Tell us about yourself and how your interest in mathematics began.
My name is Alessio Falocchi and I am currently an associate professor at the Department of Mathematics at the Politecnico di Milano. Mathematics began to intrigue me during high school, though it was not an immediate passion. Rather, I realized it gave me a kind of satisfaction: the result was either right or wrong, with no room for uncertainty.
At university I enrolled in engineering, and over time I understood that my interest was more focused on courses related to mathematics. So, after graduating, I decided to pursue a PhD in applied mathematics, thanks to an opportunity at the Politecnico di Milano.
Specifically, which applied problems have you studied?
During my PhD I worked on mathematical models for suspension bridges. The goal was to explain, through partial differential equations, particular oscillatory phenomena observed in these structures. A well-known example, also famous for the many videos available online, is the Tacoma Narrows Bridge, whose collapse was caused by the onset of large torsional oscillations.
These phenomena also depend on the external conditions acting on the bridge: in particular, wind plays a crucial role, making it necessary to study fluid–structure interaction models.
Have you also worked on fluid–structure interaction problems?
Yes, I began working on problems related to fluids and their interaction with structures during my postdoctoral research at the Politecnico di Torino, and then continued as a researcher at the Politecnico di Milano. Today this represents the main focus of my research; in this context, I am part of the Department of Excellence Project, line 1 “Fluid-structure interactions”, with which the Department of Mathematics has been awarded by the Ministry.
How do these studies fit within the scientific community?
The scientific community working on these topics is very large and active. One of the Millennium Prize Problems concerns the Navier–Stokes equations, which describe the motion of fluids (air, water, etc.). To date, it has not yet been proven in three dimensions, for arbitrary and physically realistic initial data, whether solutions to the Navier–Stokes equations can develop singularities in finite time or remain regular and global in time. Solving this problem would clarify the theoretical foundations of turbulence, one of the most complex phenomena in physics, and would represent an extraordinary result for mathematical analysis.
In addition to research, do you teach?
Yes, I teach Mathematical Analysis 1 and Analytical and Numerical Methods for Engineering. These are courses I am passionate about for several reasons: the first is the enthusiasm of first-year students who are approaching a rigorous study of mathematics; the second is the maturity of third-year students who can directly experience the many applications of mathematics.
What advice would you give to a student who wants to pursue a research career?
Research in mathematics is very demanding, so a strong passion is essential and, especially in the initial phase, a supervisor who can guide the young researcher. Along the way, there is a continuous opportunity to grow, also by meeting scholars from all over the world. At the same time, moments of discouragement are frequent: it may happen that you think about a proof for days without finding a solution and then, perhaps, a hike in the mountains is enough… and the insight comes!
What are your hobbies?
My hobbies are mainly related to sports and nature. Having been born in Valle Camonica, I have a strong passion for the mountains and trekking, which for me represent a way to clear my mind. I have always practiced sports: I played volleyball as a middle blocker at an amateur level and I closely follow athletics, particularly high jump, in which my brother is directly involved as a professional athlete.