My name is Antonino De Martino, and I have been a tenure-track researcher (RTT) at the Department of Mathematics of the Polytechnic University of Milan since July 2024.
What were the main stages of your path before arriving in Milan?
I obtained my degree in Mathematics from the University of Ferrara in 2019. During my master’s thesis, I became interested in mathematical research and was fascinated by it; for this reason, I decided to pursue a PhD, which I completed in December 2022 at the Polytechnic University of Milan.
The PhD experience had a very significant impact on my training, strongly shaping my approach to research from several perspectives. I also had the opportunity to take part in research visits and conferences, as much as the pandemic period allowed.
Another key stage was my postdoctoral period in Los Angeles, at Chapman University, which allowed me to engage with new techniques and theories related to my research area. The collaborations I started during my PhD and postdoc have continued over time and are still very active.
What is your main research focus?
My research area concerns operator theory and hypercomplex analysis. The latter aims to extend the concepts of complex analysis to non-commutative algebras, such as quaternions. Despite the loss of commutativity, hypercomplex analysis makes it possible to work in higher dimensions using techniques typical of a single variable.
In particular, these techniques allow for the definition of a notion of spectrum for vector operators. This spectrum, known in the literature as the S-spectrum, has numerous applications, for example in quantum mechanics and in the study of new fractional diffusion problems based on fractional powers of vector operators.
Have you also worked on superoscillations?
Yes, I began studying the mathematical theory of superoscillations during my postdoc in Los Angeles and then continued this line of research at the Polytechnic University of Milan. In particular, I have worked on the connections between superoscillations, integral transforms, and time-frequency analysis.
Recently, we have been trying to understand possible links between superoscillations and certain machine learning problems. On this topic, I am part of the Excellence Project Line 3, “Mathematical features of quantum mechanics,” through which the Department of Mathematics has been recognized by the Ministry.
What do you like most about your work?
Among the aspects I appreciate most about my work are the opportunities for discussion, both with students and with colleagues in the context of scientific collaborations. At the same time, I also find moments of individual work very stimulating, such as when I am writing a paper or preparing a lecture or a seminar.
Do you teach? Do you enjoy it?
Yes, I enjoy teaching. I believe it is a great responsibility toward future generations and should therefore be approached with the utmost seriousness.
So far, I have mainly taught “Analisi 1” courses in engineering programs. Since it is one of the first subjects students encounter, I like trying to convey rigor and the beauty of mathematics. In particular, I greatly appreciate discussions with students at the end of lectures, about exercises or questions that emerged during the class.
Outside of mathematics, what are your hobbies and passions?
I really enjoy reading, both great classics and novels by contemporary authors. I also love running during the spring and summer seasons and, whenever possible, traveling.