My research interests are various: from the branch of probability and stochastic analysis to mathematical physics, also using several concepts of differential geometry. In the past I have also approached the world of quantum gravity (the subject of my master thesis), which still fascinates me.
During my Ph.D. studies (2017/2020), I have investigated the theory of infinite dimensional oscillatory integrals. In particular, I was involved in the study of functional integration techniques and applications to quantum dynamical systems. More specifically, I worked with S. Mazzucchi and S. Albeverio on the formulation of a three-dimensional Feynman path integral for the Schrödinger equation with magnetic field by means infinite dimensional oscillatory integrals. Furthermore, in 2018 S. Mazzucchi and I defined a renormalization term for the Ogawa integral in the multidimensional case, by using a result due by R. Ramer.
In 2020, I started a research around the Schauder and Sobolev estimates in the theory of parabolic equations (joint work with Lorenzo Marino), with the aim of generalizing a result obtained by N. V. Krylov and E. Priola.
From 2021, my research has moved also in the field of philosophy of science (especially mathematics and physics, see also below). My main focus regards the interpretation of Feynman diagrams that could be considered as depiction representing physical phenomena as well as merely mathematical tools.
On the side of mathematics, in 2022 I began working on several topics in mathematical analysis. On the one hand, I have investigated some ODE systems (with with Marco Capolli, Sara Sottile, and Mattia Sensi) for modeling social and biological phenomena (fromt the generaliziatio of the famous Lanchester's model, concerning the military strategies during a conflict between twom, or more, armies to the survey of compartmental models in epidemiology). On the other hand, my resarch has moved also in the field of PDE systems, by considering both Klein-Gordon-Maxwell equations and Schrödinger-Maxwell equations driven by mixed local-nonlocal operators (this is a jont project with Maicol Caponi, Alberto Maione, and Enzo Vitillaro).
There are many more topics of mathematics that I love. For instance, I am really interested in the formalization of the mathematical aspects for the economic theory and the related models developed in the last century (as the Cobb-Douglas model and the Solow-Swan model). My colleague Mattia Sensi and I have generalized some results concerning the models quoted above, by using classical tools of differential geometry and analysis. More recently, we started to investigate some problems regarding Benford's law from a number-theoretical point of view.
During the 2020 lockdown, I started studying the history and the properties of a very particular set of numbers: the normal numbers. With my colleague Daniele Taufer, we are trying to propose different points of view to face the issues linked with these numbers that still today are mysterious objects.
Since 2022, I'm cooperating with Stefano Grasso with the purpose of understanding the techniques coming from the quantum field theroy (as the S-matrix and Feynman diagrams) in the context of RNA-folding theory.
In 2021 I started two collaborations in the fields of phiolosophy of science, epistemology, and moral philosophy. The first project regards the role of analogies in mathematical discovery. This work is carried on jointly with Francesco Nappo. Our aim is to provide a novel epistemological account of analogical reasoning in pure mathematics. The second collaboration is a joint work with Michele Loi. We propose a comprehensive account of justice and fairness in the language of probability theory.