Nicolò De Ponti (https://sites.google.com/view/nicolodeponti) is a researcher
at the Department of Mathematics. We talk with him about his educational
background and his research activity.
Who are you and what has been your academic path?
My name is Nicolò De Ponti and I am a tenure-track researcher (RTT) at
the Department of Mathematics of the Politecnico di Milano. I obtained my
bachelor’s and master’s degrees in Mathematics at the University of Insubria
and earned my PhD in 2019 at the University of Pavia. After my PhD, I carried
out research activities as a postdoctoral fellow at SISSA in Trieste and at the
University of Milano-Bicocca.
What is your research about?
I deal with analysis, with interests ranging from optimal transport, geometric
analysis, the analysis of metric spaces and metric measure spaces, diffusion
PDEs, and some mathematical aspects of cosmology.
You listed many different topics: why these multiple interests?
One aspect that I have always liked about mathematics is the possibility
of letting oneself be guided by curiosity in choosing the problems to tackle. It
is fascinating to see how seemingly disconnected fields are instead intimately
connected. I must also confess that it would bore me to have to focus on a
single specific sector.
Do you therefore think it is important for a mathematician to work
in different fields?
It is certainly important that there are mathematicians who range across
different branches, because an impulse for research often arises from problems
that emerge in one area but prove relevant for others too, or are solved thanks
to techniques developed elsewhere. Nevertheless, I also consider important the
presence of mathematicians heavily specialized in a single area, as well as those
who produce a lot of research on more accessible problems, and those who
publish few papers solving problems of great relevance and difficulty. In short,
the right mix is the real strength.
You mentioned that certain theories later prove important in sectors
different from those for which they were developed: could you
give us some examples?
A well-known example is given by optimal transport. This theory has a
very ancient history and was born in a 1781 article by Gaspard Monge, who
was interested in how to transport the earth needed to build fortifications as
efficiently as possible. About twenty years ago, it was discovered how this theory
is very useful for defining a good concept of curvature bounded from below in
not necessarily smooth geometric spaces, a problem of great interest also for
physical applications.
On a smaller scale, another example happened to me just in these past few
months, in a research project I am finalizing with some collaborators. The problem
arises from understanding how the geometry of a space influences the existence
of non-trivial solutions to certain partial differential equations and could
therefore be classified as a problem of geometric analysis. In certain contexts,
however, we noticed that the problem translates into a purely number theory
question, a field that might seem completely disconnected, and the literature in
this sector has been useful to us in obtaining unknown results.
Do you teach? Do you have any advice for students and in particular
for those who want to approach research?
Since I arrived at the Politecnico in 2024, I have taught the ”Analysis and
Geometry 1” and ”Mathematical Analysis 2” courses. I would advise students
to let themselves be guided by personal interests in choosing their path and
to commit themselves to studying. For those who want to approach research,
I think it is useful to fantasize about problems one would like to solve as a
personal challenge, but also to engage with those who have more experience to
better discover this world.
Do you have other passions besides mathematics?
Lately, I enjoy playing chess and I am trying to improve. I am also a big
basketball fan and I follow the Italian league in particular. I also really like
hiking in the mountains, especially with friends.