with the introduction of new ideas and extremely refined mathematical tools that have launched unexpected bridges between different parts of mathematics.
The meeting was held at the University Library Headquarters (U6 Building | Piazza dell'Ateneo Nuovo 1, Milano) and was introduced by Prof. Gianmario Tessitore, Director of the Department.
Formerly Professor of Higher Geometry at “Tor Vergata” University, Ciro Ciliberto was born in Naples on 14 October 1950. He graduated in Mathematics from the University of Naples in 1973. Assistant Professor at the University of Naples from 1974 to 1980. Professor of Mathematics at the University of Naples from 1977 to 1978 and of Algebraic Geometry from 1978 to 1980. Extraordinary Professor of Higher Mathematics at the University of Lecce in 1980-1981. Subsequently, he was first extraordinary then full professor of Algebraic Geometry at the University of Naples from 1981 to 1985. Then Professor of Superior Geometry at the University of Rome Tor Vergata. Deputy President of the National Institute of High Mathematics “Francesco Severi” in the years 1990-1995 and member of the Scientific Commission of the same Institute from 1995 to 1999. Director of the Doctorate School in Mathematics at the University of Rome Tor Vergata in the years 1990-1994, and subsequently member of the Scientific Committee of that School. Detached Professor at the "Inter-disciplinary Centre B. Segre" of the Accademia Nazionale dei Lincei in the years 1993-1996. President of the Italian Mathematical Union from 2012 to 2018. Member of the Meetings Committee of the European Mathematical Society since 2013 and President of the aforementioned committee since 2018. Member of the Accademia Nazionale dei Lincei, the Accademia delle Scienze Fisiche e Matematiche in Naples and the Accademia Gioenia in Catania. Website: https://www.mat.uniroma2.it/~cilibert/
Ciliberto is the author of more than 200 scientific publications. His main area of interest is Algebraic Geometry and the history of the discipline. His main research topics are: projective curves; algebraic surfaces; degeneracy techniques and their applications: families of nodal curves, Noether-Lefschetz theory, extensionality problems, Gauss maps, classification of Fano varieties, linear systems of plane curves and nodal curves on K3 surfaces, obstructions to degeneracy; abelian varieties, curves and their moduli spaces; projective-differential geometry of special varieties, focal properties, secant-defective varieties.
On 11/03/25, the 7th meeting of the cycle Please don’t Delete: Maths Dialogues was held with Prof. Alessandra CARACENI as speaker.
Title: Inevitable crossings and random demonstrations
Abstract: It is 1944; in a labour camp on the outskirts of Budapest, mathematician Pál Turán has the task of transporting bricks from the kilns to the storage areas by loading them into wagons that must then be pushed along tracks by hand. Each kiln is connected by a track to each storage area; running the wagons does not require much effort, except at the junction of two tracks, where they invariably derail and most of the bricks end up on the ground. Pál asks why is the track network built so wastefully, with so many exasperating crossings? How could the number of crossings be minimised, while still connecting each kiln to each storage area? This is perhaps the first question ever asked (still fundamentally open!) about the ‘crossing number’, an important concept in graph theory; in tracing its history and investigating some of its applications we will ‘’cross‘’ constructivist artists, computer scientists, sceptical mathematicians, and finally come across one of the most valuable parts of Pál Erdős' legacy: the so-called Probabilistic Method.
The meeting was held at the University Library Headquarters (U6 Building | Piazza dell'Ateneo Nuovo 1, Milano) and was introduced by Prof. Gianmario Tessitore, Director of the Department.
Alessandra Caraceni is currently a Type B Fixed-Term Researcher (RTdB) at the Scuola Normale Superiore, where she has been working since 2021. Previously, she held the position of INdAM researcher at the same institution, consolidating her commitment to high-level research.
Alessandra’s academic career is characterised by a continuous deepening of her mathematical skills. After obtaining her PhD at the Scuola Normale Superiore in Pisa in 2015 with first-class honours, she went on to undertake prestigious international research experiences. Between 2019 and 2021, she was a Florence Nightingale Fellow at the University of Oxford and Lady Margaret Hall.
Previously, she worked as a postdoctoral researcher at the University of Bath (2016–2019) and held teaching and research positions at Université Paris-Sud – Orsay, both on a full-time (2015–2016) and part-time (2014–2015).
Alessandra attended the Ordinary Course in the Science Class at the Scuola Normale Superiore in Pisa and completed both her Bachelor’s and Master’s Degrees in Mathematics with honors at the University of Pisa.
In addition to research, Alessandra is actively involved in the promotion and education of mathematics. Since 2014, she has been a member of the ‘Olympic Commission’, the Italian national committee for the Maths Olympics. In this context, she regularly gives lectures and seminars aimed to high school students and teachers, covering topics related to teaching and maths competitions.
Her passion for learning and knowledge is also reflected in the field of art: in 2004, she obtained the diploma of “Compimento Medio” in Cello at the Luigi Boccherini Music Institute in Lucca.
A cycle of meetings to talk about moments in the history of mathematics and aspects of its method. With a style that is not necessarily technical, the aim is to highlight the cultural, aesthetic, creative, playful and didactic value of hypothetical-deductive thinking and the actuality of the landscapes it is able to draw.
In progress
On 09/06/26, the 11th meeting of the cycle Please don’t Delete: Maths Dialogues was held with Prof. Alberto COGLIATI as speaker.
Title: Bernhard Riemann, a duecento anni dalla nascita
Abstract: Bernhard Riemann was certainly one of the most influential mathematicians in history. The audacity of his insights, the fruitfulness of his methods and the breadth of his interests make him one of the principal architects of contemporary mathematics. A mathematician of universal vocation, Riemann was among the last to master with equal depth the most different fields of the discipline, such as geometry, analysis, mathematical physics and number theory.
The extraordinary power of his thought is, however, set against a life marked by personal fragility - precarious health, anxiety, and hesitation in self-expression - which limited the immediate dissemination of his ideas. Recognition of the scale of his contribution was largely posthumous, even though it proved decisive for the subsequent developments of mathematics and modern physics.
In a mix of human story and scientific research, two hundred years after his birth, this talk aims to outline the scientific biography of one of the most original and profound minds in modern science.
The meeting will be held in Room U4-01 (U4 Building | Piazza della Scienza 4, Milano) and will be introduced by Prof. Gianmario Tessitore, Director of the Department.
Alberto Cogliati is a full professor of the History of Mathematics at the Department of Mathematics, University of Padova. His main field of research concerns the history of geometry, and in particular the history of differential geometry between the nineteenth and twentieth centuries. His recent publications include: Non-Euclidean Geometry: A Brief History from Antiquity to Poincaré, Carocci, 2024. He is currently working on a new annotated edition of Gauss’s Disquisitiones generales circa superficies, for the Classic Texts in the Sciences series.