Alfonso Sorrentino
Professor of Mathematical Analysis - University of Rome Tor Vergata
Alfonso Sorrentino has been professor of Mathematical Analysis at University of Rome Tor Vergata (Italy) since 2014.
He got a Ph.D. in Mathematics at Princeton University (USA) in 2008, under the supervision of John Mather.
After his graduation, he has worked as: Junior Research Fellow at Fondation des Sciences Mathématiques de Paris (2008-2009), Herschel-Smith Research Fellow at University of Cambridge UK (2009-2012), Newton Trust Fellow of Pembroke College, Cambridge UK (2009-2012) and Researcher at University Roma Tre in Italy (2012-2014).
His main scientific interests are in the field of dynamical systems, more specifically, in the study of Lagrangian and Hamiltonian dynamics by means of variational methods (Aubry-Mather theory), PDE techniques (weak KAM theory and Hamilton-Jacobi equation) and geometric approaches (symplectic geometry and topology).
How would you define your field of study? What is your vision about it? Which are the topics you're most passionate about?
My research interests lie in the field of dynamical systems. Human beings have been always longing for understanding the world around (and above) them, from the physical laws ruling their everyday life to the mystic motions of heavenly bodies.
This innate quest for order recognised in mathematics its extraordinary means of investigation and expression. In fact, the modelling of an evolving system and the mathematical description of the laws that underlie its evolution are the fundamental premises for capturing its key aspects and describing its changes.
One of the most important conceptual advances of the past century was the acknowledgement that many systems exhibit a very sensitive dependence on the initial conditions. This phenomenon goes by the name of deterministic chaos, and stands in direct opposition to the order that Newton and the founding fathers of mechanics found in many important systems.
The recognition of a complex coexistence between order and chaos has led to a new way of tackling the study of dynamical systems, stimulating researchers to constantly look for different viewpoints, transforming this this field into one of the most transversal - and, in my opinion, fascinating! - of the whole mathematical panorama.
Recently, I have been focusing on the study of mathematical billiards, a mathematical generalisation of the well-known billiard game: a model describing the frictionless motion of a ball inside a planar domain, reflecting elastically at the boundary.
Over the last decades, billiards have been capturing the attention of researchers in various areas of mathematics. Despite their simple description, their dynamical properties are profoundly intertwined with the shape of the domain: while it is clear how this determines the billiard dynamics, a more subtle and intriguing question is to which extent dynamical information can be used to reconstruct the shape of the billiard domain. This translates into several intriguing open problems and enthralling conjectures, that have been the focus of my research over the last few years.
How do you expect your experience in IMM to be? Why did you accept to teach for this project?
When I was offered the possibility of participating to this new project, I accepted without any hesitation and with great excitement. I am firmly convinced that sharing knowledge and ideas is one of the main responsibilities of any academic, particularly in mathematics and science, whose life force comes from their universality.
Nonetheless, I am a passionate traveler and I enjoy getting to know other cultures and customs, particularly through personal interactions with other people.
I have already visited Pakistan once in 2017, in occasion of an international workshop organised by the Centre for Mathematics and Its Applications at University of Management and Technology in Lahore. Besides the warmest hospitality, I still remember vividly the many interesting conversations I had with students and other researchers, each of us eager to learn more of the scientific and cultural background of the other.
I am sure that also this experience will be extremely rewarding from this point of view and it will positively contribute to both my personal and my academic growth.
What is your teaching philosophy? What would you like to transmit to your students? How do you motivate them?
Communicating mathematics is a fundamental part of the academic life of any mathematician. From addressing a qualified audience to lecturing to students, we soon find ourselves forced to look out of our ivory tower and invest as much energy as it takes to engage whoever stands in front of us. Teaching, in particular, may well represent the most exciting endeavour.
“Tell me and I’ll forget; show me and I may remember; involve me and I’ll understand”. Probably I would choose this Chinese proverb if I were asked to describe in a nutshell my teaching philosophy.
In my opinion, teaching should be more more than a one-way flow of notions. Besides clarity, correctness, and - why not - creativity, a good teacher has to do something more: has to inspire her/his students, has to help them to develop their own understanding and intuition. This does not mean that rigor should be understated, but it should be made meaningful and understandable, in a balanced proportion with specific examples and concrete motivations.
Therefore, I like posing questions, asking students to use their intuition to define the objects that I am about to introduce, working through motivating examples together, challenging them and being challenged too. I believe that this way of approaching the subject, rather than passive learning, better suits the nature of mathematical thinking itself.
In order to achieve this, it is fundamental to create an interactive learning environment for students, in which they feel comfortable asking questions and discussing their ideas. It might be challenging at times, but definitely rewarding.
Do you have one of two favorite quotes you would like to share and/or a personal “motto”?
"Rien n’est plus fécond, tous les mathématiciens le savent, que ces obscures analogies, ces troubles reflets d’une théorie à une autre, ces furtives caresses, ces brouilleries inexplicables; rien aussi ne donne plus de plaisir au chercheur. Un jour vient où l’illusion se dissipe; le pressentiment se change en certitude; les théories jumelles révèlent leur source commune avant de disparaître [...]''
(Translation: "Nothing is more fecund, all the mathematicians know it, than those obscure analogies, those blurred reflections from one theory to another, those furtive caresses, those inexplicable scrambles; nothing gives more pleasure to the researcher. One day the illusion drifts away, the premonition changes to a certitude: the twin theories reveal their common source before disappearing [...]")
André Weil, De la métaphysique aux mathématiques, 1960.
“Sire, Je n'avais pas besoin de cette hypothèse-là”
(Translation: "Your Excellency, I had no need of this hypothesis").
(Reputedly attributed to Pierre-Simon Laplace, in reply to Emperor Napoleon I, who had asked why he had not mentioned God in his discourse on secular variations of the orbits of Saturn and Jupiter)